Electromagnetic inerter high-precision model construction and dynamic performance simulation analysis method

Abstract

The invention discloses a high-precision model construction and dynamic performance simulation analysis method for an electromagnetic inerter. The method comprises the following steps: (1) establishing a mathematical model; (2) defining parameters; (3) carrying out grid division; (4) performing transient simulation; (5) analyzing a result; the method has the beneficial effects that finite element model construction of a hydraulic system and an electromagnetic system is realized, and further performance analysis of an integrated design scheme of the electromagnetic inerter is completed; according to the method, a technical point mathematical model and a dynamic finite element method are improved, the mathematical model and COMSOL numerical simulation software are adopted, high-precision dynamic performance simulation analysis is conducted on the electromagnetic inerter, and transient simulation of a hydraulic system and an electromagnetic system is achieved; and a novel grid division strategy is introduced, so that the simulation precision and the calculation efficiency are remarkably improved.

Description

Technical Field

[0001] The invention relates to the technical field of engineering vibration reduction, and in particular to a method for constructing a high-precision model of an electromagnetic inertial vessel and simulating and analyzing its dynamic performance. Background Art

[0002] As a new type of electromechanical vibration isolation element, the electromagnetic inertia vessel is gradually changing the traditional vibration control field. Through the coupling of the hydraulic system and the electromagnetic system, it solves the problems of the traditional "inertia vessel-spring-damper" (ISD) vibration isolation system, which is bulky, complex in structure, and difficult to integrate. This device uses the structural topology capability of the hydraulic system and the electromechanical simulation function of the electromagnetic system to realize a complex vibration isolation network within a limited volume, which is particularly suitable for scenarios with strict requirements on weight and volume.

[0003] This study is based on the electromagnetic inertial device, and uses mathematical models and dynamic finite element methods to conduct in-depth design theory, system matching and optimization, manufacturing and performance testing research on the device. The existing simulation methods have some shortcomings in the finite element simulation of electromagnetic inertial devices. Difficulty 1: In the fluid domain, complex fluid-solid coupling problems are often accompanied by high time costs and a large amount of calculations, and lead to large errors in the calculation of damping force and inertial 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 meshing may cause mesh deformation and produce poor quality meshes, which may cause the calculation to not converge. Difficulty 3: In the electromagnetic domain, the influence of the geometric dimensions of the primary core teeth and yoke on the motor performance has not been accurately analyzed, and the law of the change of the motor coefficient with the movement speed has not been accurately explored. Difficulty 4: In the electromagnetic domain, the ability of the linear motor as a converter between the two networks and the feasibility of simulating the impedance of a complex mechanical network through an electrical network have not been verified.

[0004] In view of the above situation, it is necessary to improve the existing simulation method of electromagnetic inertia container so that it can adapt to the current needs of using electromagnetic inertia container. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a high-precision model construction and dynamic performance simulation analysis method of an electromagnetic inertial vessel, which proves its performance advantages in the vibration isolation system and promotes its progress in engineering applications.

[0006] To achieve the above purpose, the technical solution adopted by the present invention is: a method for constructing a high-precision model of an electromagnetic inertial vessel and simulating and analyzing dynamic performance, comprising the following steps:

[0007] Step (1): Establish a mathematical model of the hydraulic system. In the hydraulic system, the calculation of the inertia coefficient follows the principles of conservation of volume and energy of the hydraulic cylinder. The expression of the inertia coefficient is derived through the formula; the inertia coefficient b can be expressed as:

[0008]

[0009] Among them, S1 and S2 are the cross-sectional areas of the hydraulic cylinder and the spiral tube respectively; r1 is the radius of the piston rod, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the spiral tube, r4 is the rotation radius of the spiral tube, h is the lead of the spiral tube, J is the moment of inertia of the fluid during flow, m is the mass of the fluid in the spiral tube, ρ is the density of the fluid, l is the length of the spiral tube, b is the inertia coefficient, θ is the angle of rotation of the fluid in the spiral tube, n is the number of turns of the spiral tube, is the linear velocity of the piston in the hydraulic cylinder, is the angular velocity of the fluid flowing in the spiral tube;

[0010] Establish a 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 that describe the relationship between the electric field, magnetic field, charge density, and current density. It consists of the following equations:

[0011]

[0012] in, 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, and μ0 is the magnetic permeability; the equations include: Gauss's law, Gauss's magnetic field law, Faraday's induction law and Maxwell-Ampere's law;

[0013] Step (2): fluid domain and electromagnetic domain parameter definition;

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

[0015] Step (4): using COMSOL numerical simulation software to perform transient simulation on the electromagnetic inertial vessel; the simulation takes into account the piston motion of the hydraulic system and the current change of the electromagnetic system, as well as the interaction between them;

[0016] Step (5): Analyze the simulation results, including the comparison of the calculated results of damping force and inertial force with theoretical predictions, and the output characteristics of electromagnetic force.

