A simulation method for electromagnetic motion coupling with variable thickness air gap

Abstract

The present invention provides a method for electromagnetic motion coupling simulation of an air gap with variable thickness, comprising the following steps: inputting the air gap thickness that changes with time into an air gap shell unit; analyzing the electromagnetic field of a thin air gap with dynamic tension and compression; the analysis includes: electromagnetic field equations, circuit equations, motion equations, and the coupling relationship between the above equations. Based on the axisymmetric thin air gap shell unit, the present invention introduces a variable thickness parameter to realize the coupled simulation of transient circuit-electromagnetic field-motion based on the air gap shell unit. Compared with the traditional air gap meshing method, the modeling flexibility and calculation efficiency of the dynamic tension and compression air gap problem in equipment such as solenoid valves can be improved, and the difficulties encountered in the air gap meshing when the air gap is very thin can be avoided.

Description

Technical Field

[0001] The present invention relates to the technical field of coupled simulation, and more particularly, to an electromagnetic motion coupling simulation method with a variable-thickness air gap. Background Art

[0002] For a thin air gap surrounded by ferromagnetic materials, it can be assumed that the magnetic field in the air gap is parallel to the direction of the air gap thickness. That is, in the equation described based on the magnetic vector potential, the magnetic vector potential is a constant in the direction of the air gap thickness. Through the degradation of the air gap thickness, an air gap shell element with a thickness factor can be established [Nakata T, Ishihara Y, Takahashi N. Finite element analysis of magnetic fields by using gap element [C]. Proceedings of Compumag Conference, 1978, 5:7.][Nakata T, Takahashi N. 3D magnetic field analysis using special elements [J]. IEEE Transactions on Magnetics, 1990, 26(5):2379-2381.][Ren Z, Degenerated Whitney prism elements-general nodal and edge shell elements for field computation in thin structures [J]. IEEE Transactions on Magnetics, 1998, 34(5):2547–2550.]. The air gap shell element takes the air gap thickness as a mathematical parameter of the model. When the air gap thickness changes, there is no need to change the geometry and mesh of the model, which has high modeling convenience; since there is no need to divide the mesh too densely at the air gap, the amount of calculation is reduced, so it also has high calculation efficiency. In the problem of thin air gaps surrounded by ferromagnetic materials, the construction of two-dimensional plane and three-dimensional air gap shell elements has been reported in the literature [Kameari A. Improvement of ICCG convergence for thin elements in magnetic field analyses using the finite-element method [J]. IEEE Transactions on Magnetics, 2008, 44(6):1178–1181.]. The numerical performance of the incomplete Cholesky CG method for iterative solution of air gap shell elements has also been studied. In the construction of axisymmetric air gap shell elements, it is necessary to consider both the degradation of the air gap thickness and the magnetic field accuracy near the central axis at the same time. At present, there is little discussion in the literature on the construction of axisymmetric air gap shell elements based on the discretization of the magnetic vector potential.In dynamic simulation problems such as solenoid valves, the thickness of the air gap is related to the displacement of mechanical motion, and the mechanical motion is coupled with the electromagnetic field and the external circuit. Therefore, it is necessary to further study the problem of the thin air gap with dynamic tension and compression in the simulation of moving electromagnetic fields. Summary of the Invention

[0003] In view of the technical problem of errors in simulation caused by the fact that in dynamic simulation problems such as solenoid valves, the thickness of the air gap is related to the displacement of mechanical motion, and the mechanical motion is coupled with the electromagnetic field and the external circuit, a method for simulating electromagnetic motion coupling with a variable-thickness air gap is provided. A method for simulating electromagnetic motion coupling with a variable-thickness air gap according to the present invention includes the following steps:

[0004] Step S1: Input the air-gap thickness d that changes with time g into the air-gap shell element;

[0005] Step S2: Analyze the electromagnetic field with a dynamically tensioned and compressed thin air gap; the analysis includes: electromagnetic field equations, circuit equations, motion equations, and the coupling relationships between the above equations;

[0006] For the external circuit, assume that the voltages at nodes i and j at both ends of the circuit component are V i and V j , and the currents are I i and I j respectively; then for a resistor component with a resistance of R, the potential and current at both ends satisfy the following equation:

