Space gravitational wave detection inertial sensor plaque field effect simulation and related physical quantity calculation method

Abstract

The invention discloses a spatial gravitational wave detection inertial sensor plaque field effect simulation and related physical quantity calculation method, a sensitive structure of an inertial sensor comprises an electrode cage and a test mass, and the plaque field effect comprises that bumps appear on the outer surface of the test mass and / or the inner surface of the electrode cage; chemical pollution is formed to change the local potential and influence the electric field; the method comprises the following steps: respectively dividing the outer surface of a test mass without plaques and the inner surface of an electrode cage into a plurality of triangular units; moving partial dissection nodes which are not on the edges to enable the dissection nodes to leave the original plane to simulate bumps caused by plaques; based on a set condition that the potential at the centroid of the triangular unit is the same as the potential of the area where the triangular unit is located, simulating the influence of plaques on the potential; based on setting of uniform distribution of charges on the surface of the same triangular unit, the charge density of the surface of each triangular unit is solved; and according to the solved charge density, calculating the electric field force borne by the test mass and the rigidity of the electric field force.

Description

Technical Field

[0001] The present invention belongs to the field of intersection of physics and computer simulation, and specifically relates to a method for simulating the plaque field effect of an inertial sensor for space gravitational wave detection and calculating related physical quantities. Background Art

[0002] Space gravitational wave detection is one of the current research hotspots, and gravitational reference sensors (also called inertial sensors) are important components of space gravitational wave detection missions. The sensitive structure of the inertial sensor includes an electrode cage and a test mass (sometimes abbreviated as "TM"). The test mass is located in the electrode cage, and a number of sensing electrodes and injection electrodes are installed on the surface of the electrode cage. The test mass is a cube made of gold-platinum alloy, and each of its faces forms a capacitor with the electrodes opposite to it. The inertial sensor is fixed on the spacecraft, and the test mass moves without drag along the sensitive axis. When the gravitational wave signal passes by, the test mass and the spacecraft will be affected by the gravitational wave signal and move. The functions of the electrodes include detecting the relative displacement between the test mass and the electrode cage and controlling the position and attitude of the test mass.

[0003] Not only gravitational wave signals, but also various noise signals can cause the test mass to move. These noises may come from residual gas in sensitive structures, magnetic fields around the test mass, etc. Among the many noises, electric field-related noise is more complex and more important. To study electric field-related noise, it is necessary to calculate the electric field force and electric field force stiffness on the test mass.

[0004] Ideally, the electric field in the sensitive structure is determined by the voltage applied to each electrode and the induced potential on the surface of the test mass. The electrodes in the sensitive structure, the area of ​​the electrode cage without electrodes installed, and the test mass can all be considered to be composed of multiple smooth rectangular planes. However, in actual situations, the outer surface of the test mass and the inner surface of the electrode cage are not absolutely smooth, and plaque is one of the factors that affect smoothness. Plaques are formed when contaminants adhere to the test mass or the electrode cage. On the one hand, plaques will cause the outer surface of the test mass or the inner surface of the electrode cage to "bulge"; on the other hand, plaques may form chemical pollution that changes the local potential and affects the electric field. The impact of plaques is also called the "plaque field effect."

[0005] To study the impact of different degrees of plaque field effects, if the traditional "modeling first, then segmentation" method is used, it is necessary to repeatedly model the shape of the outer surface of the test mass and the inner surface of the electrode cage as well as the potential distribution, which is a large workload and has low feasibility. A fast modeling and simulation method is urgently needed. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the prior art and propose a method for simulating the plaque field effect of an inertial sensor for space gravitational wave detection and calculating related physical quantities.

[0007] In order to achieve the above-mentioned purpose, the present invention proposes a method for simulating the plaque field effect of an inertial sensor for space gravitational wave detection and calculating related physical quantities. The sensitive structure of the inertial sensor includes an electrode cage and a test mass. The plaque field effect includes the appearance of bulges on the outer surface of the test mass and / or the inner surface of the electrode cage, and the formation of chemical contamination to change the local potential and affect the electric field. The method includes:

[0008] Step S1) dividing the outer surface of the test mass without plaques and the inner surface of the electrode cage into a plurality of triangular units respectively;

[0009] Step S2) moving some of the split nodes that are not on the edge to make them leave the original plane to simulate the bulge caused by the plaque;

[0010] Step S3) simulating the influence of the plaque on the electric potential based on the setting condition that the electric potential at the centroid of the triangular unit is the same as the electric potential of the region where it is located;

[0011] Step S4) based on the setting of uniform charge distribution on the surface of the same triangular unit, solving the charge density on the surface of each triangular unit;

[0012] Step S5) Calculate the electric field force and electric field force stiffness on the test mass according to the solved charge density.

