A high-precision model construction and dynamic performance simulation analysis method of an electromagnetic inerter

Abstract

The application discloses a kind of electromagnetic inerter high-precision model construction and dynamic performance simulation analysis method, comprising the following steps: (1): establishing mathematical model;(2): parameter definition;(3): meshing;(4): transient simulation;(5): result analysis;The beneficial effects of the application are that the finite element model construction of hydraulic system and electromagnetic system is realized, and the further performance analysis of the integrated design scheme of electromagnetic inerter is completed;The application improves mathematical model and dynamic finite element method, uses mathematical model and COMSOL numerical simulation software, carries out high-precision dynamic performance simulation analysis to electromagnetic inerter, realizes the transient simulation of hydraulic system and electromagnetic system;A novel meshing strategy is introduced, which significantly improves the simulation accuracy and calculation efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of engineering vibration reduction technology, in particular to a high-precision model construction and dynamic performance simulation analysis method of an electromagnetic inertial actuator. BACKGROUND

[0002] As a new type of electromechanical vibration isolation element, the electromagnetic inertial actuator is gradually changing the traditional field of vibration control. It solves the problem of large volume, complex structure and high difficulty of integrated design of traditional "inertial-spring-damping" (ISD) vibration isolation system through the coupling of hydraulic system and electromagnetic system. This device uses the structural topology ability of the hydraulic system and the electromechanical simulation function of the electromagnetic system to realize a complex vibration isolation network in a limited volume, especially suitable for scenes with strict requirements on weight and volume.

[0003] Based on the electromagnetic inertial actuator device, this research applies mathematical models and dynamic finite element methods to conduct in-depth design theory, system matching and optimization, manufacturing and performance testing research. The existing simulation method has some shortcomings in the finite element simulation of the electromagnetic inertial actuator. Difficulty 1: In the fluid domain, the complex fluid-structure coupling problem often accompanies high time cost and large amount of calculation, which may cause large errors in the calculation of damping force and inertia force, which may affect the accuracy of the simulation results. Difficulty 2: In the fluid domain, when the piston in the fluid domain moves, traditional mesh division may cause mesh deformation, resulting in poor quality mesh, which may cause calculation not to converge. Difficulty 3: In the electromagnetic domain, the influence of the geometric size of the primary core tooth and yoke on the performance of the motor is not accurately analyzed, and the law of motor coefficient changing with movement speed is not accurately explored. Difficulty 4: In the electromagnetic domain, the ability of the linear motor as a converter between two networks and the feasibility of simulating complex mechanical network impedance through the electric network are not verified.

[0004] In view of the above situation, it is necessary to improve the existing electromagnetic inertial actuator simulation method to adapt to the needs of the use of electromagnetic inertial actuator. SUMMARY

[0005] To solve the above technical problems, the present application provides a high-precision model construction and dynamic performance simulation analysis method of an electromagnetic inertial actuator, which proves its performance advantage in vibration isolation system and promotes the process in engineering application.

[0006] To achieve the above purpose, the technical scheme adopted by the present application is as follows: a high-precision model construction and dynamic performance simulation analysis method of an electromagnetic inertial actuator, comprising the following steps:

[0007] Step (1): Establishing the mathematical model of the hydraulic system, in the hydraulic system, the calculation of the mass coefficient follows the principle of volume conservation and energy conservation of the hydraulic cylinder, and the expression of the mass coefficient is derived through formula; the mass coefficient b can be expressed as:

[0008]

[0009] Wherein, S1 and S2 are the cross-sectional area of the hydraulic cylinder and the cross-sectional area of the spiral pipe respectively; r1 is the piston rod radius, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the spiral pipe, r4 is the spiral pipe rotation radius, h is the lead of the spiral pipe, J is the rotational inertia when the fluid flows, m is the mass of the fluid in the spiral pipe, ρ is the density of the fluid, l is the length of the spiral pipe, b is the inertia coefficient, θ is the angle of the fluid rotating in the spiral pipe, n is the number of spiral pipe turns, is the linear movement speed of the piston in the hydraulic cylinder, is the angular velocity of the fluid flowing in the spiral pipe;

[0010] Establishing the mathematical model of the electromagnetic system, the calculation in the electromagnetic field is based on Maxwell's equations, which is a set of partial differential equations describing the relationship between electric field, magnetic field and charge density, current density, which is composed of the following equations:

[0011]

[0012] Wherein, is the Hamiltonian operator, E is the electric field intensity, B is the magnetic induction intensity, J is the conduction current intensity, ρ is the charge density, ε0 is the dielectric constant, μ0 is the magnetic permeability; The equation set includes: Gauss law, Gauss magnetic field law, Faraday induction law and Maxwell-Ampere law;

[0013] Step (2): Definition of fluid domain and electromagnetic domain parameters;

[0014] Step (3): Grid division of fluid domain and electromagnetic domain;

[0015] Step (4): Using COMSOL numerical simulation software to perform transient simulation on the electromagnetic inductor; In the simulation, the piston movement of the hydraulic system and the current change of the electromagnetic system, as well as the interaction between them, are considered;

[0016] Step (5): Analyzing the simulation results, including the comparison between the calculation results of damping force, inertia force and theoretical prediction, and the output characteristics of electromagnetic force.