[0007]

[0008] For an inductor component with an inductance of L, the voltage and current at both ends satisfy the following equation:

[0009]

[0010] For a capacitor component with a capacitance of C, the voltage and current at both ends satisfy the following equation:

[0011]

[0012] For a voltage source with a voltage drop of U, the voltage at both ends satisfies the following equation:

[0013] V i -V j = U; (6)

[0014] When only considering the rigid-body translational motion of ferromagnetic components under the action of electromagnetic force and spring force, it is described by a single-degree-of-freedom motion equation as:

[0015]

[0016] Among them, m represents the total mass of the ferromagnetic component, represents the acceleration of motion of the ferromagnetic component, represents the velocity of motion, x represents the current position coordinate of the ferromagnetic component, and it is assumed that the motion range is x min ≤ x ≤ x max x 0 represents the initial position coordinate of the ferromagnetic component, λ represents the motion damping, F em represents the electromagnetic force, k s represents the spring stiffness coefficient;

[0017] The electromagnetic field equation in the winding coil region is:

[0018]

[0019]

[0020]

[0021] Among them, S c is the cross-sectional area of the coil, N c is the number of turns of the coil, Ω c is the coil region, E is the back electromotive force of the coil, R is the coil resistance, ΔV is the voltage drop of the coil, and I is the coil current. The static magnetic field equation is used to describe the non-winding coil region with an air gap.

[0022] Compared with the prior art, the present invention has the following advantages:

[0023] Based on the axisymmetric thin air gap shell element, the present invention introduces a variable thickness parameter to realize the coupled simulation of transient circuit - electromagnetic field - motion based on the air gap shell element. Compared with the traditional air gap mesh division method, it can improve the modeling flexibility and calculation efficiency of dynamic tension and compression air gap problems in devices such as solenoid valves, and avoid the difficulties encountered in air gap mesh division when the air gap is very thin. Description of the Drawings

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0025] Figure 1 This is the triangular prism unit of the present invention degenerated into a triangular shell element, where (a) is the edge unit of the triangular prism; (b) is the edge shell element of the triangle.

[0026] Figure 2For the present invention, the quadrangular prism unit degenerates into a quadrilateral shell element, where (a) is the edge element of the quadrangular prism; (b) is the edge shell element of the quadrilateral.

[0027] Figure 3 Schematic diagrams of the axisymmetric geometric model and the external circuit model of the brake body of the present invention, where (a) is the axisymmetric geometric model; (b) is the external circuit model.

[0028] Figure 4 Schematic diagram of the axisymmetric finite element model of the brake body of the present invention; where (a) is the modeling with mesh division of the air gap; (b) is the cross-region modeling of the shell with the air gap.

[0029] Figure 5 Schematic diagram of the comparison of the coil current and the back electromotive force time history of the present invention; where (a) is the comparison of the current time history; (b) is the comparison of the back electromotive force time history.

[0030] Figure 6 Schematic diagram of the comparison of the force on the spool valve and the displacement time history of the present invention; where (a) is the comparison of the electromagnetic force time history; (b) is the comparison of the displacement time history.

[0031] Figure 7 Schematic diagram of the overall process of the present invention. Detailed implementation manners

[0032] In order to enable those skilled in the art of the present technology to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0033] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order different from those illustrated or described here. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0034] Such as Figure 1-7As shown, the present invention provides an electromagnetic motion coupling simulation method with a variable-thickness air gap.

[0035] In dynamic simulation modeling, the air gap thickness that varies with time can be used as a variable parameter of the air gap shell element. For the air gap problem surrounded by ferromagnetic materials with high magnetic permeability, it is generally assumed that the air gap magnetic field is along the thickness direction of the air gap, so that the magnetic field energy functional at the air gap can be simplified. In the simplified magnetic field energy functional of the air gap, the integral along the thickness direction of the air gap becomes multiplying by the thickness factor.

[0036] In three-dimensional magnetic field analysis, Figure 1 (a) and Figure 2 (a) are respectively the triangular prism edge element ABC-DEF and the quadrangular prism edge element ABCD-EFGH. The unknown vector field in the air gap thickness direction is only tangential and remains unchanged. The integration of the element matrix only needs to be defined within the triangular edge shell element ABC and the quadrilateral edge shell element ABCD, as shown in Figure 1 (b) and Figure 2 (b).