[0017] As a 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 the fluid in the pipe based on the Reynolds number to determine whether it is laminar flow, transitional flow or turbulent flow; based on the judgment of the Reynolds number, 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:

[0019]

[0020] Among them, 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;

[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 tube, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral tube, the rotation radius of the spiral tube, and the lead of the spiral tube;

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

[0023] As a further supplement to the technical solution, the electromagnetic domain parameter definition process in step (2) is as follows:

[0024] Step (2.1): Accurately describe the dimensions 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 connection method of the winding;

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

[0027] Step (2.4): Select appropriate external circuit components based on design requirements and expected performance.

[0028] As a further supplement to the technical solution, the fluid domain meshing in step (3) includes the following steps:

[0029] Step (3.1): Use SolidWorks software to build a model of the fluid inertia container, then use Boolean operations in SolidWorks to extract the fluid domain model inside the fluid inertia container 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 regard both ends of the oil-gas isolation piston as open boundaries to simplify the model and reduce the computational complexity;

[0031] Step (3.3): Divide the fluid domain into three parts: piston, hydraulic main cylinder, and spiral tube, and mesh them separately. This can avoid mesh deformation and poor quality mesh when the piston moves, which makes it difficult for the model to converge.

[0032] Step (3.4): For the piston part, in order to compensate for the volume change caused by the piston rod during movement, we set an open boundary; theoretically, 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 movement, it avoids dealing with the fluid-solid 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 grid movement, a relatively coarse tetrahedral grid is used for division;

[0033] Step (3.5): For the connection between the hydraulic main cylinder and the spiral pipe, since the geometric shape is complex and does not have much impact on the simulation results, tetrahedral mesh is also used for division to reduce the complexity of calculation;

[0034] Step (3.6): For the hydraulic main cylinder fluid domain and the spiral tube fluid domain, since the pressure and velocity of the liquid in them are mainly simulated with high precision, better mesh quality, better stability and convergence are required, and at the same time, memory usage and solution time can be reduced. Therefore, hexahedral meshes are used for sweeping. Except for the hexahedrons obtained by sweeping the two sections in the hydraulic cylinder, the meshes are stretched and compressed in the vertical direction, and the remaining meshes do not change in shape;

[0035] Step (3.7): When meshing the spiral tube, increasing the number of distributions of the mesh sweep can more accurately capture the bending characteristics of the spiral tube;

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

[0037] As a further supplement to the technical solution, the electromagnetic domain grid division in step (3) includes the following steps:

[0038] Step (3.1): Use SolidWorks software to build a model for the electromagnetic domain part, and import the obtained model into Comsol software for subsequent model simulation;

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

[0040] Step (3.3): Sweep the mesh of the motor primary and magnetic poles, increase the mesh density in the key areas of the primary core teeth and yoke, 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 where the physical field gradient is large, and set a looser mesh where the gradient is small;

[0041] Step (3.4): In view of the possible displacement of the motor primary and magnetic poles during movement, a mapping boundary is set in the air gap. This technology can prevent the mesh of the left magnetic pole from being deformed, while allowing the mesh of the right motor primary to move along the Z axis as a whole, with only the quadrilateral mesh deforming along the Z axis.

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

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

[0044]

[0045] Among them, 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;

[0046] Step (4.2): Connect a 10Ω resistor to the outer 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 measure, change the size of the teeth and yoke of the primary core to explore its effect on the motor performance;

[0048] Step (4.4): Connect the outer ends of the linear motor to capacitors, inductors and resistors respectively, and analyze the influence of capacitors, inductors and resistors on the phase of the electromagnetic force by comparing the electromagnetic force output under different external circuit connection methods.