[0017] Further supplement to the technical solution, the fluid domain parameter definition in step (2) includes the following steps:

[0018] Step (2.1): Determine the flow state of fluid in the pipeline according to the Reynolds number to determine whether it is laminar flow, transition flow or turbulent flow; based on the judgment of Reynolds number, select the appropriate turbulent flow model to describe the fluid flow characteristics, and use the wall function approximation to reduce the memory requirement The calculation method of Reynolds number is as follows:

[0019]

[0020] Where, ρ is the fluid density, V is the fluid viscosity, μ is the dynamic viscosity, d is the characteristic length, and in the circular pipeline, the characteristic length is the diameter of the pipeline;

[0021] Step (2.2): Define the key parameters in the hydraulic system, including the cross-sectional area of the hydraulic cylinder, the cross-sectional area of the spiral pipe, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral pipe, the spiral pipe rotation radius, and the spiral pipe pitch;

[0022] Step (2.3): Consider the physical properties of the fluid medium.

[0023] Further supplement to the technical solution, the electromagnetic domain parameter definition process in step (2) is:

[0024] Step (2.1): Accurately describe the size and material properties of each component of the linear motor;

[0025] Step (2.2): Define the material of the motor winding and the layout of the winding, including the number of turns and the connection method of the winding;

[0026] Step (2.3): Set the voltage coefficient and thrust coefficient of the motor;

[0027] Step (2.4): According to the design requirements and expected performance, select appropriate external circuit elements.

[0028] Further supplement to the technical solution, the grid division in the fluid domain in step (3) includes the following steps:

[0029] Step (3.1): Use SolidWorks software to build a model of the fluid inerter, then use Boolean operation in SolidWorks to extract the fluid domain model inside the fluid inerter to form a complete hydraulic system geometry, and then import the obtained fluid domain model into Comsol software for subsequent model simulation;

[0030] Step (3.2): Import the fluid domain model of Comsol, and consider the two ends of the oil-gas isolation piston as open boundaries, which can simplify the model and reduce the complexity of calculation;

[0031] Step (3.3): The fluid domain is divided into three parts, i.e., the piston, the hydraulic master cylinder, and the spiral pipe, and the mesh is divided respectively, so that the poor mesh caused by mesh deformation during the movement of the piston can be avoided, and the model can be converged;

[0032] Step (3.4): For the piston part, an open boundary is set to compensate for the volume change caused by the movement of the piston rod; in theory, the volume change caused by the movement of the piston rod should be equal to the inflow or outflow of the fluid at the open boundary; the volume flow rate measured by the boundary probe is very close to the volume change rate of the piston rod, and the curves of the two are almost completely consistent; although this simplification ignores the influence of the mass of the piston on the dynamic characteristics during the movement, it avoids dealing with the fluid-structure coupling boundary and effectively reduces the complexity of the calculation; since it does not participate in any calculation of the fluid domain and only plays a role in coordinating the mesh movement, a relatively coarse tetrahedral mesh is used for division;

[0033] Step (3.5): For the connection between the hydraulic master cylinder and the spiral pipe, a tetrahedral mesh is used for division due to the complex geometry and little influence on the simulation results, so as to reduce the complexity of the calculation;

[0034] Step (3.6): For the fluid domain of the hydraulic master cylinder and the spiral pipe, since the pressure, velocity, etc. of the liquid inside are mainly simulated with high precision, better mesh quality, stability and convergence are required, and the memory occupation and solving time are reduced, so a hexahedral mesh is used for sweeping, and the hexahedral mesh obtained by sweeping the two sections in the hydraulic cylinder is stretched and compressed vertically, and the rest of the mesh does not change in shape;

[0035] Step (3.7): When dividing the mesh of the spiral pipe part, increasing the number of mesh sweeps can more accurately capture the bending characteristics of the spiral pipe;

[0036] Step (3.8): After the fluid domain mesh is divided, the influence of the increasing number of boundary layer mesh layers on the simulation results is confirmed by taking the damping force as the measurement index, and the number of boundary layer mesh layers is gradually increased to confirm its influence on the calculation results;

[0037] Further supplement to the technical solution, the mesh division of the electromagnetic domain in step (3) comprises the following steps:

[0038] Step (3.1): The model of the electromagnetic domain part is constructed using SolidWorks software, and the obtained model is imported into Comsol software for subsequent model simulation;

[0039] Step (3.2): A two-dimensional axisymmetric model is used for the electromagnetic domain to simplify the calculation of the primary segmented linear motor;

[0040] Step (3.3): Perform mesh sweeping on the primary and magnetic poles of the motor. In the key areas of the primary core teeth and yoke, increase the mesh density and refine the mesh by specifying the number of cells to ensure that the physical field changes in these areas can be accurately captured. Set a denser mesh in areas with large physical field gradients and a looser mesh in areas with small gradients.

[0041] Step (3.4): To address the possible displacement of the motor primary and magnetic poles during movement, a mapping boundary is set in the air gap. This technique prevents the grid of the left magnetic pole from deforming, while allowing the grid of the right motor primary to move as a whole along the Z-axis, with only the quadrilateral grid deforming along the Z-axis.

