Method for measuring surface charge of double-sided asymmetric basin-type insulator
By designing a coaxial electrode system and using an active probe method, combining a rotating motor and a three-axis displacement platform, the charge of the double-sided asymmetric basin insulators is achieved, and the charge problem of difficult to measure such complex structures in the prior art is solved, and standardized and comparable data are provided.
Patent Information
- Application Number
- CN202510276535.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-10
- Publication Date
- 2025-05-13
AI Technical Summary
The prior art is difficult to effectively measure the surface charge of double-sided asymmetric basin insulators, especially at high voltage levels, and common methods cannot adapt to the measurement requirements of such complex structures.
A coaxial electrode system was designed, combining a rotating motor and a three-axis displacement platform to measure the surface potential of the basin insulator through the active probe method, collect data and obtain charge density data through inversion calculation, so as to achieve rapid and accurate measurement of the surface charge of the double-sided asymmetric basin insulator.
This method can quickly and accurately measure the surface charge of double-sided asymmetric basin insulators, provide standardized conditions and comparable data, solve the problem that measurement results cannot be compared, and is suitable for insulator measurement in practical engineering applications.
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Figure CN119986177A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of electrical material measurement, and in particular relates to a method for measuring the surface charge of a double-sided asymmetric pot-type insulator. Background Art
[0002] High-voltage direct current (HVDC) power transmission and transformation is an important way to realize the flexible allocation and consumption of long-distance cross-regional electric energy, with many advantages such as low cost, low loss, and long transmission distance. Compared with traditional power transmission and transformation equipment, gas-insulated switchgear (GIS) has many advantages such as small footprint, high assembly flexibility, and strong resistance to external interference. Due to the intrinsic difference between solid medium and gas medium, a large amount of charge accumulates at the gas-solid interface of the basin insulator inside the DC GIS under the action of long-term unipolar voltage, which is considered to be a key problem that damages the insulation performance of GIS and restricts the development of DC GIS.
[0003] The carrier traps at the air-solid interface of the pot-type insulator will capture freely moving charges. Once the charges are captured, local charge accumulation will occur, causing electric field distortion, thereby damaging the insulation performance of the insulator and greatly increasing the probability of flashover accidents. At present, the methods for observing the surface charge accumulation of pot-type insulators include dust map method, active probe method, Pockels effect method, etc. Since the dust map method requires spraying charged dust on the surface of the pot-type insulator, the introduced dust will cause harm to the insulation safety. The Pockels effect method has very strict requirements on the thickness and shape of the test sample, which is not convenient for application in the production and operation of GIS. The active probe method measures the surface potential data of the insulator according to the potential induced in the probe by placing the Kelvin probe close to the surface of the insulator. It has a wide measurement range and high measurement accuracy, and is very suitable for the measurement of surface charge of pot-type insulators.
[0004] However, considering the mechanical, insulation margin, installation and other issues, the pot insulators installed inside the GIS often have very complex surface contours. These complex contours will interfere with the measurement of pot insulators, and the scanning trajectory of the Kelvin probe on the surface potential of the pot insulator will be affected by the complex shape.
[0005] At present, the common means of measuring the surface charge of pot-type insulators are often used for pot-type insulators with a double-sided symmetrical structure, and the voltage level applicable to these insulators is often low. As the voltage level increases, the surface of high-voltage pot-type insulators often presents a double-sided asymmetrical structure, making it difficult to measure the surface charge of such a structure. Summary of the invention
[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for measuring the surface charge of a double-sided asymmetric pot insulator. The experimental platform for measuring surface potential based on the active probe method can quickly and accurately measure the surface charge of the pot insulator, and has more standardized conditions and more comparable data.
[0007] The present invention solves the technical problem by the following technical solutions:
[0008] A method for measuring the surface charge of a double-sided asymmetric pot-type insulator, characterized in that the steps of the method are:
[0009] S1. Design a coaxial electrode system matched with a pot-type insulator, the coaxial electrode system comprising a pot-type insulator, a center conductor and a grounding electrode. The pot-type insulator is a nearly conical structure and is divided into a concave surface and a convex surface according to the surface shape. Each surface is divided into region A and region B, wherein region A forms an angle of 30° with the grounding electrode, and region B is perpendicular to the grounding electrode.
