Generalized magnetic network model building method of magnetic force lifting type CRDM

Abstract

The invention relates to the technical field of magnetic force lifting type control rod drive mechanisms (CRDM), and particularly discloses a generalized magnetic network model establishment method of a magnetic force lifting type CRDM, which comprises the following steps: acquiring a sectional view of the magnetic force lifting type CRDM, acquiring a solution boundary of an electromagnetic valve in any one of a lifting unit, a moving unit and a holding unit, and vertex coordinates of each magnetic conductive component, and establishing a generalized magnetic network model of the magnetic force lifting type CRDM; obtaining a geometric model diagram; dividing the geometric model diagram into a fixed area and a moving area according to whether the geometric model diagram moves or not, and subdividing the fixed area and the moving area by adopting orthogonal grid lines to obtain a grid subdivision diagram; and calculating the magnetic resistance of each grid unit in the fixed area and the moving area according to the size data and the material attribute of each grid unit in the grid subdivision diagram, and connecting the magnetic resistance of the adjacent grid units to obtain a generalized magnetic network model. During dynamic change, only the size or position of the grid of the motion area needs to be adjusted, redundant modeling is avoided, and fewer computing resources and shorter computing time are needed under the condition that the computing precision is guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic lifting type control rod drive mechanisms (CRDMs), and particularly to a method for establishing a generalized magnetic network model of magnetic lifting type CRDMs. Background Art

[0002] In commercial nuclear power plants, the control rod drive mechanism (CRDM) is a key actuator for reactor power regulation and system protection, and is classified as a safety class I equipment. According to different driving methods, CRDMs can be divided into rotary motor driven type, magnetic lifting type (ML-CRDM), hydraulic driven type, and linear motor driven type. Among them, the magnetic lifting type CRDM is widely used in third-generation pressurized water reactor nuclear power plants due to its advantages such as simple structure, high reliability, and large lifting force. However, failures of the magnetic lifting type CRDM will cause serious impacts, including unplanned reactor shutdowns, power reduction, economic losses, and psychological burdens on maintenance personnel.

[0003] The excitation unit of the magnetic lifting type CRDM is similar to a special solenoid valve mechanism. It completes actions such as the attraction and release of the armature by energizing and demagnetizing the coil. However, its structure, electromagnetic characteristics, and dynamic characteristics are different from those of traditional solenoid valve mechanisms. First, the air gap is relatively large (15.875 mm), and the internal magnetic leakage is serious. Second, it works in an environment of high temperature, high pressure, and strong radiation for a long time. To ensure operation safety and reliability, the current flowing through the coil is relatively large (40 A), resulting in serious magnetic saturation. At the same time, the moving parts are immersed in the primary loop cooling water for a long time, and their movement process is affected by electromagnetic force, spring force, water resistance, friction force, etc., and has characteristics such as nonlinearity and time-variation. Therefore, the research conclusions of traditional solenoid valve mechanisms are difficult to apply to magnetic lifting type CRDMs. Summary of the Invention

[0004] The present invention provides a method for establishing a generalized magnetic network model of magnetic lifting type CRDMs, and the technical problem to be solved is that: the dynamic process of magnetic lifting type CRDMs is complex due to the cross-coupling among current response, magnetic circuit saturation, and motion state, and it is difficult to predict. The research conclusions of traditional solenoid valve mechanisms are difficult to apply to magnetic lifting type CRDMs.

[0005] To solve the above technical problems, the present invention provides a method for establishing a generalized magnetic network model of magnetic lifting type CRDMs, including the steps of:

[0006] S1. Obtain the cross-sectional view of the magnetic lifting type CRDM, and obtain the solution boundary of the solenoid valve and the vertex coordinates of each magnetic conductive component in any one of the lifting unit, moving unit, and holding unit to obtain a geometric model diagram;

[0007] S2. Divide the geometric model diagram into upper and lower fixed areas and moving areas according to whether the model is in motion, and use orthogonal grid lines to divide the fixed area and the moving area to obtain a grid division diagram;

[0008] S3. Calculate the magnetic resistance of each grid cell in the fixed area and the moving area based on the size data and material properties of each grid cell in the grid segmentation diagram, and connect the magnetic resistances of adjacent grid cells to obtain a generalized magnetic network model.

[0009] Furthermore, in step S2, the fixed area and the moving area are divided by orthogonal grid lines to obtain a grid division diagram, specifically:

[0010] The vertical and horizontal grid lines are generated simultaneously through the vertex coordinates of each magnetic component. The horizontal grid lines run through the entire solution area, and the vertical grid lines terminate at the boundary between the fixed area and the moving area.

[0011] Vertical and horizontal grid lines are inserted between the current grid lines of the fixed area and the moving area respectively, and the rectangular grid containing more than two media is converted into a single medium grid to obtain a grid subdivision diagram.

[0012] Furthermore, in step S3, each grid unit has two axial magnetic resistances R zl , R zr and the upper and lower radial magnetic resistances R ru , R rd , according to the size data and material properties of each grid cell, the axial reluctance is integrated along the axial flux path, and the radial reluctance is integrated along the radial flux path.