[0042] As a further supplement to this technical solution, the transient simulation in step (4) includes the following steps:

[0043] Step (4.1): Run the simulation to calculate the fluid pressure, velocity, and stress distribution under different operating conditions, through:

[0044]

[0045] Among them, F d τ is the damping force, dA is the shear stress, and F is the differential area element. i It is the inertial force, ρ is the fluid density, and A is the cross-sectional area of ​​the fluid. It is the acceleration of the fluid;

[0046] Step (4.2): Connect a 10Ω resistor to the external end of the linear motor to verify whether the linear motor has an external circuit that affects the electromagnetic force;

[0047] Step (4.3): Using electromagnetic force as a standard, change the size of the teeth and yoke of the primary iron core and explore its effect on motor performance;

[0048] Step (4.4): Connect the capacitor, inductor and resistor to the external end of the linear motor respectively. By comparing the electromagnetic force output under different external circuit connection methods, the influence of capacitor, inductor and resistor on the phase of electromagnetic force is analyzed.

[0049] As a further supplement to this technical solution, the analysis of the simulation results in step (5) includes the following steps:

[0050] Step (5.1): According to the simulation results of step (4.1), the performance of the linear motor at different speeds is obtained, and it is found that when the relative motion speed of the motor exceeds 0.3 m / s, the motor coefficient decreases significantly, which is due to the magnetic saturation of the motor primary core at high speed, resulting in reduced permeability and inability to continue to enhance the magnetic induction, thereby affecting the output performance of the motor;

[0051] Step (5.2): According to the simulation results of step (4.2), in the absence of external circuit, the electromagnetic force only shows the fluctuation of motor thrust caused by the cogging effect, and when the external circuit is connected, an electromagnetic force of about 55N opposite to the direction of motion is generated;

[0052] Step (5.3): According to the simulation results of step (4.3), the yoke thickness and tooth width need to be kept within a reasonable range, and too small yoke thickness will greatly limit the size of electromagnetic force, and after reaching a certain limit, enlarging it will not bring much improvement to the electromagnetic force; the width of the tooth foot is more likely to affect the electromagnetic force than the height of the tooth foot;

[0053] Step (5.4): According to the simulation results of step (4.4), when the external circuit is connected with a capacitor, the electromagnetic force produces an advanced phase; when connected with an inductor, it produces a lagging phase; when connected with a resistor, the phase remains consistent with the excitation, thereby proving that the electrical network can simulate complex mechanical network impedance.

[0054] The beneficial effects are that the finite element model of the hydraulic system and the electromagnetic system is realized, and the performance analysis of the integrated design scheme of the electromagnetic inerter is further completed; in the hydraulic system, the results prove that the calculation results of the mathematical equation and the finite element model in the inertial force aspect can be verified with each other, and there is a large deviation in the damping force; in the electromagnetic system, it is found that the motor coefficient changes with the change of the motion speed; at the same time, it is also affected by the material, and the magnetic saturation will make the magnetic induction unable to be enhanced, thereby affecting the output performance of the motor; the effect law of the parameters of the motor internal parts on the electromagnetic force is verified; and it is proved that the electrical network can simulate complex mechanical network impedance;

[0055] The present application improves the mathematical model and dynamic finite element method, adopts the mathematical model and COMSOL numerical simulation software, and performs high-precision dynamic performance simulation analysis on the electromagnetic inerter, realizes the transient simulation of the hydraulic system and the electromagnetic system; this method improves the simulation accuracy, makes the optimization of the device design more accurate, and can more accurately predict and analyze the dynamic characteristics of the electromagnetic inerter; this not only helps to improve the vibration isolation performance, but also can predict possible problems in the design stage, thereby reducing the trial and error cost in actual manufacturing;

[0056] The improvement of technical point parameter definition, in the parameter definition stage, the flow state of fluid in the pipeline is judged according to the Reynolds number, so that the suitable turbulent flow model, namely k-omega model, is selected to accurately describe the dynamic behavior of fluid; The key parameters in the hydraulic system are defined, including the cross-sectional area of the hydraulic cylinder and the spiral pipe, the inner and outer radius of the piston rod and the hydraulic cylinder, the rotation radius and the lead of the spiral pipe and the physical properties of the fluid medium such as density and viscosity; For the electromagnetic system, the size parameters and material properties of the linear motor are described in detail, the voltage coefficient and thrust coefficient of the motor are set, and appropriate external circuit elements are selected according to the design requirements; These accurate parameter definitions, combined with optimized mesh division, make the mathematical model of the electromagnetic inductor more accurately map the actual physical phenomenon, providing reliable data support for the engineering design and performance prediction of the device;