[0010] S2. Place the pot insulator and the coaxial electrode system on the rotating motor in the experimental cavity. The grounding electrode of the coaxial electrode system is connected to the grounding side through the experimental cavity. The central conductor is connected to the high-voltage electrode of the experimental cavity. The rotating motor and the three-axis displacement platform are controlled by the rotating motor controller and the three-axis displacement controller respectively. The electrostatic probe is connected to the electrometer. The potential result measured by the electrostatic probe is recorded in the electrometer.
[0011] S3, using a voltage regulator as a high-voltage DC power source to apply a high voltage to the high-voltage electrode of the experimental cavity through a current-limiting water resistor to charge the pot-type insulator, and removing the central conductor after charging to a stable state;
[0012] S4, move the electrostatic probe to the concave surface area B of the pot-type insulator, and use the rotating motor and the three-axis mobile platform to drive the movement of the electrostatic probe to sequentially complete the potential data collection of 2 circles at the concave surface area B and 17 circles at the concave surface area A of the pot-type insulator; similarly, collect the potential data of 2 circles at the convex surface area B and 17 circles at the convex surface area A of the pot-type insulator, and record the collected potential data in the electrometer;
[0013] S5. The collected potential data are calculated as charge density data through inversion calculation. The concave and convex surfaces of the pot-type insulator are divided into 1368 cells in the radial direction and 72 in the circumferential direction. The surface potential of each cell is independently affected by the charge of itself and the other 1367 cells. The influence of the charge of each cell on the potential of a cell is superimposed. The relationship between the surface potential and the surface charge density is shown in formula (1):
[0014]
[0015] in: is a matrix containing 1368 grid potentials;
[0016] σ is a matrix containing 1368 grid surface charge densities;
[0017] H is the coefficient matrix;
[0018] As shown in equations (2) to (4):
[0019]
[0020] in: is the potential of the ith unit;
[0021] σ j is the surface charge density of the jth unit;
[0022] h i,j represents the contribution coefficient of the surface charge of the jth unit to the potential of the i-th unit;
[0023] Using COMSOL Multiphysics simulation software, the surface charge density σ of the jth unit is j Set to 1pC / mm 2 , the charge density of the other 1367 units is set to 0, and the potential value on the surface of the insulator is calculated, as shown in formula (5):
[0024]
[0025] Traversing j=1,…,1368, the calculated potential value is the jth column of the coefficient matrix H, and the coefficient matrix H can be obtained. By inverting the coefficient matrix H, the surface charge density is calculated by equation (6), and the Origin drawing software is used to complete the imaging of the three-dimensional charge distribution on the insulator surface:
[0026]
[0027] Moreover, the grounding electrode is made of metal aluminum, the insulator is formed by mixing epoxy resin and Al2O3 in a mass ratio of 1:3, the radius of the pot-type insulator is 231mm, the height is 140mm, and the height of the grounding electrode is 180mm.
[0028] Moreover, the S4 is specifically as follows: the electrostatic probe is moved to the concave surface area B of the insulator 5 mm away from the ground electrode through the three-axis displacement platform, and the electrostatic probe is perpendicular to the surface of the insulator and the distance is 5 mm; at the same time, the rotating motor and the electrostatic probe acquisition are synchronously turned on, and the acquisition speed is set to 4 times per second, and the rotation speed is 20° / s. After the first rotation of 18s, 72 potential data located in the starting circle will be recorded in the electrometer;
[0029] After the initial circle test is completed, the electrostatic probe is translated 10 mm toward the center conductor side, and the potential data collection of the second circle of the concave surface area B is started. The rotation is also 18 seconds, and 72 potential data are collected;
[0030] After the measurement of area B is completed, the electrostatic probe is rotated 30 degrees to be perpendicular to the insulator area A. The starting position of a new circle of measurement is opposite to the starting position of area B. That is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is the 180° circumference position;
[0031] The rotation speed and the electrostatic probe collection speed are controlled to remain unchanged. After each circle of potential collection is completed, the probe is controlled by the three-axis displacement platform to move toward the central conductor side in the direction parallel to area A, moving 10 mm each time, and waiting for 18 seconds for the insulator to complete the rotation, completing the potential collection of 17 circles in area A;
[0032] Similarly, 19 circumferential potentials of the convex surface areas A and B are collected. Unlike the concave surface, after the measurement of the convex surface area B is completed, the measurement starting position of the convex surface area A is consistent with that of area B, that is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is also the 0° circumferential position.