[0013] Furthermore, in step S3, for the grid cells that are completely aligned above and below the regional boundary line, the magnetic resistances of adjacent grid cells are directly connected; for the grid cells that are not completely aligned above and below the regional boundary line and overlap, a connection relationship between the geometric centers of the grid cells is established, and the branch magnetic resistance between the two overlapping geometric centers is calculated based on the proportion of overlap between the upper and lower grid cells.

[0014] Furthermore, when the magnetic conductive component in the moving area moves, while keeping the total number of grids unchanged, only the grid sizes of the air gap area and the end air area at both ends of the magnetic conductive component are adjusted, and at the same time, the grid position of the middle area where the magnetic conductive component is located is updated, and the connection relationship between the geometric centers of the upper and lower grid units on the area boundary line is re-determined, and the magnetic resistance is recalculated.

[0015] Further, in the case of performing parametric calculations or dynamic process calculations by repeatedly calling the generalized magnetic network model, the iterative value calculated in the previous working condition is used as the initial iterative value for the next working condition; the initial iterative values for the initial working condition are the magnetic permeability or magnetic flux density and the corresponding magnetic field strength, all of which are selected from the linear section, transition section, and saturation section of the B-H curve of each magnetic conductive component.

[0016] Further, according to the relationship between the number of grids and the calculation accuracy and calculation time, the number of grids that meets the requirements of calculation accuracy and calculation time is determined.

[0017] Further, the lifting solenoid valve equipped with the lifting unit is composed of a lifting yoke, a lifting magnetic pole, a lifting coil, a lifting armature, and a lifting magnetic conductive ring; the moving solenoid valve equipped with the moving unit is composed of a moving yoke, a moving coil, a moving armature, a moving magnetic conductive ring, a moving claw, and a moving connecting rod; the holding solenoid valve equipped with the holding unit is composed of a holding yoke, a holding magnetic pole, a holding coil, a holding armature, a holding magnetic conductive ring, a holding claw, and a holding connecting rod.

[0018] The method for establishing the generalized magnetic network model of the magnetic force lifting type CRDM provided by the present invention is as follows: First, obtain the cross-sectional view of the magnetic force lifting type CRDM, and obtain the solution boundary of the solenoid valve and the vertex coordinates of each magnetic conductive component in any one of its lifting unit, moving unit, and holding unit to obtain a geometric model diagram; then, divide the geometric model diagram into a fixed area and a moving area according to whether it moves, and use orthogonal grid lines to divide the fixed area and the moving area to obtain a grid division diagram; finally, according to the size data and material properties of each grid unit in the grid division diagram, calculate the magnetic resistance of each grid unit in the fixed area and the moving area, and connect the magnetic resistances of adjacent grid units to obtain a generalized magnetic network model. Aiming at the misalignment problem between the fixed grid unit and the moving grid unit, establish its connection relationship and the calculation method of the branch magnetic resistance to realize the continuous movement of the armature. The present invention uses orthogonal grid lines to divide the grids of each area of the CRDM, thereby unifying the magnetic resistance calculation formula and realizing the rapid modeling of the GEMN. When dynamically changing, only need to adjust the grid size or position of the moving area, avoiding redundant modeling and reducing the calculation error caused by grid differences. Under the condition of ensuring the calculation accuracy, less computing resources and shorter calculation time are required. Description of the Drawings

[0019] Figure 1 is a schematic cross-sectional view of the magnetic force lifting type CRDM provided by the embodiment of the present invention;

[0020] Figure 2 is a geometric model diagram of the lifting unit provided by the embodiment of the present invention;

[0021] Figure 3 is a schematic diagram of the magnetic resistance equivalence of a rectangular grid in a cylindrical coordinate system provided by the embodiment of the present invention;

[0022] Figure 4 It is the mesh division diagram of the solenoid valve provided by the embodiment of the present invention;

[0023] Figure 5 It is the comparison diagram of mesh units before and after the conversion of the rectangular mesh of the mixed medium provided by the embodiment of the present invention;

[0024] Figure 6 It is the relationship diagram between the coordinates of the grid lines and the grid cell indices provided by the embodiment of the present invention;

[0025] Figure 7 It is the initial GEMN model of the local area of the solenoid valve provided by the embodiment of the present invention;

[0026] Figure 8 It is the connection relationship diagram between the upper and lower nodes of the regional boundary line provided by the embodiment of the present invention;

[0027] Figure 9 It is the variation relationship diagram of the branch reluctance provided by the embodiment of the present invention;

[0028] Figure 10 It is the mesh change diagram of the lifting armature before and after movement provided by the embodiment of the present invention;

[0029] Figure 11 It is the spatial distribution diagram of the magnetomotive force provided by the embodiment of the present invention;

[0030] Figure 12 It is the schematic diagram for calculating the electromagnetic lifting force provided by the embodiment of the present invention;

[0031] Figure 13 It is the convergence situation diagram of different combinations at all test points provided by the embodiment of the present invention;

[0032] Figure 14 It is the average number of iterations diagram of different combinations at all test points provided by the embodiment of the present invention;

[0033] Figure 15 It is the calculation flow chart based on variable iteration initial values provided by the embodiment of the present invention;

[0034] Figure 16 It is the convergence analysis diagram of the GEMN model provided by the embodiment of the present invention;

[0035] Figure 17 It is the relationship diagram between the number of meshes, calculation accuracy, and calculation time provided by the embodiment of the present invention;

[0036] Figure 18 It is the magnetic density distribution nephogram of the solenoid valve under FEA and GEMN provided by the embodiment of the present invention;

[0037] Figure 19 It is a diagram showing the calculation results of the coil inductance under FEA and GEMN provided by an embodiment of the present invention;

[0038] Figure 20 It is a distribution diagram of electromagnetic force under different current and air gap conditions under FEA and GEMN provided by an embodiment of the present invention. Specific Embodiments

[0039] The following specifically illustrates the embodiments of the present invention in conjunction with the accompanying drawings. The given embodiments are only for illustrative purposes and should not be construed as limiting the present invention. The accompanying drawings are only for reference and illustration, and do not constitute a limitation on the scope of patent protection of the present invention, because many changes can be made to the present invention without departing from the spirit and scope of the present invention.