[0037]

[0038] where i and j are the local edge numbers of the air gap shell element . is the edge shape function of the three-dimensional air gap shell element.

[0039] In axisymmetric magnetic field analysis, according to the magnetic field energy functional formula at the air gap, the coefficient matrix of the axisymmetric air gap shell element can be derived as:

[0040]

[0041] where i and j are the local node numbers of the air gap shell element , is the node shape function of the axisymmetric shell element.

[0042] The electromagnetic field analysis of the dynamic tensile and compressive thin air gap includes electromagnetic field equations, circuit equations, motion equations, and the coupling relationships between the equations.

[0043] The external circuit is a network composed of circuit components such as resistors and inductors. The electric potential at node i of the network is V i , and the current is I i . Suppose the voltages at nodes i and j at both ends of the circuit component are V i and V j respectively, and the currents are I i and I j respectively. For a resistor component with a resistance of R, the electric potential and current at both ends satisfy the following equation:

[0044]

[0045] For an inductor component with an inductance of L, the voltage and current at both ends satisfy the following equation:

[0046]

[0047] For a capacitor component with a capacitance of C, the voltage and current at both ends satisfy the following equation:

[0048]

[0049] For a voltage source with a voltage drop of U, the voltage at both ends satisfies the following equation:

[0050] V i -V j = U(6);

[0051] This section only considers the rigid body translational motion of the ferromagnetic component under the action of electromagnetic force and spring force, and it can be described by a single-degree-of-freedom motion equation:

[0052]

[0053] Among them, m is the total mass of the ferromagnetic component, is the motion acceleration of the ferromagnetic component, is the motion velocity, x is the current position coordinate of the ferromagnetic component, and the motion range is set as x min ≤ x ≤ x max , x0 is the initial position coordinate of the ferromagnetic component, λ is the motion damping, F em is the electromagnetic force, k s is the stiffness coefficient of the spring.

[0054] In the circuit - electromagnetic field - motion coupling analysis, the circuit is coupled with the winding coil in the electromagnetic field, and the electromagnetic field is coupled with the motion. In the electromagnetic field - circuit coupling, the voltage drop degree of freedom U of the electromagnetic field winding coil is coupled with the voltages V i and V j at both ends of the circuit connected to the coil, and the coupling equation is written as:

[0055] V i -V j = U(8);

[0056] In the electromagnetic field - motion coupling, there is a coupling relationship between the motion position x of the ferromagnetic component in the motion equation and the air gap thickness d g :

[0057] x + d g = x max (9);

[0058] Among them, xmax is the upper limit of the moving position coordinates of the ferromagnetic component. At the same time, the magnetic force F em received by the ferromagnetic component in the motion equation (7) is determined by the magnetic field distribution, that is, it has a coupling relationship with the air gap thickness d g d and the current magnitude I in the current coil.

[0059] The electromagnetic field equations for the coil regions in other areas are as follows:

[0060]

[0061]

[0062]

[0063] Among them, S c is the cross-sectional area of the coil, N c is the number of turns of the coil, Ω c is the coil region, E is the back electromotive force of the coil, R is the resistance of the coil, ΔV is the voltage drop of the coil, and I is the current of the coil. The non-twisted coil region with an air gap is described by the static magnetic field equation.

[0064] In three-dimensional analysis, the edge element is used to discretize the magnetic vector potential A, and the node element is used to discretize the voltage drop ΔV and the electromotive force E, and the finite element equation can be obtained:

[0065]

[0066] Among them, I i is the current discrete vector of the node, A j is the magnetic vector potential discretized by the edge, ΔV j is the voltage drop of the coil node, which is coupled with the external circuit, and E j is the electromotive force of the coil node. The expressions of D ij and H ij are the magnetic flux matrix and the conduction matrix respectively. The reluctance matrix K ij (|B|) is expressed as:

[0067]

[0068] Among them, is the solid element discrete matrix of the double curl operator in the non-air gap region, is the shell element discrete matrix of the double curl operator in the air gap region, where the thickness d g of the air gap shell element is a variable parameter, which is coupled with the object motion displacement in the motion equation.