[0013] Preferably, the step S1) comprises:

[0014] Divide the length and width of the rectangular plane into several equal parts, and then divide it into several small rectangular units;

[0015] Traverse each small rectangular unit and connect its diagonal lines to form four triangular units.

[0016] Preferably, in step S2), the probability of moving the node that is not on the edge is p, and the moving distance is subject to [d min ,d max ], the moving direction is the outer normal direction of the outer surface of the test mass or the inner surface of the electrode cage, where d min ,d max Respectively represent the minimum and maximum moving distance.

[0017] Preferably, the step S3) comprises:

[0018] For a bulge, there are multiple triangular units with the moving segmentation node as a vertex. The potential changes at the centroids of the surfaces of the multiple triangular units are the same, and the changes obey [Δumin ,Δu max ] uniform distribution on the min ,Δu max They represent the minimum and maximum values ​​of the potential change, respectively.

[0019] Preferably, the potential u at the centroid of the i-th triangle unit is i is the sum of the potentials generated by n triangular units at their centroids, satisfying the following formula:

[0020]

[0021] Where n is the number of triangular elements, q j is the relative charge density, λ j is the charge density of the jth triangular unit, ∈0 is the vacuum dielectric constant, S j is the area corresponding to the jth triangular unit, Q is S j Up one point, r i (Q) is the distance from point Q to the centroid of the i-th triangular element.

[0022] Preferably, the step S4) comprises:

[0023] Construct the following set of equations to calculate the relative charge density q on the surface of each triangular unit j :

[0024]

[0025] in

[0026] For g ij The value of is calculated when i = j, g ij The value of can be calculated accurately, and the kth vertex of the jth triangle unit is denoted as P j,k ,k∈{1,2,3}, the centroid is O j , pass O j Draw perpendicular lines to the three sides, P j,2 P j,3 , P j,1 P j,3 , P j,1 P j,2 The feet of the perpendiculars are H j,1 , H j,2 , H j,3 ,but

[0027]

[0028] When i≠j, g ij The value of is approximated using the following method:

[0029]

[0030] Among them, M j,k For point P j,k With point O j The midpoint of the line connecting i (M j,k ) indicates M j,k The distance to the centroid of the i-th triangular element, is the area of ​​the jth triangular unit.

[0031] Preferably, the electric field force F exerted on the test mass in step S5) is:

[0032]

[0033] Among them, n TM The number of the test quality subdivision units, among all the subdivision units, from 1 to n TM The first one is in the test quality, the nth TM +1 to n are located on the electrode cage, and the electric field force F of the i-th triangle unit in the x, y, and z directions x,i 、F y,i 、F z,i Use the following method to approximate calculation:

[0034]

[0035] Among them, λ i is the charge density of the ith triangle unit, is the area of ​​the i-th triangular unit, M i,l is the midpoint of the line connecting the lth vertex of the ith triangular unit and the centroid of the ith triangular unit, M i,l,x 、M i,l,y 、M i,l,z M i,l The three coordinate components of M j,k is the midpoint of the line connecting the kth vertex of the jth triangular unit and the centroid of the jth triangular unit, M j,k,x 、M j,k,y 、M j,k,z M j,k The three coordinate components of r(M i,l ,M j,k ) is M i,l and M j,k The distance between.