[0040] The method for establishing a generalized magnetic network model of a magnetic force-lifting type CRDM provided by an embodiment of the present invention specifically includes the following steps:

[0041] S1. Obtain the cross-sectional view of the magnetic force-lifting type CRDM, and obtain the solution boundary of the solenoid valve and the vertex coordinates of each magnetic conductive component in any one of the lifting unit, moving unit, and holding unit, so as to obtain a geometric model diagram;

[0042] S2. Divide the geometric model diagram into a fixed area and a moving area according to whether it moves, and use orthogonal grid lines to divide the fixed area and the moving area to obtain a grid division diagram;

[0043] S3. Calculate the magnetic resistance of each grid unit in the fixed area and the moving area according to the size data and material properties of each grid unit in the grid division diagram, and connect the magnetic resistances of adjacent grid units to obtain a generalized magnetic network model.

[0044] (1) Step S1: Construct a geometric model

[0045] In step S1, Figure 1 It is a schematic cross-sectional view of the magnetic force-lifting type CRDM. As Figure 1As shown, the magnetic-levitation type CRDM has a columnar structure, which successively includes a coil assembly, a pressure-resistant shell assembly, a claw assembly, and a drive rod assembly from outside to inside. The coordinate axes "r" and "z" represent the radial direction and the axial direction respectively. According to the structural similarity, the magnetic-levitation type CRDM can be divided into three units: the upper, middle, and lower units, which are named the lifting unit, the moving unit, and the holding unit respectively. Each unit is equipped with a solenoid valve. The lifting solenoid valve equipped in the lifting unit consists of a lifting yoke, a lifting magnetic pole, a lifting coil, a lifting armature, and a lifting magnetic conductive ring; the moving solenoid valve equipped in the moving unit consists of a moving yoke, a moving coil, a moving armature, a moving magnetic conductive ring, a moving claw, and a moving connecting rod; the holding solenoid valve equipped in the holding unit consists of a holding yoke, a holding magnetic pole, a holding coil, a holding armature, a holding magnetic conductive ring, a holding claw, and a holding connecting rod. Due to limited space, the moving yoke and the moving magnetic conductive ring of the moving unit, and the holding yoke and the holding magnetic conductive ring of the holding unit are not shown in Figure 1 . The connecting rod in the moving unit and the holding unit is combined with the claw to form a crank-slider mechanism. The function of the solenoid valve is to realize the attraction or release between the armature and the magnetic pole, and the crank-slider mechanism converts the linear motion of the armature into the inner and outer swing of the claw to realize the engagement and separation of the claw and the annular groove of the drive rod. It should be particularly noted that in order to realize actions such as lifting or inserting the drive rod into the core, these solenoid valves need to be energized and de-energized in a certain order.

[0046] In step S1, in order to simplify the analysis model, the following reasonable assumptions are made in this paper:

[0047] 1) The magnetic coupling effect between the three solenoid valve mechanisms is ignored;

[0048] 2) The minor structural changes caused by the process are ignored;

[0049] 3) The magnetic hysteresis effect of the magnetic conductive material is ignored;

[0050] 4) The magnetic permeability of non-magnetic materials is regarded as the vacuum magnetic permeability. For example, in the lifting solenoid valve mechanism, only the lifting magnetic conductive ring, the lifting yoke, the lifting coil, the lifting armature, and the lifting magnetic pole are magnetic conductive materials, and the others are non-magnetic materials.

[0051] Taking the lifting unit as an example, the geometric model diagram of the lifting unit obtained after step S1 is as shown in Figure 2 . Since the lifting solenoid valve is a symmetric structure, Figure 2 only half of it is shown. The solution boundary here is a rectangular area containing the lifting solenoid valve, and the undefined part is defaulted to the air domain.

[0052] (2) Step S2: Mesh generation

[0053] The equivalent magnetic network (EMN) model based on a magnetic resistance grid does not rely on the magnetic flux distribution for modeling and is more convenient. Common magnetic resistance grid shapes include rectangular grids, diamond grids, pentagonal grids, hexagonal grids, etc. However, diamond grids, pentagonal grids, and hexagonal grids are prone to deformation during the meshing process, making it difficult to unify the magnetic resistance calculation formula. In contrast, the rectangular grid has a stable shape, and its size can be freely stretched or compressed, facilitating the unified calculation of magnetic resistance and the adaptive meshing of the grid. In addition, the rectangular grid can directly obtain the radial and axial electromagnetic components in the local area, and it is easier to calculate the electromagnetic lifting force using the tensor method. Therefore, this paper uses a rectangular grid to establish a generalized equivalent magnetic network (GEMN) model.