[0033] The advantages and beneficial effects of the present invention are:
[0034] The present invention can realize the rapid and accurate measurement of the surface charge of double-sided asymmetric pot-type insulators, facilitate the comparative analysis of the charge distribution under different surfaces of the insulator, and is conducive to further exploring the charge accumulation behavior. The method can be used for insulator measurement in practical engineering applications, providing a theoretical and experimental basis for guiding practice; the charge distribution characteristics of the two surfaces are comparable, which solves the problem that the charge distribution results of different shapes of the same insulator cannot be compared. The program control, uniform time step scanning, and recording of surface potential are adopted to overcome the disadvantage of long time consumption of single sample measurement. The measurement results are matrixed to enrich the statistical characteristics of the charge distribution and improve the analysis speed and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 A diagram of a basin-type insulator and a coaxial electrode system of the present invention;
[0036] Figure 2 It is a schematic diagram of the experimental chamber of the present invention;
[0037] Figure 3 It is a schematic diagram of an experimental circuit of the present invention;
[0038] Figure 4 It is a schematic diagram of the surface potential measurement process of the present invention;
[0039] Figure 5 It is a schematic diagram of the division of cells on the surface of the pot-type insulator of the present invention. DETAILED DESCRIPTION
[0040] The present invention is further described in detail below through specific examples. The following examples are only illustrative and not restrictive, and the protection scope of the present invention cannot be limited thereto.
[0041] The invention discloses a method for measuring the surface charge of a double-sided asymmetric pot-type insulator, the innovation of which lies in the following steps:
[0042] S1. Design a coaxial electrode system that matches the pot-type insulator. Figure 1 As shown, the coaxial electrode system includes a pot insulator, a center conductor and a grounding electrode. The pot insulator is a nearly conical structure and is divided into a concave surface and a convex surface according to the surface shape. Each surface is divided into region A and region B, wherein region A forms an angle of 30° with the grounding electrode, and region B is perpendicular to the grounding electrode. Moreover, the grounding electrode is made of metal aluminum. The insulator is formed by mixing epoxy resin and Al2O3 in a mass ratio of 1:3. The pot insulator has a radius of 231 mm and a height of 140 mm. The height of the grounding electrode is 180 mm.
[0043] S2. Place the pot insulator and coaxial electrode system as follows: Figure 2 On the rotating motor of the experimental cavity shown, the ground electrode of the coaxial electrode system is connected to the ground side through the experimental cavity, the central conductor is connected to the high-voltage electrode of the experimental cavity, the rotating motor and the three-axis displacement platform are controlled by the rotating motor controller and the three-axis displacement controller respectively, the electrostatic probe is connected to the electrometer, and the potential result measured by the electrostatic probe is recorded in the electrometer;
[0044] S3, such as Figure 3 As shown, a voltage regulator is used as a high-voltage DC power source to apply a high voltage to the high-voltage electrode of the experimental cavity through a current-limiting water resistor to charge the pot-type insulator. After charging to a stable state, the central conductor is removed;
[0045] S4, such as Figure 4As shown, the electrostatic probe is moved to the concave surface area B of the pot-type insulator, and the electrostatic probe is driven by the rotating motor and the three-axis mobile platform to sequentially complete the potential data collection of 2 circles at B and 17 circles at A of the concave surface area of the pot-type insulator; similarly, the potential data of 2 circles at B and 17 circles at A of the convex surface area of the pot-type insulator are collected, and the collected potential data are recorded in the electrometer;
[0046] Specifically, the electrostatic probe is moved to the concave surface area B of the insulator 5mm away from the ground electrode through the three-axis displacement platform. The electrostatic probe is perpendicular to the surface of the insulator and the distance is 5mm. At the same time, the rotating motor and the electrostatic probe acquisition are synchronously turned on, and the acquisition speed is set to 4 times per second and the rotation speed is 20° / s. After the first rotation of 18s, the 72 potential data located in the starting circle will be recorded in the electrometer.