[0057] Compared with the traditional method, a novel mesh division strategy is introduced, which significantly improves the accuracy and computational efficiency of the simulation; In the hydraulic system, the geometric structure of the hydraulic master cylinder is accurately constructed through Boolean operation, and the open boundary is used at the oil-gas isolation piston, which effectively coordinates the fluid volume change caused by the piston rod and reduces the computational load of the model; The application of hybrid mesh technology combines coarse tetrahedral mesh and fine hexahedral mesh, optimizing the mesh quality and promoting the convergence of the model; The mesh division of the electromagnetic system benefits from the use of two-dimensional axisymmetric model, which greatly reduces the consumption of computational resources and time; The introduction of mapping boundary technology allows the primary mesh of the motor to deform reasonably in motion without affecting the stability of the overall structure; In addition, careful optimization of the number of grid sweep distribution at the spiral pipe ensures the simulation accuracy while avoiding excessive consumption of computational resources; The comprehensive application of these technologies not only improves the simulation accuracy of the electromagnetic inductor model, but also significantly improves the computational efficiency, providing strong data support for the engineering design and performance prediction of the electromagnetic inductor, promoting the optimization of vibration isolation performance and the compactness of device design. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 The workflow schematic diagram of the present application;

[0059] Figure 2 Boolean operation of the fluid domain;

[0060] Figure 3 Boundary condition setting (without spiral pipe);

[0061] Figure 4 Mesh division scheme;

[0062] Figure 5 The number of spiral pipe grid sweep distribution;

[0063] Figure 6For the mathematical equation and FEM damping force comparison chart;

[0064] Figure 7 For the change of piston load under sinusoidal velocity excitation;

[0065] Figure 8 For the indicator diagram obtained by the two calculation methods of ideal state and FEM. DETAILED DESCRIPTION

[0066] In order to make the technical solution more clear to those skilled in the art, the technical solution will be described in detail below with reference to the accompanying drawings Figures 1-8 The technical solution of the application will be described in detail:

[0067] The electromagnetic inerter is one of the important components of the electromagnetic inertial suspension. The electromagnetic inerter used in the patent is an integrated design, which combines a hydraulic system and an electromagnetic system to achieve high-precision vibration isolation performance.

[0068] Specifically, the electromagnetic inerter includes a hydraulic system and an electromagnetic system.

[0069] The hydraulic system is composed of a hydraulic cylinder and a spiral pipe. The hydraulic cylinder is filled with an incompressible fluid medium, usually water, as a medium for generating inertial force. The design of the spiral pipe allows the fluid to flow between the two chambers of the hydraulic cylinder, thereby generating the desired mass coefficient. In the hydraulic system, the key parameters include the cross-sectional area of the hydraulic cylinder, the cross-sectional area of the spiral pipe, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral pipe, the spiral pipe rotation radius, the spiral pipe lead, etc. These parameters together determine the size of the mass coefficient.

[0070] The electromagnetic system is composed of a linear motor. The primary of the motor is connected to the piston rod in the hydraulic system. When the piston moves, the coil in the primary of the linear motor is connected to the external circuit, thereby generating an electromechanical analog conversion. In the design of the electromagnetic system, the key size parameters include the axial thickness, the radial width, the inner radius, the pole pitch, the tooth pitch, the air gap and the primary outer radius of the permanent magnet.

[0071] The electromagnetic inerter, like other similar electromechanical coupling inerter, combines mechanical and electrical networks, uses the electrical network to simulate complex mechanical impedance, and thereby builds a complex vibration isolation system with a smaller volume and weight, thereby significantly improving the vibration control capability of the vibration isolation system compared to traditional vibration isolation devices.

[0072] The method for constructing a high-precision model of an electromagnetic inerter and simulating dynamic performance of the electromagnetic inerter, uses COMSOL numerical simulation software to construct a finite element model describing the dynamic behavior of the two subsystems of the electromagnetic inerter, and realizes transient simulation of the hydraulic system and the electromagnetic system respectively; for example, Figure 1The steps include: (1) creating mathematical models of the hydraulic system and the electromagnetic system; (2) parameter definition; (3) meshing; (4) transient simulation; and (5) result analysis.

[0073] The key innovation of the application lies in the meshing in step (3), which is a core step for ensuring the accuracy of the high-precision model construction and dynamic performance simulation analysis method of the electromagnetic inductor. Compared with the traditional electromagnetic inductor, a novel method is adopted to perform meshing of the hydraulic system and the electromagnetic system, which has significant advantages in improving simulation accuracy and calculation efficiency. In the hydraulic system, a hybrid meshing technique and an open boundary simplified model are adopted to adapt to fluid volume changes and reduce calculation intensity. In the electromagnetic system, a two-dimensional axisymmetric model and a mapping boundary technique are used to simplify motor calculation and allow dynamic mesh deformation. In addition, the mesh sweep distribution of the spiral pipe is optimized to ensure simulation accuracy and avoid resource waste, which provides strong support for high-precision model construction and dynamic performance simulation analysis of the electromagnetic inductor.

[0074] In step (1), the mathematical model of the hydraulic system is established. In the hydraulic system, the calculation of the mass coefficient b is based on the volume conservation and energy conservation principles of the hydraulic cylinder, and the expression of the mass coefficient b is derived by formula.