[0054] Figure 3 Figure 4 shows the magnetic resistance equivalent schematic diagram of a rectangular grid in the cylindrical coordinate system. In Figure 3 , the geometric center of the rectangular grid is defined as a node. There are four magnetic resistances (the left and right axial magnetic resistances R zl , R zr and the upper and lower radial magnetic resistances R ru , R rd ) extending from this node to the four boundaries of the rectangular grid. Each magnetic resistance needs to be calculated according to the direction of the magnetic flux flowing through it, that is, the axial magnetic resistance is integrated along the axial magnetic flux path, and the radial magnetic resistance is integrated along the radial magnetic flux path.

[0055] According to the magnetic flux tube principle, Figure 3 the magnetic resistance calculation formulas in

[0056]

[0057] are as follows: ru , R rd , R zl and R zr represent the upper, lower, left, and right magnetic resistances respectively; μ represents the magnetic permeability; l z is the axial length of the rectangular grid unit; r o and r i are the outer radius and inner radius of the rectangular grid unit respectively. It should be noted that the calculation formulas for the upper and lower magnetic resistances are different due to different integration upper and lower limits.

[0058] Figure 4Shows a sectional view of the lifting solenoid valve. To generate rectangular grid cells, orthogonal grid lines are used in this paper to quickly section the lifting solenoid valve. Before sectioning, the solution domain is divided into upper and lower regions: the region above the dividing line is the fixed region, and the region below the dividing line is the moving region. The fixed region includes the lifting yoke, the lifting magnetic conductive ring, and the lifting coil; the moving region includes the lifting pole and the lifting armature. The fixed region and the moving region are sectioned independently to improve the flexibility of sectioning.

[0059] The sectioning process is divided into two steps: (1) Coarse sectioning. By the vertex coordinates of each magnetic conductive component, vertical and horizontal grid lines are generated simultaneously. The horizontal grid lines run through the entire solution region, and the vertical grid lines terminate at the region dividing line. The purpose of coarse sectioning is to align the grid lines with the material boundary to ensure that each rectangular grid contains only one medium. (2) Fine sectioning. On the basis of coarse sectioning, more vertical and horizontal grid lines are inserted between the current grid lines in the fixed region and the moving region to densify the grid. It should be noted that the number and position of the inserted grid lines determine the grid discretization degree of the GEMN model in the local region. Usually, to balance the calculation time and calculation accuracy, the region around the air gap is sectioned more densely, while other regions are sectioned more coarsely.

[0060] As can be seen from Figure 4 it, the rectangular grids on the hypotenuse of the lifting yoke contain more than two media (such grids are called rectangular grids with mixed media), which increases the complexity of magnetic resistance calculation. To solve this problem, this paper follows the principle of higher medium proportion and converts the rectangular grids containing two or more media into single-medium grids. The comparison of the grid cells before and after conversion is as Figure 5 shown. It can be seen that the inclined boundary of the lifting yoke is equivalent to a stepped boundary. Although this processing method may reduce the modeling accuracy of the hypotenuse, the error can be reduced by densifying the grid lines on the hypotenuse.

[0061] (3) Step S3: Calculate the magnetic resistance and construct the generalized magnetic network model

[0062] Assume that the fixed region and the moving region are divided into grid cells with p rows and q columns and m rows and n columns respectively. Use (i, j) to represent the grid cell in the i-th row and the j-th column. Taking the fixed region as an example, the relationship between the coordinates of the grid lines and the grid cell indices is as Figure 6 shown. Among them, r and z respectively represent the radial coordinate value of the horizontal grid line and the axial coordinate value of the vertical grid line, with the subscripts starting from 0, and there are p + 1 horizontal grid lines and q + 1 vertical grid lines in total.

[0063] After obtaining the size data and material properties of each grid cell, the four magnetic resistances of each grid cell in the fixed region and the moving region can be calculated respectively using equations (1)-(3):

[0064]

[0065] In the formula, (*) can be optionally filled with "sta" or "mov" to represent the fixed area or the moving area respectively; μ ru , μ rd , μ zl and μ zr respectively represent the upper, lower, left, and right permeabilities. Since this article unifies the magnetic resistance calculation formula for all grid cells, the magnetic resistance of all grids can be calculated by matrix operation through formula (4), thereby improving the calculation speed.

[0066] Based on the magnetic resistance equivalent method of rectangular grid cells, by connecting the magnetic resistances of adjacent grid cells, an initial GEMN model of the lifting solenoid valve can be constructed. Figure 7 shows the initial GEMN model of the local area of the lifting solenoid valve. From Figure 7 it can be seen that in the fixed area or the moving area, the branch between the nodes of two adjacent grid cells is connected by two magnetic resistances. For any node (i, j), its branch magnetic resistance can be expressed as:

[0067]

[0068] In the formula, R bu , R bd , R bl and R br respectively represent the upper, lower, left, and right branch magnetic resistances of the node.

[0069] It can be known from formula (5) that usually, the branch magnetic resistance is the algebraic sum of all magnetic resistances between two adjacent nodes. However, from Figure 7 it can be seen that due to the different grid divisions in the fixed area and the moving area, the grid cells above and below the regional boundary line cannot be completely aligned, so that the branch magnetic resistance between its upper and lower nodes cannot be calculated by formula (5). In this article, for the grid cells that cannot be completely aligned above and below the regional boundary line in the initial generalized magnetic network model, the connection relationship between their nodes is established, and the branch magnetic resistance between the two overlapping nodes is calculated according to the overlapping ratio between the upper and lower grid cells, and the final generalized magnetic network model is obtained.