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

[0050] Step (5.1): From the simulation results of step (4.1), it can be found that the performance of the linear motor at different speeds, when the relative movement speed of the motor exceeds 0.3m / s, the motor coefficient decreases significantly. This phenomenon is attributed to the magnetic saturation phenomenon of the primary iron core of the motor when running at high speed, resulting in a decrease in magnetic permeability and the inability of the magnetic induction intensity to continue to increase, thereby affecting the output performance of the motor;

[0051] Step (5.2): From the simulation results of step (4.2), it can be seen that in the absence of an external circuit, the electromagnetic force only manifests the motor thrust fluctuation caused by the cogging effect, and when the external circuit is connected, an electromagnetic force of about 55N is generated in the opposite direction of the movement;

[0052] 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. Too small yoke thickness will greatly limit the magnitude of the electromagnetic force. After reaching a certain limit, unlimited amplification 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;

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

[0054] Its beneficial effect is that it realizes the construction of finite element models of hydraulic system and electromagnetic system, and completes further performance analysis of integrated design scheme of electromagnetic inertial vessel; in hydraulic system, the results show that the calculation results of mathematical equation and finite element model in inertial force can confirm each other, but there is a large deviation in damping force; in electromagnetic system, it is found that the motor coefficient changes with the change of movement speed; at the same time, it is also affected by the material, and magnetic saturation will make the magnetic induction intensity unable to increase, thus affecting the output performance of the motor; verify the effect of internal motor parts parameters on electromagnetic force; prove that the electrical network can simulate the impedance of complex mechanical network;

[0055] The present invention improves the technical point mathematical model and dynamic finite element method, adopts the mathematical model and COMSOL numerical simulation software, performs high-precision dynamic performance simulation analysis on the electromagnetic inertial device, and 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 precise, and can more accurately predict and analyze the dynamic characteristics of the electromagnetic inertial device; 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] Improvement of technical point parameter definition. In the parameter definition stage, the flow state of the fluid in the pipeline is determined based on the Reynolds number, so as to select a suitable turbulence model, namely the k-ω model, to accurately describe the dynamic behavior of the fluid; the key parameters in the hydraulic system are defined, including the cross-sectional area of ​​the hydraulic cylinder and the spiral tube, the inner and outer radii of the piston rod and the hydraulic cylinder, the rotation radius and lead of the spiral tube, and the physical properties of the fluid medium such as density and viscosity; for the electromagnetic system, the dimensional 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 precise parameter definitions, combined with optimized grid division, enable the mathematical model of the electromagnetic inertial device to more accurately map the actual physical phenomena, providing reliable data support for the engineering design and performance prediction of the device;

[0057] Compared with traditional methods, we introduced a novel meshing strategy, which significantly improved the simulation accuracy and computational efficiency. In terms of hydraulic systems, we accurately constructed the geometric structure of the hydraulic master cylinder through Boolean operations, and adopted open boundaries at the oil-gas isolation piston to effectively coordinate the fluid volume changes caused by the piston rod and reduce the computational load of the model. The application of hybrid meshing technology combines coarse tetrahedral meshes with fine hexahedral meshes to optimize mesh quality and promote model convergence. The meshing of the electromagnetic system benefits from the use of a two-dimensional axisymmetric model, which greatly reduces the consumption of computing resources and time. The introduction of mapping boundary technology allows the primary mesh of the motor to deform reasonably during motion without affecting the stability of the overall structure. In addition, the meticulous optimization of the number of mesh sweep distributions at the spiral tube ensures the simulation accuracy while avoiding excessive consumption of computing resources. The comprehensive application of these technologies not only improves the simulation accuracy of the electromagnetic inertial device model, but also significantly improves the computational efficiency, providing strong data support for the engineering design and performance prediction of the electromagnetic inertial device, and promoting the optimization of vibration isolation performance and the compactness of device design. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the workflow of the present invention;

[0059] Figure 2 Boolean operations for fluid domains;

[0060] Figure 3 Set up boundary conditions (excluding spiral tubes);

[0061] Figure 4 is the grid partitioning scheme;

[0062] Figure 5 The number of spiral tube mesh sweep distributions;

[0063] Figure 6The comparison diagram between mathematical equation and FEM damping force;

[0064] Figure 7 is the change of piston load under sinusoidal speed excitation;

[0065] Figure 8 The dynamometer diagrams are obtained by the ideal state and FEM calculation methods. DETAILED DESCRIPTION

[0066] In order to make the technical solution more clear to those skilled in the art, Figure 1-8 The technical solution of the present invention is described in detail:

[0067] The electromagnetic inertia container is one of the important components of the electromagnetic inertia suspension. The electromagnetic inertia container used in this patent is an integrated design that combines the hydraulic system and the electromagnetic system to achieve high-precision vibration isolation performance.