[0069] In the axisymmetric analysis, a coordinate transformation auxiliary potential is introduced into the axisymmetric electromagnetic field equations. Meanwhile, an air-gap assumption is introduced and discretized using the finite element method. A finite element equation in the same form as Equation (13) can also be obtained. However, the unknown degrees of freedom of the magnetic field are not the magnetic vector potential A at the nodes, j , but the coordinate transformation auxiliary potential λ at the nodes j .

[0070] Figure 3 The axisymmetric geometric model and external circuit model of the brake body are shown as follows, Figure 4 which is the axisymmetric finite element model of the brake body. It is assumed that the magnetic flux leaking from the brake in this model is very small and negligible. Therefore, the peripheries of the yoke and armature are set as magnetic flux parallel boundaries. To perform dynamic simulation of the brake, a coupled analysis of circuit - electromagnetic field - rigid body motion needs to be established.

[0071] In Figure 3 (b)'s circuit model, the winding coil is part of the circuit, forming a loop with a 24V power supply and a voltage-controlled switch, and is connected in parallel with a freewheeling resistor with a resistance of 100Ω and a diode. The cross-sectional area of the winding coil is 2.0×10 -4 m 2 , the number of turns is 2548, the volume is 2.826×10-5m 3 , and the total resistance of the coil is 50Ω. The total simulation time of the field-circuit coupling model is 0.2s, and the time step is 5.0×10 -4 s. The first-order backward Euler method is used for the discretization format. The relative residual of the nonlinear iteration convergence is set to 1.0×10 -5 , and the maximum number of iteration steps is 30. The upper and lower limits of the movement position of the suction cup are 0m and -0.002m respectively. The mass of the suction cup is 0.025kg, and the spring stiffness coefficient is 1000N / m. The switch is closed at the beginning and opened at 0.1s. To control the movement grid deformation, a method based on solving the Laplacian equation is used to realize the movement of internal nodes.

[0072] The methods of mesh generation and air-gap shell element modeling and simulation are respectively used for the air gap between the armature and the yoke, as Figure 4 shown. Among them, the air-gap thickness of the air-gap shell element is a variable parameter, which has a coupling relationship with the movement displacement of the suction cup. To verify the simulation accuracy and efficiency of this section based on the air-gap shell element, the simulation results and time based on air-gap mesh generation are used as the comparison benchmark. The relative magnetic permeabilities of the armature and the yoke are set to 2000 and 1000 respectively.

[0073] Figure 5 The time histories of the coil current and back electromotive force are given, Figure 6The time history of the force and displacement of the valve core is given. It can be found that the results of the method of the present invention are in good agreement with those of the air-gap grid division method, thus verifying the accuracy of the method of the present invention. The calculation times of the simulation method based on the air-gap shell and the air-gap grid division method of the present invention are 2 min 12 s and 3 min 43 s respectively. It can be found that the method of the present invention saves about one-third of the calculation time of the air-gap grid division method and has a high calculation efficiency.

[0074] It can be found from the simulation results that the brake is initially in a stationary state. At the initial moment, the switch is closed. After the winding coil is excited by the voltage, a magnetic field is generated and drives the suction cup to move until the suction cup moves to the bottom and stops. Subsequently, at 0.1 s, the voltage stabilizing switch is turned off, and the branch where the freewheeling resistor and the diode are located forms a closed loop with the winding coil. The winding coil provides a voltage to generate a gradually decreasing current in the loop. Since the current decreases, the magnetic field in the brake weakens, and the suction force received by the suction cup also decreases, and the suction cup moves away.

[0075] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages and disadvantages of the embodiments.