[0075]

[0076] wherein S1 and S2 are the cross-sectional areas of the hydraulic cylinder and the spiral pipe respectively, r1 is the piston rod radius, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the spiral pipe, r4 is the spiral pipe rotation radius, h is the lead of the spiral pipe, J is the rotational inertia of the fluid flow, m is the mass of the fluid in the spiral pipe, ρ is the density of the fluid, l is the length of the spiral pipe, b is the inertia coefficient, θ is the angle of rotation of the fluid in the spiral pipe, and n is the number of spiral pipe turns. is the linear movement speed of the piston in the hydraulic cylinder, is the angular velocity of the fluid flow in the spiral pipe.

[0077] The mathematical model of the electromagnetic system is established. The calculation in the electromagnetic field is based on the Maxwell equations, which are a set of partial differential equations describing the relationship between electric field, magnetic field, charge density and current density, and are composed of the following equations:

[0078]

[0079] wherein For Hamiltonian operator, E is electric field intensity, B is magnetic induction intensity, J is conduction current intensity, p is charge density, e0 is dielectric constant, and m0 is magnetic permeability; the equation set includes: Gauss law, Gauss magnetic field law, Faraday induction law, and Maxwell-Ampere law;

[0080] The fluid domain parameter definition in step (2) includes the following steps:

[0081] Step (2.1): Determine the flow state of the fluid in the pipe according to the Reynolds number to determine whether it is laminar flow, transition flow or turbulent flow; based on the judgment of the Reynolds number, select an appropriate turbulent flow model (such as the k-ω model) to describe the fluid flow characteristics, and use the wall function approximation to reduce the memory requirement The calculation method of Reynolds number is as follows:

[0082]

[0083] Where p is the fluid density, V is the fluid viscosity, m is the dynamic viscosity, and d is the characteristic length, which is the pipe diameter when flowing in a circular pipe;

[0084] Step (2.2): Define the key parameters in the hydraulic system, including the cross-sectional area of the hydraulic cylinder, the cross-sectional area of the spiral pipe, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral pipe, the rotation radius of the spiral pipe, and the pitch of the spiral pipe. These parameters together determine the size of the inertia coefficient;

[0085] Step (2.3): Consider the physical properties of the fluid medium, such as density and viscosity, as well as the length and rotation angle of the spiral pipe. These factors together affect the dynamics of the fluid;

[0086] Wherein the electromagnetic domain parameter definition in step (2) includes the following steps:

[0087] Step (2.1): Accurately describe the size and material properties of each component of the linear motor; this includes determining the key size parameters of the permanent magnet, such as the axial thickness, radial width, inner radius, pole pitch, tooth pitch, air gap, and primary outer radius.

[0088] Step (2.2): Define the material of the motor winding and the layout of the winding, including the number of turns and the connection method of the winding;

[0089] Step (2.3): Set the voltage coefficient and thrust coefficient of the motor, and according to the design requirements and expected performance, select appropriate external circuit elements such as resistance, capacitance and inductance to achieve the required electromechanical simulation effect.

[0090] Step (2.4): Select appropriate external circuit elements such as resistors, capacitors, and inductors based on design requirements and expected performance to achieve the desired electromechanical analog effects.

[0091] The fluid domain meshing in step (3) includes the following steps:

[0092] Step (3.1): Use SolidWorks software to build a model of the fluid inerter, then use Boolean operations in SolidWorks to extract the fluid domain model inside the fluid inerter, as shown in Figure 2 , to form the complete hydraulic system geometry, and then import the resulting fluid domain model into Comsol software for subsequent model simulation;

[0093] Step (3.2): Import the fluid domain model into Comsol, and consider the two ends of the oil-gas isolation piston as open boundaries to simplify the model and reduce computational complexity; because the hydraulic master cylinder is divided into two chambers, the up and down movement of the piston rod causes fluid to flow through the spiral pipe between the two chambers for hydraulic compensation. If the two chambers are not isolated by the piston, the complexity of the model will increase significantly, affecting the calculation efficiency and accuracy. By simplifying the piston as an open boundary, we can effectively simulate the dynamic changes of fluid on both sides of the piston, while avoiding unnecessary computational burden.

[0094] Step (3.3): Divide the fluid domain into three parts: the piston, the hydraulic master cylinder, and the spiral pipe, and perform meshing separately, which can avoid the poor quality mesh caused by mesh deformation when the piston moves, making the model difficult to converge;

[0095] Step (3.4): For the piston part, in order to compensate for the volume change caused by the movement of the piston rod, we set an open boundary at the position shown in Figure 3 ; in theory, the volume change caused by the movement of the piston rod should be equal to the inflow or outflow of fluid at the open boundary; the volume flow rate measured by the boundary probe is very close to the volume change rate of the piston rod, and the curves of the two are almost completely consistent; although this simplification ignores the influence of the mass of the piston on the dynamic characteristics during movement, it avoids dealing with fluid-structure coupling boundaries and effectively reduces the complexity of calculation; since it does not participate in any calculation of the fluid domain, it only plays a role in coordinating the mesh movement, so a relatively coarse tetrahedral mesh is used for division;

[0096] Step (3.5): For the connection between the hydraulic master cylinder and the spiral pipe, since the geometric shape is complex and does not have much impact on the simulation results, a tetrahedral mesh is also used for division to reduce the complexity of calculation;

[0097] Step (3.6): For the hydraulic master cylinder fluid domain and the spiral tube fluid domain part, since the pressure, velocity, etc. of the liquid inside are simulated with high precision, better grid quality is required, with better stability and convergence, while reducing memory occupation and solving time. Therefore, hexahedral grid is used for sweeping; Figure 4 The coordination of the moving grid when the piston moves is shown in FIG. 8. It can be seen that the hexahedrons obtained by sweeping the two sections in the hydraulic cylinder are stretched and compressed in the vertical direction, and the rest of the grid does not change in shape. This method eliminates the generation of poor quality grid during grid deformation, and avoids the calculation divergence caused by poor grid quality.