[0068] Specifically, this electromagnetic inertia container includes a hydraulic system and an electromagnetic system:

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

[0070] The electromagnetic system consists of a linear motor whose primary 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 dimensional parameters include the axial thickness, radial width, inner radius, pole pitch, tooth pitch, air gap and primary outer radius of the permanent magnet.

[0071] The electromagnetic inertial device is similar to other similar electromechanical coupled inertial devices. It combines mechanical networks and electrical networks, and uses the electrical network to simulate complex mechanical impedance, thereby building a complex vibration isolation system with a smaller volume and weight. The vibration control capability of the vibration isolation system is significantly improved compared to traditional vibration isolation devices.

[0072] The invention provides a method for constructing a high-precision model and simulating and analyzing the dynamic performance of an electromagnetic inertial device. The finite element model describing the dynamic behavior of two subsystems of the electromagnetic inertial device is constructed using COMSOL numerical simulation software to realize transient simulation of the hydraulic system and the electromagnetic system respectively. Figure 1As shown, it includes: (1): creating mathematical models of hydraulic system and electromagnetic system; (2): parameter definition; (3): grid division; (4): transient simulation; (5): result analysis.

[0073] The key innovation of the present invention lies in the grid division in step (3), which is the core link to ensure the accuracy of the high-precision model construction and dynamic performance simulation analysis method of the electromagnetic inertial device; compared with the traditional electromagnetic inertial device, we adopt a novel method to carry out the grid division of the hydraulic system and the electromagnetic system, which has significant advantages in improving the simulation accuracy and calculation efficiency. In the hydraulic system, hybrid grid technology and open boundary simplified model are adopted to adapt to the change of fluid volume and reduce the calculation intensity. In the electromagnetic system, the two-dimensional axisymmetric model and mapping boundary technology are used to simplify the calculation of the motor and allow dynamic grid deformation. In addition, by optimizing the grid sweep distribution of the spiral tube, the simulation accuracy is ensured while avoiding resource waste. These improvements provide strong support for the high-precision model construction and dynamic performance simulation analysis of the electromagnetic inertial device.

[0074] Among them, step (1): establish a mathematical model of the hydraulic system. In the hydraulic system, the calculation of the inertia coefficient follows the principles of conservation of hydraulic cylinder volume and conservation of energy. The expression of the inertia coefficient is derived through the formula; the inertia coefficient b can be expressed as:

[0075]

[0076] Among them, S1 and S2 are the cross-sectional areas of the hydraulic cylinder and the spiral tube respectively; r1 is the radius of the piston rod, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the spiral tube, r4 is the rotation radius of the spiral tube, h is the lead of the spiral tube, J is the moment of inertia of the fluid during flow, m is the mass of the fluid in the spiral tube, ρ is the density of the fluid, l is the length of the spiral tube, b is the inertia coefficient, θ is the angle of rotation of the fluid in the spiral tube, n is the number of turns of the spiral tube, is the linear velocity of the piston in the hydraulic cylinder, is the angular velocity of the fluid flowing in the spiral tube;

[0077] Establish a 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 that describe the relationship between the electric field, magnetic field, charge density, and current density. It consists of the following equations:

[0078]

[0079] in, 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, and μ0 is the magnetic permeability; the equations include: Gauss's law, Gauss's magnetic field law, Faraday's induction law and Maxwell-Ampere's 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 based on the Reynolds number to determine whether it is laminar flow, transitional flow or turbulent flow; based on the judgment of the Reynolds number, select an appropriate turbulence model (such as the k-ω 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:

[0082]

[0083] Among them, 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;

[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 tube, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral tube, the rotation radius of the spiral tube, the lead of the spiral tube, etc.; 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 tube. These factors together affect the dynamic behavior of the fluid;

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

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

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

[0089] Step (2.3): Set the voltage coefficient and thrust coefficient of the motor, and select appropriate external circuit components such as resistors, capacitors, and inductors according to design requirements and expected performance to achieve the desired electromechanical simulation effect.

[0090] Step (2.4): According to the design requirements and expected performance, select appropriate external circuit components, such as resistors, capacitors, and inductors, to achieve the desired electromechanical simulation effect.