[0036] Preferably, the electric field force stiffness matrix K of the test mass in step S5) is:

[0037]

[0038] Among them, K xx,i , K xy,i , K xz,i They respectively represent the rate of change of the electric field force on the ith triangular unit in the x direction with respect to the displacement of the test mass in the x direction, y direction, and z direction;

[0039] K yx,i , K yy,i , K yz,i They represent the rate of change of the electric field force on the ith triangular unit in the y direction with respect to the displacement of the test mass in the x, y, and z directions respectively;

[0040] K zx,i , K zy,i , K zz,i They represent the rate of change of the electric field force on the ith triangular unit in the z direction with respect to the displacement of the test mass in the x, y, and z directions, respectively, and are approximately calculated using the following method:

[0041]

[0042] Compared with the prior art, the advantages of the present invention are:

[0043] 1. Based on the scheme of "dividing first and modeling later", it is easy to simulate the patch field effects of different scales, without the need to re-model and divide the patch field effects of different scales as in the "modeling first and dividing later" method;

[0044] 2. The segmentation scheme used takes advantage of the geometric characteristics of the sensitive structure and is easy to implement;

[0045] 3. Fewer parameters need to be set when generating plaques;

[0046] 4. The method for calculating relevant physical quantities is simple, the theory is easy to understand, and the results are relatively accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of the method of the present invention;

[0048] Figure 2 A schematic diagram of dividing a rectangular plane into several triangular units;

[0049] Figure 3 A schematic diagram of the way in which the bulge is formed;

[0050] Figure 4 The bulge distribution of the outer surface of the test mass in the embodiment;

[0051] Figure 5 The distribution of bulges on the inner surface of the electrode cage in the embodiment;

[0052] Figure 6 The potential distribution of the outer surface of the test mass in the embodiment;

[0053] Figure 7 is the potential distribution on the inner surface of the electrode cage in the embodiment;

[0054] FIG8 is a curve showing the change of res in the process of iteratively solving the equation group when solving the charge distribution in the embodiment; wherein the ordinate of FIG8(a) is a linear scale, and the ordinate of FIG8(b) is a logarithmic scale;

[0055] Fig. 9 is the relative charge density distribution of the outer surface of the test mass obtained in the embodiment;

[0056] Fig.10 is the relative charge density distribution on the inner surface of the electrode cage obtained in the embodiment. DETAILED DESCRIPTION

[0057] Based on the idea of ​​"division first, modeling later", this paper proposes a method for simulating the patch field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities. The general process is as follows: Figure 1 As shown, specifically including:

[0058] Step 1: segment the outer surface of the ideal test mass and the inner surface of the electrode cage;

[0059] Ideally, the outer surface of the test mass and the inner surface of the electrode cage can be regarded as a combination of multiple smooth rectangular planes. For a rectangular plane, it is divided into several triangular units. This process can be divided into two steps (such as Figure 2 As shown, taking the division into 16 triangular units as an example):

[0060] 1. Divide the length and width of the rectangular plane into several equal parts, and then divide it into several small rectangular units;

[0061] 2. For each small rectangle, connect its diagonal lines to form four triangular units. These small triangular units are the basic units for subdivision.

[0062] Step 2: forming a bulge;

[0063] By moving the splitting nodes, in theory, a variety of shapes can be simulated. For simplicity, one "bulge" can correspond to only one splitting node. The node is moved away from the surface of the test mass or electrode cage where it was originally located. Each triangular unit with the node as one of its vertices becomes the surface of the "bulge". Figure 3 This process is shown in Figure 1. When node M moves to M′, the four triangular elements are affected and a bulge is formed.

[0064] The selected node cannot be located on the edge of the test mass or electrode cage. The direction of node movement is selected as the outer normal of the outer surface of the test mass or the inner surface of the electrode cage (for the outer surface of the test mass, the outer normal points to the outside of the test mass; for the inner surface of the electrode cage, the outer normal points to the inside of the electrode cage).

[0065] For each node that is not on the edge, each node has a certain probability of moving, and the probability is recorded as p. Then

[0066]

[0067] For the node that is determined to move, it is assumed that the moving distance obeys [d min ,d max ] uniform distribution on the min ,d max Respectively represent the minimum and maximum moving distance.

[0068] Step 3: Determine the surface potential distribution;

[0069] The test mass, each electrode, and the area of ​​the electrode cage where no electrode is installed are all conductors. When there are no plaques, they can be regarded as equipotential bodies. The potential on the surface of each electrode is a set value. The potential on the surface of the test mass is the induced potential formed by each electrode on the test mass, which is calculated as follows:

[0070]

[0071] Where V i is the surface potential of the ith electrode or the area on the electrode cage where no electrode is installed, C i is the capacitance between the ith electrode or the area on the electrode cage where no electrode is installed and the test mass. The potential of the area on the electrode cage where no electrode is installed is approximately 0, Q TM The amount of charge accumulated to test mass as a result of factors such as cosmic rays.