[0070] Specifically, this article establishes the connection relationship between the nodes above and below the regional boundary line, as shown in Figure 8 . Figure 8 In, the node (1, j') in the moving area overlaps with the nodes (p, j) and (p, j + 1) in the fixed area, and R bc (j, j') represents the branch magnetic resistance between the node (p, j) and the node (1, j'), and the numbering of other branch magnetic resistances follows this analogy. The branch magnetic resistance R bc (j, j') is calculated according to the overlapping ratio between the upper and lower grids. The specific formula is as follows:

[0071]

[0072] Figure 9 The variation relationship of the branch reluctance is shown. It can be seen that the branch reluctance shows a "U"-shaped variation trend. Specifically, the smaller the overlap degree between the grid units in the moving area and the fixed area, the larger the branch reluctance; on the contrary, the larger the overlap degree, the smaller the branch reluctance. When the grid units do not overlap, the branch reluctance tends to infinity.

[0073] As Figure 10 shown, when the magnetic conductive component (lifting armature) in the moving area moves, such as being attracted, the grid units in the air gap area are compressed, and the grid units in the end air area are stretched. To realize the dynamic change of the GEMN model, in this paper, on the premise of keeping the total number of grids unchanged, only the grid sizes in the air gap area and the end air area are adjusted, and at the same time, the grid positions in the lifting armature area are updated to realize the continuous movement of the lifting armature. After the grid units are updated, the magnetic resistance connection relationship between the fixed area and the moving area remains unchanged, and only the connection relationship between the upper and lower nodes on the regional boundary line needs to be re-determined according to Equation (6). This method avoids redundant modeling to the greatest extent and reduces the calculation error caused by grid meshing differences.

[0074] The excitation source of the ML-CRDM comes from the energization of the coil. Since the number of turns of the lifting coil is large and its distribution in the axial direction is long, considering the spatial distribution effect of the coil, the lifting coil area is divided into multiple sub-areas in the axial direction in this paper. Then, the magnetomotive force generated by the lifting coil in each sub-area is radially projected onto the lifting yoke. As Figure 11 shown, it is assumed that the lifting yoke area in the radial direction of the lifting coil is divided into u rows and h columns of grid units. The dividing line of the lifting coil is located exactly in the middle of two adjacent vertical grid lines and divides the lifting coil area into h + 1 sub-areas. Assuming that the coil current direction is perpendicular to the paper surface and outward, according to the right-hand screw rule, the magnetic flux generated by the coil axially passes through the yoke area, so the magnetomotive force is axially placed in the middle of two adjacent grid units to form the branch magnetomotive force.

[0075] From Figure 11 it can be seen that except for the nodes at both ends, there are magnetomotive forces on the left and right branches of other nodes, and the magnetomotive force on the right branch of the left node is equal in magnitude and opposite in direction to the magnetomotive force on the left of the right node. Therefore, the branch magnetomotive force of the above nodes can be expressed as:

[0076]

[0077] Among them, F mmf_br and F mmf_blThey respectively represent the magnetomotive force of the right branch and the left branch of the node. y is the number of grid cell columns outside the left end face of the coil, N1 is the number of turns of the lifting unit coil, and I1 is the current of the lifting unit coil. Among them, u, y, and h can all be determined through the geometric coordinates of the coil.

[0078] Applying Gauss's law of magnetism to the node magnetic potential analysis, the general form of its node equation can be obtained:

[0079]

[0080] In the formula, U m_(i,j) represents the magnetic potential of node (i, j); this parameter is the variable to be solved. G m_bu , G m_bd , G m_bl , G m_br respectively represent the magnetic conductances of the upper, lower, left, and right branches of the node, which are the reciprocals of the magnetic resistances of the upper, lower, left, and right branches respectively. φ m_bu , φ m_bd , φ m_bl , φ m_br respectively represent the magnetic flux sources of the upper, lower, left, and right branches of the node.

[0081] Based on the basic form of the node equation in Equation (9), the system matrix equation of all nodes in the GEMN model is:

[0082]

[0083] In the formula, and respectively represent the node magnetic potential vectors with dimensions of [pq×1] and [mn×1], which are the vectors to be solved; and respectively represent the node magnetic conductance submatrices with dimensions of [pq×pq] and [mn×mn] in the fixed area and the moving area; represents the coupling magnetic conductance submatrix with a dimension of [pq×mn] between the fixed area and the moving area; and respectively represent the magnetic flux source vectors with dimensions of [pq×1] and [mn×1].

[0084] The arrangement order of the nodes in the vector follows row first and column second. Therefore, for any node (i, j), the serial number P (i,j) in the vector is:

[0085]

[0086] The calculation method of the magnetic flux source of node (i, j) is as follows:

[0087]

[0088] In the formula, b is the node connected to the node (i, j); respectively represent the magnetomotive force of the right branch and the magnetomotive force of the left branch between the node (i, j) and the node b, and R m_br , R m_bl respectively represent the magnetic resistance of the right branch and the magnetic resistance of the left branch between the node (i, j) and the node b. There is magnetomotive force only in some branches, and the magnetomotive force of the remaining branches is 0. The calculation method of the elements in G m is as follows:

[0089]

[0090] The number of non-zero elements in the magnetic conductance matrix is much smaller than the number of zero elements. Therefore, in the process of constructing the magnetic conductance matrix, using a sparse matrix to store the magnitude and position of non-zero elements can greatly reduce the storage space and improve the matrix operation speed.