[0098] Step (3.7): When dividing the grid for the spiral tube part, the present patent finds that increasing the number of grid sweeps can more accurately capture the bending characteristics of the spiral tube. Experimental data show that when the number of sweeps increases from 2000 to 2500, the change in damping force is only 0.44%, as shown in FIG. 9. This small increase shows that the accuracy improvement brought by the number of sweeps exceeding 2000 is negligible. Therefore, setting the number of sweeps to more than 2000 can ensure the accuracy of the simulation, avoid unnecessary consumption of computing resources, and achieve an optimized balance between efficiency and accuracy. Figure 5

[0099] Step (3.8): After the fluid domain grid is divided, in order to confirm the influence of the number of boundary layer grid increments on the simulation results, the number of boundary layer grid increments is gradually increased to confirm its influence on the calculation results, taking the damping force as the measurement index. The present patent finds that when the number of boundary layers increases from 1 to 5, the calculation cost increases by 7 times, and the calculation accuracy only increases by 0.55%. Therefore, no boundary layer is selected.

[0100] Among them, the primary segmented linear motor in the electromagnetic domain of the electromagnetic inductor is in the shape of a cylinder, so a two-dimensional axisymmetric model is used to simplify the calculation of the primary segmented linear motor, which can significantly reduce the demand for computing resources and time consumption. The grid division of the electromagnetic domain in step (3) includes the following steps:

[0101] Step (3.1): Use SolidWorks software to build a model of the electromagnetic domain part, and import the obtained model into Comsol software for subsequent model simulation;

[0102] Step (3.2): A two-dimensional axisymmetric model is used to simplify the calculation of the primary segmented linear motor in the electromagnetic domain. This significantly improves the calculation efficiency, simplifies the model setting and parameterization research, and reduces the consumption of computing resources. This model is particularly suitable for systems or structures with axisymmetric characteristics, and can more accurately control the setting of boundary conditions and physical fields, thereby improving the calculation accuracy.

[0103] ​Step (3.3): Grid sweeping is performed on the motor primary and magnetic poles. In the key areas of the primary core teeth and yoke, the grid density is increased, and the grid is refined by specifying the number of cells to ensure that the physical field changes in these areas can be accurately captured. More dense grids are set in places with large physical field gradients, while more sparse grids are set in places with small gradients.

[0104] Step (3.4): For the displacement that may occur during the movement of the motor primary and magnetic poles, a mapping boundary is set in the air gap. This technique prevents the grid of the left magnetic pole from deforming, while allowing the grid of the right motor primary to move as a whole along the Z-axis. Only the quadrilateral grid deforms along the Z-axis.

[0105] Step (4): Transient simulation of the electromagnetic inerter is performed using COMSOL numerical simulation software. The simulation takes into account the piston movement of the hydraulic system and the current change of the electromagnetic system, as well as their interaction. The transient simulation in step (4) includes the following steps:

[0106] Step (4.1): Run the simulation to calculate the fluid pressure, velocity, and stress distribution under different working conditions by:

[0107]

[0108] where F d is the damping force, τ is the shear stress, dA is the differential area element, F i is the inertial force, ρ is the fluid density, A is the cross-sectional area of the fluid, is the acceleration of the fluid.

[0109] Step (4.2): Connect a 10Ω resistor to the outer end of the linear motor to verify whether the external circuit of the linear motor has an effect on the electromagnetic force.

[0110] Step (4.3): Change the size of the tooth and yoke of the primary core to explore its effect on the performance of the motor.

[0111] Step (4.4): Connect the capacitor, inductor, and resistor to the outer end of the linear motor, respectively. By comparing the electromagnetic force output under different external circuit connection methods, the effects of the capacitor, inductor, and resistor on the phase of the electromagnetic force are analyzed.

[0112] Step (5): Analyze the simulation results, including the comparison of the calculated results of the damping force and the theoretical prediction, and the output characteristics of the electromagnetic force, such as Figure 6 the comparison of the damping force obtained by the finite element method (FEM) and the mathematical equation method. In this figure, there is a significant difference between the damping force values obtained by the two calculation methods:

[0113] Step (5.1): From the simulation results of step (4.1), the performance of the linear motor at different speeds was obtained, and it was found that when the relative speed of the motor exceeds 0.3 m / s, the motor coefficient decreases significantly, which is due to the magnetic saturation phenomenon of the motor primary core at high speed, resulting in a decrease in permeability and a failure to continue to enhance the magnetic induction, thereby affecting the output performance of the motor;

[0114] Step (5.2): From the simulation results of step (4.2), it can be seen that without an external circuit, the electromagnetic force only shows the motor thrust fluctuation caused by the cogging effect, and when the external circuit is connected, an electromagnetic force of about 55 N opposite to the direction of motion is generated.