[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 inertia container, and then use Boolean operations in SolidWorks to extract the fluid domain model inside the fluid inertia container, such as Figure 2 As shown, a complete hydraulic system geometry is formed, and then the obtained fluid domain model is imported into Comsol software for subsequent model simulation;

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

[0094] Step (3.3): Divide the fluid domain into three parts: piston, hydraulic main cylinder, and spiral tube, and mesh them separately. This can avoid mesh deformation and poor quality mesh when the piston moves, which makes it difficult for the model to converge.

[0095] Step (3.4): For the piston part, in order to compensate for the volume change caused by the piston rod during movement, we Figure 3 An open boundary is set at the position shown; theoretically, 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-solid 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;

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

[0097] Step (3.6): For the hydraulic main cylinder fluid domain and the spiral tube fluid domain, since the pressure and velocity of the liquid inside are mainly simulated with high precision, better mesh quality, better stability and convergence are required, and the memory usage and solution time can be reduced, so hexahedral mesh is used for sweeping; Figure 4 The figure shows how the moving mesh is coordinated when the piston moves. It can be seen that except for the hexahedrons obtained by the two sweeps in the hydraulic cylinder, which undergo mesh stretching and compression in the vertical direction, the remaining meshes do not change in shape. This method prevents the generation of extremely poor quality meshes when the mesh is deformed, and avoids non-convergence of calculations caused by poor mesh quality.

[0098] Step (3.7): When meshing the spiral tube, the present invention concludes that increasing the number of mesh sweeps can more accurately capture the bending characteristics of the spiral tube. Experimental data show that when the number of sweeps is increased from 2000 to 2500, the change in damping force is only 0.44%. Figure 5 As shown in the figure, this small increase shows that the accuracy improvement brought by the sweep number exceeding 2000 is negligible. Therefore, setting the sweep number above 2000 can ensure the accuracy of the simulation while avoiding unnecessary consumption of computing resources, achieving an optimal balance between efficiency and accuracy.

[0099] Step (3.8): After the fluid domain grid is divided, in order to confirm the influence of the increasing number of boundary layer grid layers on the simulation results, the damping force is used as a measurement indicator to gradually increase the number of boundary layer grid layers to confirm its influence on the calculation results; this patent concludes that the calculation cost increases by 7 times from 1 layer to 5 layers of boundaries, and the calculation accuracy only increases by 0.55%, so no boundary layer is selected.

[0100] Among them, the primary segmented linear motor in the electromagnetic domain of the electromagnetic inertial container is cylindrical in shape, 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 electromagnetic domain meshing in step (3) includes the following steps:

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

[0102] Step (3.2): Use a two-dimensional axisymmetric model for the electromagnetic domain to simplify the calculation of the primary segmented linear motor; significantly improve the computational efficiency, simplify the model setup and parameterization studies, and reduce 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): Sweep the mesh of the motor primary and magnetic poles, increase the mesh density in the key areas of the primary core teeth and yoke, 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 where the physical field gradient is large, and set a looser mesh where the gradient is small;

[0104] Step (3.4): In view of the possible displacement of the motor primary and magnetic poles during movement, a mapping boundary is set in the air gap. This technology can prevent the mesh of the left magnetic pole from being deformed, while allowing the mesh of the right motor primary to move along the Z axis as a whole, with only the quadrilateral mesh deforming along the Z axis.

[0105] Wherein, step (4): using COMSOL numerical simulation software, a transient simulation of the electromagnetic inertial vessel is performed; the simulation takes into account the piston motion of the hydraulic system and the current change of the electromagnetic system, as well as the interaction between them; 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] Among them, 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 linear motor has an external circuit that affects the electromagnetic force;

[0110] Step (4.3): Using electromagnetic force as a measure, change the size of the teeth and yoke of the primary core to explore its effect on the motor performance;

[0111] Step (4.4): Connect the outer ends of the linear motor to capacitors, inductors and resistors respectively, and analyze the influence of capacitors, inductors and resistors on the phase of the electromagnetic force by comparing the electromagnetic force output under different external circuit connection methods.