[0091] After obtaining the magnetic flux source vector and the node magnetic permeability matrix, the magnetic potential of each node can be obtained by using Equation (12). On this basis, the branch magnetic flux and magnetic flux density can be further calculated:

[0092]

[0093] In the formula, φ (i,j),b is the magnetic flux between the node (i, j) and the node b; U (i,j) and U b are the magnetic potentials of the node (i, j) and the node b respectively; B (i,j),b is the magnetic flux density between the node (i, j) and the node b; S (i,j),b is the magnetic flux area between the node (i, j) and the node b.

[0094] According to the definition of inductance, the coil inductance L 11 is equal to the magnetic flux generated by the coil energization divided by the energization current I1:

[0095]

[0096] In the formula, is the branch magnetic flux with magnetomotive force; is the number of turns of the coil corresponding to the magnetomotive force.

[0097] Generally, the calculation methods of electromagnetic lifting force mainly include the Maxwell stress tensor method and the energy virtual displacement method. In this paper, through GEMN calculation, the axial component and the radial component of the magnetic flux density in the air gap can be known. Therefore, the Maxwell stress tensor method is used to calculate the electromagnetic lifting force received by the lifting armature. As shown in the schematic diagram of the electromagnetic lifting force calculation in Figure 12 , the integration domain is defined as a closed frame containing the lifting armature, and the electromagnetic lifting force is accurately calculated through numerical integration:

[0098]

[0099] where B r and B z respectively represent the radial magnetic flux density and the axial magnetic flux density on the outer surface of the lifting armature.

[0100] For the GEMN model proposed in this paper, due to the small number of grids, the calculation time is usually not a problem that needs to be focused on. However, for the GEMN model proposed in this paper, due to the significant increase in the number of grids, the calculation time is correspondingly extended. In this case, the calculation efficiency of the GEMN model needs to be further optimized to avoid the loss of its advantages.

[0101] Based on the solver adopted in this paper, this paper studies two influencing factors, namely the initial iteration value and the number of grids, respectively, to improve the calculation efficiency of the GEMN model. When studying each influencing factor, the other two factors remain unchanged. The working conditions of the convergence test are set as follows: the current of the lifting coil is 40 A, the working air gap length of the lifting unit gradually increases from 0 mm to 15.875 mm, and one test point is set every 1 mm, with a total of 27 test points.

[0102] (1) Optimization of the initial iteration value

[0103] According to different change trends, the B-H curve is roughly divided into three segments: 1) linear segment; 2) transition segment; 3) saturation segment. In the research of this paper, the initial iteration value is the magnetic permeability (or magnetic flux density and the corresponding magnetic field strength), and they are all selected from the linear segment, transition segment and saturation segment of the B-H curve. Therefore, three magnetic conductive materials correspond to three initial values, and 27 combination methods can be formed. The specific values of each magnetic conductive material on the B-H curve are partially listed in Table 1.

[0104] Table 1 Settings of the initial iteration values of each material

[0105]

[0106] The convergence tests are respectively carried out on the above 27 combination methods, and the results are as Figure 13 shown. The results show that at all test points, the number of iterations of the vast majority of combinations is concentrated between 11 and 16 times. However, the number of iterations of some combinations reaches 30 times at some test points, showing a non-convergent situation. To more intuitively display the convergence of each combination, Figure 14 the average number of iterations of different combinations at all test points is statistically calculated, and the non-convergent combinations are shown as missing data. From Figure 14As can be seen, among the 27 combinations, the average number of iterations for 6 combinations is 15 times, the average number of iterations for 9 combinations is 14 times, the average number of iterations for 3 combinations is 13 times respectively, and the other 6 combinations show non-convergence. It is worth noting that among the 3 combinations with the least average number of iterations, the initial value of the yoke is selected from the linear segment, the initial values of the pole and the armature are selected from the saturation segment, and the initial value of the magnetic conductive ring can be arbitrarily selected from the linear segment, the transition segment or the saturation segment. This law is highly consistent with the magnetic flux density distribution of the ML-CRDM. Therefore, the selection of the iteration initial value should be as consistent as possible with the magnetic flux density distribution law of the ML-CRDM.

[0107] Based on the above analysis results, this paper proposes an improved calculation method for variable iteration initial values. This method is applicable to occasions where the GEMN model is called multiple times for parametric calculation or dynamic process calculation. Its core idea is to utilize the similarity of the magnetic flux density distribution law under adjacent working conditions, and use the magnetic flux density value calculated in the previous working condition and the corresponding iteration values such as magnetic field intensity as the iteration initial value of the next working condition, so as to improve the iteration efficiency of the GEMN model. The specific calculation process of this method is as Figure 15 shown. During the whole calculation process, only the iteration initial value needs to be set for the initial working condition, and the iteration initial value of the subsequent working conditions is automatically generated by the calculation results of the previous working condition. It should be emphasized that the number of grids between two working conditions should remain unchanged, because the change of the number of grids will cause the change of the number of initial values, and this calculation method will no longer be applicable.