[0072] When a plaque is formed, it is approximately assumed that only the potential of the area where the plaque is located changes slightly, and the potential of other surface areas is not affected. The potential at the centroid of the triangular unit is the potential of the area where it is located. A bulge contains a moved node and multiple triangular subdivision units with the node as one of the vertices. Assuming that the potential changes at the centroid of each triangular unit surface corresponding to a bulge are the same, the change obeys [Δu min ,Δu max ] uniform distribution, Δu min ,Δu max They represent the minimum and maximum values ​​of the potential change, respectively.

[0073] Step 4: Solve the charge density on the surface of each triangular unit;

[0074] In the following invention content, there are many processes involving the calculation of surface integrals using a certain triangular unit as the integral domain. Unless otherwise specified, all other forms such as ∫∫ S The integral of f(P)dS is used

[0075]

[0076] Approximate calculation, where S is the triangle area, P1, P2, P3 are the three vertices of the triangle, is the area of ​​the triangle, M k For point P k The midpoint of the line connecting the centroid of the triangle is hereinafter referred to as the "three-point method".

[0077] For each triangular unit, the potential at its centroid is the superposition of the potentials generated by a series of charges at that point. Since the effective charge carried by the conductor is distributed on the surface, if the triangular unit is regarded as a surface charge with uniform charge distribution, the potential u at the centroid of the i-th triangular unit is i satisfy

[0078]

[0079] Where n is the number of subdivision units, and definition is the charge density λ of the jth mesh element j Divided by the vacuum dielectric constant ∈ 0 (hereinafter referred to as q j is the “relative charge density”), S j is the area corresponding to the jth subdivision unit, Q is S j Up one point, r i (Q) is the distance from point Q to the centroid of the i-th triangular element.

[0080]

[0081] Constructing a system of equations

[0082]

[0083] It is abbreviated as

[0084] AX=b

[0085] By solving this set of equations, the charge distribution can be determined, and then the relevant physical quantities can be calculated.

[0086] In calculating g ij When i=j, then g ij The value of can be calculated accurately. Let the three vertices of the j-th triangle unit be P j,1 ,P j,2 ,P j,3 , the centroid is Oj , pass O j Draw perpendicular lines to the three sides, P j,2 P j,3 , P j,1 P j,3 , P j,1 P j,2 The feet of the perpendiculars are H j,1 , H j,2 , H j,3 ,but

[0087]

[0088] When i≠j, g ij The value of is difficult to calculate accurately, so the “three-point method” is used for approximate calculation. The specific approximate expression is:

[0089]

[0090] Among them, M j,k For point P j,k With point O j The midpoint of the line connecting is the area of ​​the jth triangular unit, r i (M j,k ) indicates M j,k The distance to the centroid of the ith triangle element.

[0091] Step 5: Calculate relevant physical quantities based on the solved charge density;

[0092] First, calculate the electric field force on the test mass. Since the effective charge carried by the conductor is distributed on the surface, the total electric field force on the test mass can be regarded as the sum of the electric field forces on all the subdivided units on the test mass surface. Assume that among all the subdivided units, the subdivided units on the test mass surface are the first n TM The total electric field force on the test mass is

[0093]

[0094] For a certain segmentation unit, the electric field force it receives comes from the other n-1 segmentation units. Therefore, the electric field force F received by the ith segmentation unit in the x, y, and z directions is x,i 、F y,i 、F z,i for:

[0095]

[0096] Where P x , P y , P zThey refer to the three coordinate components of point P, and the same goes for point Q. r(P,Q) is the distance between P and Q.

[0097] Since the surface integral is difficult to calculate accurately, the “three-point method” is still used for approximate calculation, F x,i 、F y,i 、F z,i The specific approximate expression is:

[0098]

[0099] where λ i is the charge density of the ith triangle unit, is the area of ​​the i-th triangular unit, M i,l is the midpoint of the line connecting the lth vertex of the ith triangular unit and the centroid of the ith triangular unit, M i,l,x 、M i,l,y 、M i,l,z are its three coordinate components, M j,k is the midpoint of the line connecting the kth vertex of the jth triangular unit and the centroid of the jth triangular unit, M j,k,x 、M j,k,y 、M j,k,z are its three coordinate components, r(M i,l ,M j,k ) is M i,l and M j,k The distance between.