[0115] Step (5.3): From the simulation results of step (4.3), it can be seen that the yoke thickness and tooth width need to be kept within a reasonable range, and too small yoke thickness will greatly limit the size of the electromagnetic force, and after reaching a certain limit, enlarging it will not bring great improvement to the electromagnetic force. The width of the tooth foot is more likely to affect the electromagnetic force than the height.

[0116] Step (5.4): As shown in Figure 7 , from the simulation results of step (4.4), when the external circuit is connected to the capacitor, the electromagnetic force produces an advanced phase; when connected to the inductor, it produces a lagging phase; when connected to the resistor, the phase remains consistent with the excitation, thereby proving that the electrical network can simulate complex mechanical network impedance.

[0117] Further, as shown in Figure 8 , the comparison of the ideal inerter element and the actual finite element model of the indicator diagram. Ideally, the indicator diagram should be a straight line, representing the relationship between the piston load and displacement. However, due to the existence of parasitic damping force, the actual finite element model results form a region, and the area of this region represents the energy dissipation caused by parasitic damping during the movement of the piston.

[0118] The above technical solutions only reflect the preferred technical solutions of the present application, and some changes made by the person skilled in the art to some parts thereof also embody the principles of the present application and are within the scope of protection of the present application.

Claims

1. A method for constructing a high-precision model and simulating the dynamic performance of an electromagnetic inertial container, characterized in that, Includes the following steps: Step (1): Establish a mathematical model of the hydraulic system. In the hydraulic system, the calculation of the inertia coefficient follows the principles of volume conservation and energy conservation of the hydraulic cylinder. The expression for the inertia coefficient is derived through formulas; the inertia coefficient b is expressed as: ； Where S1 and S2 are the cross-sectional areas of the hydraulic cylinder and the helical tube, respectively; r1 is the piston rod radius, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the helical tube, r4 is the rotation radius of the helical tube, h is the lead of the helical tube, J is the moment of inertia of the fluid flow, m is the mass of the fluid in the helical tube, ρ is the density of the fluid, l is the length of the helical tube, b is the coefficient of inertia, θ is the angle of rotation of the fluid in the helical tube, and n is the number of turns of the helical tube. It is the linear movement speed of the piston within the hydraulic cylinder. It is the angular velocity of the fluid flowing in the helical tube; A mathematical model of the electromagnetic system is established. Calculations in the electromagnetic field are based on Maxwell's equations, a set of partial differential equations describing the relationship between electric and magnetic fields and charge and current densities. These equations consist of the following: ； in, Here, E is the Hamiltonian operator, B is the electric field strength, J is the magnetic flux density, ρ is the charge density, ε0 ​​is the permittivity, and μ0 is the permeability. This set of equations includes: Gauss's law, Gauss's law of magnetic fields, Faraday's law of induction, and Maxwell-Ampère's law. Step (2): Define the parameters of the fluid domain and electromagnetic domain; Step (3): Mesh generation for the fluid and electromagnetic domains; Step (4): Use COMSOL numerical simulation software to perform transient simulation of the electromagnetic inertial container; the simulation considers the piston motion of the hydraulic system and the current change of the electromagnetic system, as well as their interaction. Step (5): Analyze the simulation results, including the comparison between the calculated results of damping force and inertial force and the theoretical predictions, as well as the output characteristics of electromagnetic force; The transient simulation in step (4) includes the following steps: Step (4.1): Run the simulation and calculate the damping force and inertial force using the following formulas: ； Among them, F d It is damping force. It is shear stress, dA is the differential area element, F i It is inertial force. Where A is the fluid density and A is the cross-sectional area of ​​the fluid. It is the acceleration of the fluid; Step (4.2): Connect a 10Ω resistor to the external end of the linear motor to verify whether the linear motor has an external circuit that affects the electromagnetic force; Step (4.3): Using electromagnetic force as a standard, change the size of the teeth and yoke of the primary iron core and explore its effect on the motor performance; Step (4.4): Connect a capacitor, an inductor, and a resistor to the external end of the linear motor respectively. By comparing the electromagnetic force output under different external circuit connection methods, analyze the influence of capacitor, inductor, and resistor on the phase of electromagnetic force.

2. The method for constructing a high-precision model and performing dynamic performance simulation analysis of an electromagnetic inertial container according to claim 1, characterized in that, The fluid domain parameter definition in step (2) includes the following steps: Step (2.1): Determine the flow state of the fluid in the pipe based on the Reynolds number to determine whether it is laminar, transitional, or turbulent flow; based on the Reynolds number determination, select an appropriate turbulence model to describe the fluid flow characteristics, and use the wall function approximation to reduce memory requirements. The calculation method of the Reynolds number is shown in the following formula: ； Where ρ is the fluid density, V is the fluid viscosity, μ is the dynamic viscosity, and d is the characteristic length. When flowing in a circular pipe, the characteristic length is the pipe diameter. Step (2.2): Define the key parameters of the hydraulic system, including the cross-sectional area of ​​the hydraulic cylinder, the cross-sectional area of ​​the helical tube, the piston rod radius, the inner radius of the hydraulic cylinder, the inner radius of the helical tube, the rotation radius of the helical tube, and the lead of the helical tube; and consider the physical properties of the fluid medium, including density, viscosity, length of the helical tube, and rotation angle.