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

[0113] Step (5.1): From the simulation results of step (4.1), it can be found that the performance of the linear motor at different speeds, when the relative movement speed of the motor exceeds 0.3m / s, the motor coefficient decreases significantly. This phenomenon is attributed to the magnetic saturation phenomenon of the primary iron core of the motor when running at high speed, resulting in a decrease in magnetic permeability and the inability of the magnetic induction intensity to continue to increase, 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 in the absence of an external circuit, the electromagnetic force only manifests the motor thrust fluctuation caused by the cogging effect, and when the external circuit is connected, an electromagnetic force of about 55N is generated in the opposite direction of the movement;

[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. Too small yoke thickness will greatly limit the magnitude of the electromagnetic force. After reaching a certain limit, unlimited amplification 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;

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

[0117] Furthermore, if Figure 8 Figure 1 shows the comparison of the dynamometer diagram obtained from the ideal inertia element and the actual finite element model. Ideally, the dynamometer diagram should be a straight line, representing the relationship between the piston load and displacement. However, due to the presence of parasitic damping forces, the actual finite element model results form an area, the area of ​​which represents the energy dissipated due to parasitic damping during the piston movement.

[0118] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that may be made to certain parts thereof by technicians in this technical field all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A method for constructing a high-precision model of an electromagnetic inertial vessel and simulating and analyzing its dynamic performance, characterized in that: The following steps are involved: Step (1): Establish a mathematical model of the hydraulic system. In the hydraulic system, the calculation of the inertia coefficient follows the principles of conservation of volume and energy of the hydraulic cylinder. The expression of the inertia coefficient is derived through the formula; the inertia coefficient b can be expressed as: Among them, S1 and S2 are the cross-sectional areas of the hydraulic cylinder and the spiral tube respectively; r1 is the radius of the piston rod, r2 is the inner radius of the hydraulic cylinder, r3 is the inner radius of the spiral tube, r4 is the rotation radius of the spiral tube, h is the lead of the spiral tube, J is the moment of inertia of the fluid during flow, m is the mass of the fluid in the spiral tube, ρ is the density of the fluid, l is the length of the spiral tube, b is the inertia coefficient, θ is the angle of rotation of the fluid in the spiral tube, n is the number of turns of the spiral tube, is the linear velocity of the piston in the hydraulic cylinder, is the angular velocity of the fluid flowing in the spiral tube; Establish a 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 that describe the relationship between the electric field, magnetic field, charge density, and current density. It consists of the following equations: in, 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, and μ0 is the magnetic permeability; the equations include: Gauss's law, Gauss's magnetic field law, Faraday's induction law and Maxwell-Ampere's law; Step (2): fluid domain and electromagnetic domain parameter definition; Step (3): Meshing of fluid domain and electromagnetic domain; Step (4): using COMSOL numerical simulation software to perform transient simulation on the electromagnetic inertial vessel; the simulation takes into account the piston motion of the hydraulic system and the current change of the electromagnetic system, as well as the interaction between them; Step (5): Analyze the simulation results, including the comparison of the calculated results of damping force and inertial force with theoretical predictions, and the output characteristics of electromagnetic force.

2. The method for constructing a high-precision model and simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 1 is characterized in that: The fluid domain parameter definition in step (2) comprises 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 flow, transitional flow or turbulent flow; based on the judgment of the Reynolds number, 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: Among them, 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 in the hydraulic system, including the cross-sectional area of ​​the hydraulic cylinder, the cross-sectional area of ​​the spiral tube, the radius of the piston rod, the inner radius of the hydraulic cylinder, the inner radius of the spiral tube, the rotation radius of the spiral tube, and the lead of the spiral tube; Step (2.3): Consider the physical properties of the fluid medium.