[0100] Then calculate the electric field force stiffness. The electric field force stiffness refers to the rate of change of the electric field force on the test mass with respect to the displacement after the test mass is displaced from the equilibrium position. For a certain subdivision unit on the test mass, the sources of the electric field force it is subjected to can be divided into two categories, one from the subdivision unit on the inner surface of the electrode cage, and the other from other subdivision units on the surface of the test mass. For the latter, since the subdivision units on the surface of the test mass are relatively stationary when the test mass moves, the electric field force generated by the latter will not change, and it does not contribute to the stiffness. For the test mass, its stiffness matrix can be defined

[0101]

[0102] Where K xx,i , K xy,i , K xz,i They respectively represent the rate of change of the electric field force on the ith triangular unit in the x direction with respect to the displacement of the test mass in the x direction, y direction, and z direction;

[0103] K yx,i , K yy,i , K yz,iThey represent the rate of change of the electric field force on the ith triangular unit in the y direction with respect to the displacement of the test mass in the x, y, and z directions respectively;

[0104] K zx,i , K zy,i , K zz,i They respectively represent the rate of change of the electric field force on the i-th triangular unit in the z direction with respect to the displacement of the test mass in the x, y, and z directions. They satisfy the following formulas respectively:

[0105]

[0106] The surface integrals in each formula are still calculated approximately using the “three-point method”, K xx,i , K xy,i , K xz,i , K yx,i , K yy,i , K yz,i , K zx,i , K zy,i , K zz,i The specific approximate expression is:

[0107]

[0108] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0109] Example

[0110] The embodiment of the present invention discloses a method for simulating the plaque field effect of an inertial sensor for detecting space gravitational waves and calculating related physical quantities.

[0111] It should be noted that all parameters do not represent actual values ​​and are only used to demonstrate the implementation method.

[0112] For the convenience of description and operation, the outer surface of the test mass and the inner surface of the electrode cage are regarded as rectangular shells, and the difference between the "notch" of the test mass in the z direction and the protrusions of the electrode cage at different positions on the same surface is ignored.

[0113] Table 1 shows the coordinates of each vertex of the test mass and electrode cage in the spatial rectangular coordinate system (unit: mm)

[0114] Table 1

[0115]

[0116]

[0117] Under the assumptions here, each electrode can be regarded as a two-dimensional rectangle, each side of the electrode is parallel to a coordinate axis, and the vertex coordinates of each electrode on a diagonal line are shown in the following table (only the two-dimensional coordinates in the plane are shown).

[0118] Table 2

[0119] Electrode number Electrode Type The plane Coordinate components Vertex 1 Vertex 2 1 Sensing electrode x＝-27 (y,z) (-18,-18) (-3.5,18) 2 Sensing electrode x＝-27 (y,z) (3.5,-18) (18,18) 3 Sensing electrode x＝27 (y,z) (-18,-18) (-3.5,18) 4 Sensing electrode x＝27 (y,z) (3.5,-18) (18,18) 5 Sensing electrode y＝-25.9 (x,z) (-19.1,-19.1) (19.1,-12) 6 Sensing electrode y＝-25.9 (x,z) (-19.1,12) (19.1,19.1) 7 Injection electrode y＝-25.9 (x,z) (-19.1,-8) (19.1,8) 8 Sensing electrode y＝25.9 (x,z) (-19.1,-19.1) (19.1,-12) 9 Sensing electrode y＝25.9 (x,z) (-19.1,12) (19.1,19.1) 10 Injection electrode y＝25.9 (x,z) (-19.1,-8) (19.1,8) 11 Sensing electrode z＝-26.5 (x,y) (-18.5,-18.5) (-12,18.5) 12 Sensing electrode z＝-26.5 (x,y) (12,-18.5) (18.5,18.5) 13 Injection electrode z＝-26.5 (x,y) (-8,-18.5) (8,-6.5) 14 Injection electrode z＝-26.5 (x,y) (-8,6.5) (8,18.5) 15 Sensing electrode z＝26.5 (x,y) (-18.5,-18.5) (-12,18.5) 16 Sensing electrode z＝26.5 (x,y) (12,-18.5) (18.5,18.5) 17 Injection electrode z＝26.5 (x,y) (-8,-18.5) (8,-6.5) 18 Injection electrode z＝26.5 (x,y) (-8,6.5) (8,18.5)