[0047] After the initial circle test is completed, the electrostatic probe is translated 10 mm toward the center conductor side, and the potential data collection of the second circle of the concave surface area B is started. The rotation is also 18 seconds, and 72 potential data are collected;
[0048] After the measurement of area B is completed, the electrostatic probe is rotated 30 degrees to be perpendicular to the insulator area A. The starting position of a new circle of measurement is opposite to the starting position of area B. That is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is the 180° circumference position;
[0049] The rotation speed and the electrostatic probe collection speed are controlled to remain unchanged. After each circle of potential collection is completed, the probe is controlled by the three-axis displacement platform to move toward the central conductor side in the direction parallel to area A, moving 10 mm each time, and waiting for 18 seconds for the insulator to complete the rotation, completing the potential collection of 17 circles in area A;
[0050] Similarly, 19 circumferential potentials of the convex surface areas A and B are collected. Unlike the concave surface, after the measurement of the convex surface area B is completed, the measurement starting position of the convex surface area A is consistent with that of area B, that is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is also the 0° circumferential position.
[0051] S5, such as Figure 5 As shown in the figure, the collected potential data is calculated as charge density data through inversion calculation, and the concave and convex surfaces of the pot-type insulator are divided into 1368 cells in the radial direction and 72 in the circumferential direction. The surface potential of each cell is independently affected by the charge of itself and the other 1367 cells. The influence of the charge of each cell on the potential of a cell is superimposed. The relationship between the surface potential and the surface charge density is shown in formula (1):
[0052]
[0053] in: is a matrix containing 1368 grid potentials;
[0054] σ is a matrix containing 1368 grid surface charge densities;
[0055] H is the coefficient matrix;
[0056] As shown in equations (2) to (4):
[0057]
[0058] in: is the potential of the ith unit;
[0059] σ j is the surface charge density of the jth unit;
[0060] h i,j represents the contribution coefficient of the surface charge of the jth unit to the potential of the i-th unit;
[0061] Using COMSOL Multiphysics simulation software, the surface charge density σ of the jth unit is j Set to 1pC / mm 2 , the charge density of the other 1367 units is set to 0, and the potential value on the surface of the insulator is calculated, as shown in formula (5):
[0062]
[0063] Traversing j=1,…,1368, the calculated potential value is the jth column of the coefficient matrix H, and the coefficient matrix H can be obtained. By inverting the coefficient matrix H, the surface charge density is calculated by equation (6), and the Origin drawing software is used to complete the imaging of the three-dimensional charge distribution on the insulator surface:
[0064]
[0065] Example
[0066] 1) A voltage regulator is used as a high-voltage DC power supply. The outlet end is connected to a RC voltage divider with a rated transformation ratio of 1:1000, and is connected to the high-voltage electrode of the test platform through a current-limiting water resistor. A coaxial electrode system is designed to match the basin insulator with an asymmetric surface. The system includes a central conductor with a radius of 40 mm and a height of 180 mm, and a grounding electrode with an inner radius of 200 mm, a thickness of 4 mm, and a height of 180 mm; the insulator is 140 mm high and 231 mm in radius;
[0067] like Figure 2As shown, the test platform includes a rotating motor, a three-axis displacement platform, an active electrostatic probe and other matching mechanical support components. The rotating motor is placed at the center of the bottom of the test platform, and can provide the insulator with 360° horizontal rotational movement around the axis. The three-axis displacement platform is placed near the rotating motor and is connected to the active electrostatic probe, which can drive the probe to perform translational and rotational movements. After the insulator and the coaxial electrode are assembled, they are placed on the rotating motor; a high-voltage DC voltage is applied to the insulator through a current-limiting water resistor, and after the insulator is fully charged to a stable state, the center conductor is removed.
[0068] 2) Move the probe to the concave surface area B of the insulator 5mm away from the ground electrode through the three-axis displacement platform. The probe is perpendicular to the insulator surface and the distance is 5mm. At the same time, the rotating platform and the probe acquisition are synchronously turned on, and the acquisition speed is set to 4 times per second and the rotation speed is 20° per second. After the first rotation of 18s, the 72 potential data located in the starting circle will be recorded in the electrometer.