[0108] To verify the effectiveness of the proposed improved method, this paper compares the convergence of the GEMN model under the initial working condition (lifting coil current 40A, lifting working air gap 0mm) and the next working condition (lifting coil current 40A, lifting working air gap 1mm), and the results are as Figure 16 shown. It can be seen that the calculation under the initial working condition needs 14 steps to converge, while the next working condition only needs 6 steps to converge. This shows that this improved method can significantly improve the efficiency of parametric calculation or dynamic process calculation.

[0109] (2) Grid number optimization

[0110] The number of grids affects both the calculation efficiency and directly determines the accuracy of the calculation results when calculating electromagnetic characteristics. Therefore, in order to comprehensively evaluate the comprehensive influence of the number of grids on the calculation efficiency and accuracy, this paper adjusts the discretization degree of the grid cells, calculates the coil inductance and electromagnetic lifting force at all test points, and compares them with the benchmark results of 3D FEA to determine the change trend of the accuracy under different grid densities. At the same time, record the calculation time under each grid configuration to evaluate the influence of different grid settings on the calculation efficiency. The specific grid discretization settings are shown in Table 2.

[0111] Table 2 Grid discretization settings

[0112]

[0113] As Figure 17 shown, this paper presents the distribution of the calculation accuracy of coil inductance and electromagnetic lifting force at different test points through box plots. The upper and lower edges of the box represent the maximum and minimum values of the calculation accuracy respectively, and the black line in the box represents the average value of the calculation accuracy. In addition, the average calculation time at the test points is presented in the form of a bar chart. From Figure 17 it can be seen that as the number of meshes increases, the calculation accuracy of coil inductance and electromagnetic lifting force also improves. However, when the number of meshes increases to a certain extent, the improvement of the calculation accuracy tends to level off, but the calculation time increases significantly. To balance the calculation accuracy and calculation time, this paper divides the GEMN model into 2,256 meshes. At this time, the calculation accuracies of inductance and electromagnetic lifting force are above 94.5% and 90.3% respectively, and the average calculation time is 3.49 seconds. Compared with the 3D FEA method, the GEMN model in this paper has increased the calculation speed by 2,750 times and by 72 times compared with the 2D FEA method.

[0114] To verify the effectiveness and accuracy of the proposed GEMN model in this paper, its calculation results are compared with the 3D FEA results and experimental results, including magnetic flux density distribution, coil inductance and electromagnetic force, and algorithm time.

[0115] 1) Magnetic flux density distribution

[0116] Figure 18 shows the 3D FEA results (a) and the GEMN results (b) of the magnetic flux density distribution of the lifting solenoid valve when the coil current is 40 A and the air gap length is 0 mm. After comparison, it is found that the magnetic flux density distribution laws and magnitudes of the two are very close, thus indicating the effectiveness of the GEMN model in this paper. The magnetic flux density distribution law shows that the magnetic flux density distribution of the lifting yoke is relatively uniform; the magnetic flux density of the lifting magnetic conductive ring is mainly concentrated at one end of the coil slot; the magnetic flux density of the lifting pole increases gradually from the far end to the near end of the air gap; the magnetic flux density of the lifting armature first decreases gradually from the near end to the far end of the air gap, then suddenly increases, and finally decreases again. The magnetic flux density magnitude shows that the magnetic flux density values of the lifting yoke and the lifting magnetic conductive ring are relatively small, while serious magnetic saturation occurs in the local areas of the lifting pole and the lifting armature. Therefore, it is very necessary to consider the influence of the saturation effect when studying the electromagnetic characteristics of the CRDM.

[0117] 2) Coil Inductance

[0118] Figure 19The coil inductances calculated by 3D FEA and the GEMN model proposed in this paper are compared under different currents and air gap lengths. The results show that the calculation results of the GEMN model proposed in this paper are in good agreement with the 3D FEA results under all currents and air gap lengths, and the maximum error is only 5.7%.

[0119] 3) Electromagnetic force

[0120] Figure 20 The curves of electromagnetic force variation under different currents and air gap lengths are compared. The results show that the calculation results of the GEMN model proposed in this paper are in good agreement with the 3D FEA results, and the maximum error is 0.6 kN, which only accounts for 3.4% of the simulation value. This further shows that the GEMN model proposed in this paper improves the accuracy of electromagnetic parameter prediction.

[0121] 4) Comparison of algorithm time

[0122] The calculation time and memory occupation ratios of the FEA method and the GEMN method under the same computer configuration are shown in Table 3. It can be seen that the GEMN model divides the solenoid valve into 914 units, while 3D FEA decomposes it into 1,383,051 units. It takes 160 minutes to perform one calculation using the 3D FEA method, while the GEMN method only takes 27 seconds. Obviously, compared with the 3D FEA method, the GEMN method significantly reduces the calculation resources and time while maintaining the accuracy. Even compared with 2D FEA, the GEMN model also shows significant advantages.

[0123] Table 3 Comparison of calculation time and resources

[0124]

[0125] In this embodiment, a GEMN model is proposed for the magnetic force lifting type control rod drive mechanism of the reactor, and its convergence is analyzed based on this, and the effectiveness and accuracy of the model are verified by FEA.