[0120] Step 1: segment the surface of the electrode cage and the test mass;

[0121] The outer surface of the test mass and the inner surface of the electrode cage are divided into rectangular grids. The number of equal parts of the test mass and the electrode cage in each direction is as follows:

[0122] Table 3

[0123] x direction y direction z direction Test quality 115 115 115 Electrode cage 135 132 133

[0124] This is equivalent to dividing it into 184,940 squares with a side length of approximately 0.4 mm. Then, the diagonals of these rectangular units are connected to obtain 739,760 triangular units, which are approximately isosceles right triangles with a hypotenuse length of 0.4 mm.

[0125] Step 2: forming a bulge;

[0126] For the "bulge" caused by the plaque, assuming that the probability of each node not on the edge moving is p = 0.002, for the point determined to be moved, the maximum distance d max =0.2mm, minimum distance d min =0. Figure 4 and Figure 5 The "bulging" of 12 surfaces, including the outer surface of the test mass and the inner surface of the electrode cage, is displayed.

[0127] Step 3: Determine the surface potential distribution;

[0128] Assume Q TM =0. Ideally, the potential of each electrode surface is set to: 1000 mV for all sensing electrodes and 3 mV for all injection electrodes. On this basis, it can be calculated that the induced potential of the test mass surface is approximately 314.74 mV.

[0129] For a moved node, the potential of the surface of all triangular elements with this node as one of the vertices changes by the same amount, and the maximum change is Δu max =0.5mV, minimum value is Δu min =-0.5mV. Figure 6 and Figure 7 The potential distribution on the outer surface of the test mass and the inner surface of the electrode cage is shown.

[0130] Step 4: Solve the charge density on the surface of each triangular unit;

[0131] To solve the relative charge density of each subdivided unit, a 739760-order linear equation system needs to be solved. Since the scale of the equation system is too large to be solved directly and accurately, an iterative method is used here to solve it. The iterative algorithm is GMRES, and the zero vector is selected as the initial solution. The change curve of res=‖Ax-b‖2 during the iteration process is shown in Figure 8. Figure 8(a) Before iteration, res≈3.63×10 5 mV, Figure 8(b) After the iteration, res≈9.55×10 -5 mV.

[0132] The relative charge density distribution of each subdivided unit on the outer surface of the test mass and the inner surface of the electrode cage is as follows: Fig. 9 and Fig.10 The coordinates in the figure are the centroid of the subdivided unit.

[0133] Step 5: Calculate relevant physical quantities based on the solved charge density;

[0134] According to the relative charge density on the surface of each subdivided unit, the resultant force on the test mass is calculated as:

[0135] F≈(-2.50,-1.79,0.63)×10 -14 N

[0136] The stiffness matrix is ​​calculated as

[0137]

[0138] 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 the present invention. Although the present invention is described in detail with reference to the embodiments, it should be understood by those skilled in the art that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention and should be included in the scope of the claims of the present invention.

Claims

1. A method for simulating the plaque field effect of an inertial sensor for space gravitational wave detection and calculating related physical quantities. The sensitive structure of the inertial sensor includes an electrode cage and a test mass. The plaque field effect includes the appearance of bulges on the outer surface of the test mass and / or the inner surface of the electrode cage, and the formation of chemical contamination to change the local potential and affect the electric field. The method comprises: Step S1) dividing the outer surface of the test mass without plaques and the inner surface of the electrode cage into a plurality of triangular units respectively; Step S2) moving some of the split nodes that are not on the edge to make them leave the original plane to simulate the bulge caused by the plaque; Step S3) simulating the influence of the plaque on the electric potential based on the setting condition that the electric potential at the centroid of the triangular unit is the same as the electric potential of the region where it is located; Step S4) based on the setting of uniform charge distribution on the surface of the same triangular unit, solving the charge density on the surface of each triangular unit; Step S5) Calculate the electric field force and electric field force stiffness on the test mass according to the solved charge density.