3. The method for constructing a high-precision model and simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 2 is characterized in that: The electromagnetic domain parameter definition process in step (2) is as follows: Step (2.1): Accurately describe the dimensions and material properties of each component of the linear motor; Step (2.2): Define the material of the motor winding and the layout of the winding, including the number of turns and connection method of the winding; 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 simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 3 is characterized in that: The fluid domain meshing in step (3) comprises the following steps: Step (3.1): Use SolidWorks software to build a model of the fluid inertia container, then use Boolean operations in SolidWorks to extract the fluid domain model inside the fluid inertia container to form a complete hydraulic system geometry, and then import the obtained fluid domain model into Comsol software for subsequent model simulation; Step (3.2): Import the fluid domain model of Comsol and regard both ends of the oil-gas isolation piston as open boundaries to simplify the model and reduce the computational complexity; Step (3.3): Divide the fluid domain into three parts: piston, hydraulic main cylinder, and spiral tube, and mesh them separately. This can avoid mesh deformation and poor quality mesh when the piston moves, which makes it difficult for the model to converge. Step (3.4): For the piston part, in order to compensate for the volume change caused by the piston rod during movement, we set an open boundary; theoretically, 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 movement, it avoids dealing with the fluid-solid 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 grid movement, a relatively coarse tetrahedral grid is used for division; Step (3.5): For the connection between the hydraulic main cylinder and the spiral pipe, since the geometric shape is complex and does not have much impact on the simulation results, tetrahedral mesh is also used for division to reduce the complexity of calculation; Step (3.6): For the hydraulic main cylinder fluid domain and the spiral tube fluid domain, since the pressure and velocity of the liquid in them are mainly simulated with high precision, better mesh quality, better stability and convergence are required, and at the same time, memory usage and solution time can be reduced. Therefore, hexahedral meshes are used for sweeping. Except for the hexahedrons obtained by sweeping the two sections in the hydraulic cylinder, the meshes are stretched and compressed in the vertical direction, and the remaining meshes do not change in shape; Step (3.7): When meshing the spiral tube, increasing the number of distributions of the mesh sweep can more accurately capture the bending characteristics of the spiral tube; Step (3.8): After the fluid domain is meshed, in order to confirm the impact of increasing the number of boundary layer mesh layers on the simulation results, the damping force is used as a measurement indicator to gradually increase the number of boundary layer mesh layers to confirm its impact on the calculation results.

5. The method for constructing a high-precision model and simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 4 is characterized in that: The electromagnetic domain meshing in step (3) comprises the following steps: Step (3.1): Use SolidWorks software to build a model for the electromagnetic domain part, and import the obtained model into Comsol software for subsequent model simulation; Step (3.2): Use a two-dimensional axisymmetric model for the electromagnetic domain to simplify the calculation of the primary segmented linear motor; Step (3.3): Sweep the mesh of the motor primary and magnetic poles, increase the mesh density in the key areas of the primary core teeth and yoke, 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 where the physical field gradient is large, and set a looser mesh where the gradient is small; Step (3.4): In view of the possible displacement of the motor primary and magnetic poles during movement, a mapping boundary is set in the air gap. This technology can prevent the mesh of the left magnetic pole from being deformed, while allowing the mesh of the right motor primary to move along the Z axis as a whole, with only the quadrilateral mesh deforming along the Z axis.

6. The method for constructing a high-precision model and simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 5, characterized in that: The transient simulation in step (4) comprises the following steps: Step (4.1): Run the simulation to calculate the fluid pressure, velocity and stress distribution under different working conditions by: Among them, 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; Step (4.2): Connect a 10Ω resistor to the outer 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 measure, change the size of the teeth and yoke of the primary core to explore its effect on the motor performance; Step (4.4): Connect the outer ends of the linear motor to capacitors, inductors and resistors respectively, and analyze the influence of capacitors, inductors and resistors on the phase of the electromagnetic force by comparing the electromagnetic force output under different external circuit connection methods.

7. The method for constructing a high-precision model and simulating and analyzing dynamic performance of an electromagnetic inertial device according to claim 6 is characterized in that: Analyzing the simulation results in step (5) includes the following steps: Step (5.1): From the simulation results of step (4.1), it can be found that the performance of the linear motor at different speeds, when the relative movement speed of the motor exceeds 0.3m / s, the motor coefficient decreases significantly. This phenomenon is attributed to the magnetic saturation phenomenon of the primary iron core of the motor when running at high speed, resulting in a decrease in magnetic permeability and the inability of the magnetic induction intensity to continue to increase, thereby affecting the output performance of the motor; Step (5.2): From the simulation results of step (4.2), it can be seen that in the absence of an external circuit, the electromagnetic force only manifests the motor thrust fluctuation caused by the cogging effect, and when the external circuit is connected, an electromagnetic force of about 55N is generated in the opposite direction of the movement; 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. Too small yoke thickness will greatly limit the magnitude of the electromagnetic force. After reaching a certain limit, unlimited amplification 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; Step (5.4): From the simulation results of step (4.4), it can be obtained that when the external circuit is connected to a capacitor, the electromagnetic force produces an advanced phase; when the inductor is connected, a lagging phase is produced; when the resistor is connected, the phase remains consistent with the excitation, which proves that the electrical network can simulate the impedance of a complex mechanical network.

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