[0069] 3) After the initial circle test is completed, the probe is translated 10 mm toward the center conductor side, and the concave surface area B is turned on for the second circle of potential measurement. The rotation is also 18 seconds, and 72 potential data are collected.
[0070] 4) After the measurement of area B is completed, rotate the probe 30 degrees so that it is perpendicular to the insulator area A as a whole. At this time, the starting position of a new circle of measurement is opposite to the starting position of area B. That is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is the 180° circumference position.
[0071] 5) The rotation speed and probe acquisition speed are controlled to remain unchanged. After each circle of potential acquisition is completed, the probe is controlled by the three-axis displacement platform to move closer to the central conductor in the direction parallel to area A, moving 10 mm each time, and waiting for 18 seconds for the insulator to complete rotation. Through this method, area A is divided into 17 circles with an interval of 10 mm, and each circle contains 72 potential acquisition points. Since then, 1368 potential points on the concave surface have been collected.
[0072] 6) Turn the insulator over and start measuring the convex surface. The initial acquisition position is also in area B, with the probe perpendicular to the insulator surface and 5 mm away from the insulator. Area B also contains two circles with an interval of 10 mm, totaling 72×2, or 144 potential acquisition points.
[0073] 7) Rotate the probe 30° to be perpendicular to area A, and control the probe to gradually approach the center conductor in steps of 10 mm. Wait 18 seconds for each circle to allow the insulator to complete the rotation. The initial collection point of the convex surface area A is similar to that of area B, both at the 0° position of each circle. The convex surface area A is divided into 17 circles with an interval of 10 mm. From then on, the potential of the concave and convex surface of the pot insulator with an asymmetric surface was measured.
[0074] 8) The measured potential data are calculated by formula (1) to formula (6). It should be noted that when calculating the concave surface potential, it is necessary to rearrange the potential data on the 3rd to 19th sampling circles, that is, area A, and arrange the potential points 1 to 36 of each circle to 37 to 72, while 37 to 72 are arranged from 1 to 36. This is because the sampling starting position at the concave surface area A is 180° different from that at area B. From then on, the measurement of the surface charge of the basin insulator with an asymmetric surface is completed.
[0075] The present invention is a method for measuring the surface charge of a basin-type insulator with an asymmetric surface based on a conventional active probe method. This test method can not only improve the efficiency of measurement, but also avoid the measurement difficulties caused by the asymmetric structure of the insulator during conventional testing. When using conventional methods, the surface potential difference is large due to the constraints of the shape and structure of the insulator, which makes the charge data of the asymmetric surface lack comparability, which is an important reason affecting the characterization results and analysis accuracy. Therefore, it is necessary to study a measurement method that can standardize the experimental process, weaken the above-mentioned random influence, and improve the test efficiency. Through theoretical analysis, it is proved that the method can standardize the experimental process, improve the test efficiency, eliminate the influence of randomness, and is suitable for the measurement of basin-type insulator samples with asymmetric structures. It has certain guiding significance for the characterization and detection analysis of charge accumulation in future industrial applications.
[0076] Although the embodiments and drawings of the present invention are disclosed for illustrative purposes, those skilled in the art will appreciate that various substitutions, changes and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.