2. The method for simulating the plaque field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities according to claim 1, characterized in that: The step S1) comprises: Divide the length and width of the rectangular plane into several equal parts, and then divide it into several small rectangular units; Traverse each small rectangular unit and connect its diagonal lines to form four triangular units.

3. The method for simulating the plaque field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities according to claim 1, characterized in that: In step S2), the moving part of the node that is not on the edge has a probability of p, and the moving distance is subject to [d min ,d max ], the moving direction is the outer normal direction of the outer surface of the test mass or the inner surface of the electrode cage, where d min ,d max Respectively represent the minimum and maximum moving distance.

4. The method for simulating the plaque field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities according to claim 1, characterized in that: The step S3) comprises: For a bulge, there are multiple triangular units with the moving segmentation node as a vertex. The potential changes at the centroids of the surfaces of the multiple triangular units are the same, and the changes obey [Δu min ,Δu max ] uniform distribution on the min ,Δu max They represent the minimum and maximum values ​​of the potential change, respectively.

5. The method for simulating the plaque field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities according to claim 4, characterized in that: The electric potential u at the centroid of the i-th triangle unit i is the sum of the potentials generated by n triangular units at their centroids, satisfying the following formula: Where n is the number of triangular elements, q j is the relative charge density, λ j is the charge density of the jth triangular unit, ∈0 is the vacuum dielectric constant, S j is the area corresponding to the jth triangular unit, Q is S j Up one point, r i (Q) is the distance from point Q to the centroid of the i-th triangular element.

6. The method for simulating the plaque field effect of inertial sensors for space gravitational wave detection and calculating related physical quantities according to claim 5, characterized in that: The step S4) comprises: Construct the following set of equations to calculate the relative charge density q on the surface of each triangular unit j : in For g ij The value of is calculated when i = j, g ij The value of can be calculated accurately, and the kth vertex of the jth triangle unit is denoted as P j,k ,k∈{1,2,3}, the centroid is O j , pass O j Draw perpendicular lines to the three sides, P j,2 P j,3 , P j,1 P j,3 , P j,1 P j,2 The feet of the perpendiculars are H j,1 , H j,2 , H j,3 ,but When i≠j, g ij The value of is approximated using the following method: Among them, M j,k For point P j,k With point O j The midpoint of the line connecting i (M j,k ) indicates M j,k The distance to the centroid of the i-th triangular element, is the area of ​​the jth triangular unit.

7. The method for simulating the plaque field effect and calculating related physical quantities of an inertial sensor for space gravitational wave detection according to claim 6 is characterized in that: The electric field force F exerted on the test mass in step S5) is: Among them, n TM The number of the test quality subdivision units, among all the subdivision units, from 1 to n TM The first one is in the test quality, the nth TM +1 to n are located on the electrode cage, and the electric field force F of the i-th triangle unit in the x, y, and z directions x,i 、F y,i 、F z,i Use the following method to approximate calculation: Among them, λ i is the charge density of the ith triangle unit, is the area of ​​the i-th triangular unit, M i,l is the midpoint of the line connecting the lth vertex of the ith triangular unit and the centroid of the ith triangular unit, M i,l,x 、M i,l,y 、M i,l,z M i,l The three coordinate components of M j,k is the midpoint of the line connecting the kth vertex of the jth triangular unit and the centroid of the jth triangular unit, M j,k,x 、M j,k,y 、M j,k,z M j,k The three coordinate components of r(M i,l ,M j,k ) is M i,l and M j,k The distance between.

8. The method for simulating the plaque field effect and calculating related physical quantities of an inertial sensor for space gravitational wave detection according to claim 7 is characterized in that: The electric field force stiffness matrix K of the test mass in step S5) is: Among them, K xx,i , K xy,i , K xz,i They respectively represent the rate of change of the electric field force on the ith triangular unit in the x direction with respect to the displacement of the test mass in the x direction, y direction, and z direction; K yx,i , K yy,i , K yz,i They represent the rate of change of the electric field force on the ith triangular unit in the y direction with respect to the displacement of the test mass in the x, y, and z directions respectively; K zx,i , K zy,i , K zz,i They represent the rate of change of the electric field force on the ith triangular unit in the z direction with respect to the displacement of the test mass in the x, y, and z directions, respectively, and are approximately calculated using the following method:

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