3. The method for constructing a high-precision model and performing dynamic performance simulation analysis of an electromagnetic inertial container according to claim 2, characterized in that, The electromagnetic domain parameter definition process in step (2) is as follows: Step (2.1): Provide a precise dimensional and material property description of each component of the linear motor; Step (2.2): Define the material and layout of the motor windings, including the number of turns and connection method; Step (2.3): Set the voltage coefficient and thrust coefficient of the motor; Step (2.4): Select appropriate external circuit components based on design requirements and expected performance.

4. The method for constructing a high-precision model and performing dynamic performance simulation analysis of an electromagnetic inertial container according to claim 3, characterized in that, The fluid domain mesh generation in step (3) includes the following steps: Step (3.1): Use SolidWorks software to build a model of the fluid inertial container, and then use Boolean operations in SolidWorks to extract the fluid domain model inside the fluid inertial container to form a complete hydraulic system geometry. Then import the obtained fluid domain model into Comsol software for subsequent model simulation. Step (3.2): Import the fluid domain model from Comsol and treat both ends of the oil-gas isolation piston as open boundaries; Step (3.3): Divide the fluid domain into three parts: piston, hydraulic master cylinder, and spiral tube, and perform mesh generation for each part; Step (3.4): For the piston part, an open boundary is set; the volume change caused by the movement of the piston rod should be equal to the inflow or outflow of fluid at the open boundary; the volume flow rate measured by the boundary probe is very close to the volume change rate of the piston rod, and the curves of the two are almost completely matched; since it does not participate in any calculation of the fluid domain, but only plays a role in coordinating the mesh movement, a relatively coarse tetrahedral mesh is used for partitioning. Step (3.5): For the connection between the hydraulic master cylinder and the spiral pipe, tetrahedral mesh is also used for division; Step (3.6): For the hydraulic master cylinder fluid domain and the spiral tube fluid domain, a hexahedral mesh is used for sweeping. Except for the two hexahedral sections in the hydraulic cylinder that are swept and subjected to vertical mesh stretching and compression, the remaining meshes do not undergo any shape change. Step (3.7): When meshing the helical tube section, increasing the number of mesh sweeps can more accurately capture the bending characteristics of the helical tube. Step (3.8): After the fluid domain mesh is generated, in order to confirm the effect of the increasing number of boundary layer mesh layers on the simulation results, the number of boundary layer mesh layers is gradually increased using damping force as a measure to confirm its effect on the calculation results.

5. The method for constructing a high-precision model and performing dynamic performance simulation analysis of an electromagnetic inertial container according to claim 4, characterized in that, The electromagnetic domain grid division in step (3) includes the following steps: Step (3.1): Use SolidWorks software to build a model of the electromagnetic domain, and import the obtained model into Comsol software for subsequent model simulation; Step (3.2): A two-dimensional axisymmetric model is used for the electromagnetic domain to simplify the calculation of the primary piecewise linear motor; Step (3.3): Perform mesh sweeping on the primary and magnetic poles of the motor. Increase the mesh density in the key areas of the primary core teeth and yoke. Refine the mesh by specifying the number of cells. Set a denser mesh in areas with large physical field gradients and a sparser mesh in areas with small gradients. Step (3.4): A mapping boundary is set in the air gap to account for the displacement of the motor primary and magnetic poles during the movement.

6. The method for constructing a high-precision model and performing dynamic performance simulation analysis of an electromagnetic inertial container according to claim 1, characterized in that, The analysis of the simulation results in step (5) includes the following steps: Step (5.1): Based on the simulation results of step (4.1), the performance of the linear motor at different speeds was obtained. It was found that when the relative speed of the motor exceeds 0.3m / s, the motor coefficient drops significantly. This phenomenon is attributed to the magnetic saturation phenomenon that occurs in the primary iron core of the motor during high-speed operation, which leads to a decrease in magnetic permeability and the induction intensity cannot continue to increase, thus affecting the output performance of the motor. Step (5.2): According to the simulation results of step (4.2), without external circuit, the electromagnetic force only manifests as the motor thrust fluctuation caused by the cogging effect. However, when the external circuit is connected, an electromagnetic force of 55N is generated that is opposite to the direction of motion. Step (5.3): Based on the simulation results of step (4.3), the yoke thickness and tooth width need to be kept within a reasonable range. Too small a yoke thickness will greatly limit the magnitude of the electromagnetic force. After reaching a certain limit, unlimited expansion will not bring a significant increase to the electromagnetic force. The width of the tooth foot has a greater impact on the electromagnetic force than the height. Step (5.4): The simulation results from step (4.4) show that when the external circuit is connected to a capacitor, the electromagnetic force produces a leading phase; when connected to an inductor, it produces a lagging phase; and when connected to a resistor, the phase is consistent with the excitation, thus proving that the electrical network can simulate the impedance of a complex mechanical network.

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