[0126] The specific conclusions are as follows:

[0127] 1) The rectangular grid division of the mechanism is realized by using orthogonal grid lines, which realizes the unified calculation of the equivalent magnetic resistance and speeds up the modeling speed.

[0128] 2) By changing the grid size or position of the local area, the dynamic change of the GEMN model is realized, and the calculation error caused by the grid division difference is reduced.

[0129] 3) By analyzing parameters such as the initial iteration value and grid density, the calculation efficiency of the GEMN model is optimized and the iterative convergence is enhanced.

[0130] 4) Compared with FEA, the GEMN model in this paper requires fewer computing resources and less computing time while ensuring the calculation accuracy, providing a balanced alternative for FEA analysis.

[0131] Although this paper illustrates with the example of improving the solenoid valve, the proposed GEMN model and multi-physics coupling calculation method can be extended and applied to the establishment of the EMN model, performance analysis, and rapid optimization design of the entire CRDM.

[0132] The above embodiments are the preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. Method for establishing generalized magnetic network model of magnetic-lift type CRDM, characterized in that Including the steps: S1. Obtain the sectional view of the magnetic-lifting type CRDM, and obtain the solution boundary of the solenoid valve in any one of the lifting unit, moving unit, and holding unit, as well as the vertex coordinates of each magnetic-conducting component, to obtain a geometric model diagram. S2. Divide the geometric model diagram into upper and lower fixed areas and moving areas according to whether it moves, and use orthogonal grid lines to divide the fixed area and the moving area to obtain a grid division diagram. S3. According to the size data and material properties of each grid cell in the grid division diagram, calculate the magnetic resistance of each grid cell in the fixed area and the moving area, and connect the magnetic resistances of adjacent grid cells to obtain a generalized magnetic network model.

2. The method for establishing a generalized magnetic network model of the magnetic-lifting type CRDM according to claim 1, wherein In step S2, using orthogonal grid lines to divide the fixed area and the moving area to obtain a grid division diagram, specifically: Generate vertical and horizontal grid lines simultaneously through the vertex coordinates of each magnetic-conducting component. The horizontal grid lines penetrate the entire solution area, and the vertical grid lines terminate at the regional boundary line between the fixed area and the moving area. Insert vertical and horizontal grid lines respectively between the current grid lines in the fixed area and the moving area, and convert the rectangular grid containing two or more media into a single-media grid to obtain a grid division diagram.

3. The method for establishing the generalized magnetic network model of the magnetic lifting type CRDM according to claim 2, wherein: In step S3, each grid unit has two axial magnetic resistances R zl , R zr and the upper and lower radial magnetic resistances R ru , R rd , according to the size data and material properties of each grid cell, the axial reluctance is integrated along the axial flux path, and the radial reluctance is integrated along the radial flux path.

4. The method for establishing a generalized magnetic network model of the magnetic lifting type CRDM according to claim 2, characterized in that: In step S3, for the grid cells that are completely aligned above and below the regional boundary line, directly connect the magnetic resistances of adjacent grid cells; for the grid cells that cannot be completely aligned and overlap above and below the regional boundary line, establish the connection relationship between the geometric centers of the grid cells, and calculate the branch magnetic resistance between the two overlapping geometric centers according to the overlapping ratio between the upper and lower grid cells.

5. The method for establishing the generalized magnetic network model of the magnetic lifting type CRDM according to claim 4, characterized in that: When the magnetic-conducting component in the moving area moves, on the premise of keeping the total number of grids unchanged, only adjust the grid sizes of the air gap area and the end air area at both ends of the magnetic-conducting component, update the grid positions in the middle area where the lifting magnetic-conducting component is located at the same time, and re-determine the connection relationship between the geometric centers of the grid cells above and below the regional boundary line and re-calculate the magnetic resistance.

6. The method for establishing a generalized magnetic network model of the magnetic lifting type CRDM according to any one of claims 1 to 5, characterized in that: In the case of multiple calls to the generalized magnetic network model for parametric calculation or dynamic process calculation, use the iterative value calculated in the previous working condition as the iterative initial value for the next working condition; the iterative initial value for the initial working condition is the magnetic permeability or magnetic flux density and the corresponding magnetic field strength, all of which are selected from the linear section, transition section, and saturation section of the B-H curve of each magnetic-conducting component.

7. The method for establishing a generalized magnetic network model of the magnetic lifting type CRDM according to any one of claims 1 to 5, characterized in that: Determine the number of grids that meet the requirements of calculation accuracy and calculation time according to the relationship between the number of grids and calculation accuracy and calculation time.

8. The method for establishing a generalized magnetic network model of the magnetic lifting type CRDM according to any one of claims 1 to 5, characterized in that: The lifting solenoid valve equipped in the lifting unit is composed of a lifting yoke, a lifting magnetic pole, a lifting coil, a lifting armature, and a lifting magnetic-conducting ring; the moving solenoid valve equipped in the moving unit is composed of a moving yoke, a moving coil, a moving armature, a moving magnetic-conducting ring, a moving hook claw, and a moving connecting rod; the holding solenoid valve equipped in the holding unit is composed of a holding yoke, a holding magnetic pole, a holding coil, a holding armature, a holding magnetic-conducting ring, a holding hook claw, and a holding connecting rod.

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