Claims
1. A method for measuring the surface charge of a double-sided asymmetric pot insulator, characterized in that: The steps of the method are: S1. Design a coaxial electrode system matched with a pot-type insulator, the coaxial electrode system comprising a pot-type insulator, a center conductor and a grounding electrode. The pot-type insulator is a nearly conical structure and is divided into a concave surface and a convex surface according to the surface shape. Each surface is divided into region A and region B, wherein region A forms an angle of 30° with the grounding electrode, and region B is perpendicular to the grounding electrode. S2. Place the pot insulator and the coaxial electrode system on the rotating motor in the experimental cavity. The grounding electrode of the coaxial electrode system is connected to the grounding side through the experimental cavity. The central conductor is connected to the high-voltage electrode of the experimental cavity. The rotating motor and the three-axis displacement platform are controlled by the rotating motor controller and the three-axis displacement controller respectively. The electrostatic probe is connected to the electrometer. The potential result measured by the electrostatic probe is recorded in the electrometer. S3, using a voltage regulator as a high-voltage DC power source to apply a high voltage to the high-voltage electrode of the experimental cavity through a current-limiting water resistor to charge the pot-type insulator, and removing the central conductor after charging to a stable state; S4, move the electrostatic probe to the concave surface area B of the pot-type insulator, and use the rotating motor and the three-axis mobile platform to drive the movement of the electrostatic probe to sequentially complete the potential data collection of 2 circles at the concave surface area B and 17 circles at the concave surface area A of the pot-type insulator; similarly, collect the potential data of 2 circles at the convex surface area B and 17 circles at the convex surface area A of the pot-type insulator, and record the collected potential data in the electrometer; S5. The collected potential data are calculated as charge density data through inversion calculation. The concave and convex surfaces of the pot-type insulator are divided into 1368 cells in the radial direction and 72 in the circumferential direction. The surface potential of each cell is independently affected by the charge of itself and the other 1367 cells. The influence of the charge of each cell on the potential of a cell is superimposed. The relationship between the surface potential and the surface charge density is shown in formula (1): in: is a matrix containing 1368 grid potentials; σ is a matrix containing 1368 grid surface charge densities; H is the coefficient matrix; As shown in equations (2) to (4): in: is the potential of the i-th unit; σ j is the surface charge density of the jth unit; h i,j represents the contribution coefficient of the surface charge of the jth unit to the potential of the i-th unit; Using COMSOL Multiphysics simulation software, the surface charge density σ of the jth unit is j Set to 1pC / mm 2 , the charge density of the other 1367 units is set to 0, and the potential value on the surface of the insulator is calculated, as shown in formula (5): Traversing j=1,…,1368, the calculated potential value is the jth column of the coefficient matrix H, and the coefficient matrix H can be obtained. By inverting the coefficient matrix H, the surface charge density is calculated by equation (6), and the Origin drawing software is used to complete the imaging of the three-dimensional charge distribution on the insulator surface:
2. The method for measuring the surface charge of a double-sided asymmetric pot insulator according to claim 1 is characterized in that: The grounding electrode is made of metal aluminum, the insulator is formed by mixing epoxy resin and Al2O3 in a mass ratio of 1:3, the radius of the pot-type insulator is 231 mm, the height is 140 mm, and the height of the grounding electrode is 180 mm.
3. The method for measuring the surface charge of a double-sided asymmetric pot insulator according to claim 1, characterized in that: The S4 is specifically as follows: the electrostatic probe is moved to the concave surface area B of the insulator 5 mm away from the ground electrode through the three-axis displacement platform, and the electrostatic probe is perpendicular to the surface of the insulator and the distance is 5 mm; at the same time, the rotating motor and the electrostatic probe acquisition are synchronously turned on, and the acquisition speed is set to 4 times per second, and the rotation speed is 20° / s. After the first rotation of 18s, 72 potential data located in the starting circle will be recorded in the electrometer; After the initial circle test is completed, the electrostatic probe is translated 10 mm toward the center conductor side, and the potential data collection of the second circle of the concave surface area B is started. The rotation is also 18 seconds, and 72 potential data are collected; After the measurement of area B is completed, the electrostatic probe is rotated 30 degrees to be perpendicular to the insulator area A. The starting position of a new circle of measurement is opposite to the starting position of area B. That is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is the 180° circumference position; The rotation speed and the electrostatic probe collection speed are controlled to remain unchanged. After each circle of potential collection is completed, the probe is controlled by the three-axis displacement platform to move toward the central conductor side in the direction parallel to area A, moving 10 mm each time, and waiting for 18 seconds for the insulator to complete the rotation, completing the potential collection of 17 circles in area A; Similarly, 19 circumferential potentials of the convex surface areas A and B are collected. Unlike the concave surface, after the measurement of the convex surface area B is completed, the measurement starting position of the convex surface area A is consistent with that of area B, that is, if the measurement starting position of area B is the 0° position of the circumference, the starting position of area A is also the 0° circumferential position.