[0076] In the above embodiments of the present invention, the descriptions of each embodiment have their own emphases. For the parts not detailed in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for simulating electromagnetic motion coupling with a variable thickness air gap, characterized in that: The steps include: S1: The air gap thickness d that changes with time g Input air gap shell element; S2: Analyze the electromagnetic field of the thin air gap with dynamic tension and compression; the analysis includes: electromagnetic field equations, circuit equations, motion equations, and coupling relationships between the above equations; For the external circuit, let the voltages at nodes i and j at both ends of the circuit component be V i and V j , the currents are I i and I j ; For a resistor component with a resistance of R, the voltage and current across the two ends satisfy the following equations: For an inductor component with an inductance of L, the voltage and current across the two ends satisfy the following equations: For an inductor component with capacitance C, the voltage and current across it satisfy the following equations: When only the rigid body translation motion of the ferromagnetic component under the action of electromagnetic force and spring force is considered, the single degree of freedom motion equation is described as: Where m is the total mass of the ferrous components, represents the acceleration of the ferrous component, represents the speed of movement, x represents the position of the ferrous component, and the range of movement is x min ≤x≤x max , x0 represents the initial position coordinate of the ferrous component, λ represents the motion damping, F em represents the electromagnetic force, k s Indicates the spring rate.

2. The electromagnetic motion coupling simulation method with variable thickness air gap according to claim 1, characterized in that: The coupling between the equations includes the coupling between the circuit and the electromagnetic field and the motion; during the coupling between the circuit and the electromagnetic field and the motion, the circuit is coupled with the twisted coil in the electromagnetic field, and the electromagnetic field is coupled with the motion; In the process of coupling between electromagnetic field and circuit, the voltage drop ΔV of electromagnetic field winding coil is related to the voltage of the coil. The voltage V across the circuit i and V j Coupling occurs, and the coupling equation is: V i -V j =ΔV; (5) In the coupling process of electromagnetic field and motion, the motion position x of the ferrous component in the motion equation is related to the air gap thickness d. g There is a coupling relationship between: x+d g =x max ;(6) Among them, x max is the upper limit of the coordinates of the motion position of the ferrous component; at the same time, the magnetic force F exerted on the ferrous component in the motion equation (7) is em Determined by the magnetic field distribution, that is, the air gap thickness d g There is a coupling relationship between the current I in the coil.

3. The electromagnetic motion coupling simulation method with variable thickness air gap according to claim 1, characterized in that: The analysis of the electromagnetic field containing the dynamic tensile and compressive thin air gap also includes the electromagnetic field of the twisted coil area; the equation of the electromagnetic field in the twisted coil area is: Where ν is the magnetic permeability, A is the magnetic vector potential, is the toroidal magnetic vector potential, S c Indicates the cross-sectional area of ​​the coil, N c Indicates the number of coil turns, Ω c represents the coil area, E represents the coil electromotive force, R represents the coil resistance, and I represents the coil current.

4. The electromagnetic motion coupling simulation method with variable thickness air gap according to claim 1, characterized in that: In the three-dimensional magnetic field analysis, the unknown vector field in the air gap thickness direction is only tangential and remains unchanged. The unit matrix The integral of only needs to be defined within the shell element: Where i and j represent air gap shell elements The local edge number of represents the edge shape function of the three-dimensional air gap shell element, x ′ and ′ Represents the local coordinate system defined on the shell element; At the same time, the magnetic vector potential A is discretized by edge element, and the voltage drop ΔV and electromotive force E of the electromagnetic field coil are discretized by node element, and the finite element equation can be obtained: Among them, I i A represents the discrete vector of the node current. j represents the magnetic vector potential of the edge discretization, ΔV j Represents the voltage drop at the coil node, which is coupled with the external circuit, E j Represents the electromotive force of the coil node; D ij and H ij The expressions of are flux matrix and conduction matrix respectively; magnetic resistance matrix K ij (|B|) is expressed as: in, The solid element discrete matrix representing the bi-curl operator in the non-gap region, The shell element discretization matrix representing the double curl operator in the air gap region, where the air gap thickness d g It is a variable parameter and is coupled with the object motion displacement in the motion equation.

5. The electromagnetic motion coupling simulation method with variable thickness air gap according to claim 1, characterized in that: In the axisymmetric magnetic field analysis, the axisymmetric air gap shell element matrix is ​​derived based on the magnetic field energy functional at the air gap: for: Where i and j represent air gap shell elements The local node number of Represents the nodal shape functions of axisymmetric shell elements; At the same time, the coordinate transformation auxiliary potential is introduced into the axisymmetric electromagnetic field equation, and the air gap assumption is introduced. The finite element method is used for discretization to obtain a finite element equation consistent with the form of equation (11), but the unknown degree of freedom of the magnetic field is the coordinate transformation auxiliary potential λ at the node j .

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