CN107330151B - Extraction method of small-hole electric polarization coefficient - Google Patents
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- CN107330151B CN107330151B CN201710399796.6A CN201710399796A CN107330151B CN 107330151 B CN107330151 B CN 107330151B CN 201710399796 A CN201710399796 A CN 201710399796A CN 107330151 B CN107330151 B CN 107330151B
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Abstract
The invention discloses a method for extracting a small-hole electric polarization coefficient, belonging to the technical field of electromagnetic shielding. The method comprises the following steps: creating a perforated shield model in electromagnetic field numerical calculation software, and applying material properties and boundary conditions; calculating by software to obtain the electric field intensity on the central axis of the opening in the shield body, and subtracting the uniform electric field intensity between the plates from the electric field intensity to obtain the electric field intensity related to the small hole; taking the result of the measurement at a certain distance from the center of the opening as the electric field strength suitable for calculation; and performing exponential fitting on the electric field intensity suitable for calculation and the distance between the measuring point and the center of the hole, and obtaining the electric polarization coefficient of the small hole by using the fitted coefficient. The invention obtains the calculation of the electric polarization coefficient of the open hole of the perforated shield without being limited to the creep of the shape of the open hole, and can more accurately obtain the electric polarization coefficient of the open hole in a perforated shield model with limited size.
Description
Technical Field
The invention belongs to the technical field of electromagnetic shielding, and particularly relates to a method for extracting an electric polarization coefficient of a small hole.
Background
The metal cavity is used for shielding, which is one of the commonly used technical means for inhibiting electromagnetic disturbance. In practical application, various power electronic devices as small as various power electronic devices and various test places as large as various test places are shielded by a metal cavity to isolate external electromagnetic disturbance. In fact, most shields have openings for communication, ventilation, heat dissipation, and the like. The presence of the openings provides a coupling path for electromagnetic fields inside and outside the shield, thereby greatly impairing the shielding performance of the shield. Therefore, the method has important engineering and social significance for the research of the open pore.
At present, the shielding of electromagnetic waves is studied more in the research of the perforated shielding body, but in practice, the problem of shielding low-frequency electric fields, such as shielding near transformer substations and high-voltage equipment, is also encountered. According to the standard GB8702-2014 of electromagnetic environment control limit value, in order to control public exposure caused by an electric field, the electric field intensity in the environment is less than a certain limit value, and when the frequency is within a certain range
The electric field intensity is not more than 8000V/m, and at 50Hz, the electric field intensity is not more than 4000V/m. Therefore, the electrostatic field (low-frequency electric field) is used as a research object to research, and guidance can be provided for the design of the shielding body.
The Bethe theory describes the electromagnetic leakage characteristic of the hole by using the polarization coefficient of the hole, and is an important theory for evaluating the shielding performance of the hole. From this theory, it is known that for small holes having a size much smaller than the wavelength of the incident wave, the electromagnetic field leaking from the hole to the shielded side can be expressed as a field of electric dipoles, magnetic dipoles located on the aperture, regardless of the thickness of the perforated conductor, where the electric dipole moment is proportional to the normal component of the incident electric field and the proportionality coefficient is called the electric polarisation coefficient. It can be shown that the above theory is still true when the aperture is in an electrostatic field, and that the electric susceptibility is equal to that in the case of electromagnetic waves. In the existing open pores, only circular holes and elliptical holes have analytical formulas of electric polarization coefficients, and other various open pores such as rectangular holes, cross-shaped holes and even irregular open pores can be extracted only by means of a numerical calculation method or a test method. Therefore, an object of the present invention is to obtain an electric polarization coefficient of an arbitrary shape opening by using a finite size model of a shield with holes in the case of electrostatic field simulation.
Disclosure of Invention
The invention aims to provide a method for extracting an electric polarization coefficient of a small hole, which is characterized by comprising the following steps: the method is a simulation method based on electrostatic field conditions, and utilizes electromagnetic field numerical calculation software to obtain the electric field distribution in a shield with holes, and further reversely deduces the electric polarization coefficient of the opening with any shape according to the electric field strength result at a proper position; the method specifically comprises the following steps:
step 1: creating a perforated shield model in electromagnetic field numerical calculation software, and applying material properties and boundary conditions;
step 2: calculating the electric field intensity on the central axis of the opening in the shield body through software, and subtracting the uniform electric field intensity between the plates from the electric field intensity to obtain the electric field intensity related to the small hole, wherein the uniform electric field intensity between the plates is equal to the potential difference between the upper or lower polar plate and the middle polar plate/the distance between the upper or lower polar plate and the middle polar plate;
and step 3: taking the result of the electric field intensity related to the small hole obtained in the step 2 at a certain distance from the center of the opening as the electric field intensity suitable for calculation;
and 4, step 4: performing exponential fitting on the electric field intensity suitable for calculation obtained in the step 3 and the distance between the measuring point and the center of the hole, wherein in the fitting process, y is defined as the electric field intensity on the central axis of the hole, and z is defined asThe distance from the observation point to the center of the opening and the fitting equation is E ═ azb. Where a is the coefficient related to the small-pore electric polarization coefficient and b represents the field strength variation with distance in several directions (b should theoretically be 3 according to the characteristics of the electric dipole). And obtaining the electric polarization coefficient of the small hole by using the fitted coefficient a.
The establishment of the shielding body model with the holes in the step 1 comprises the following steps:
step 101: creating a cube model, wherein the upper surface and the lower surface of the cube are square, the side length of the cube is not less than 30 times of the size of the opening of the middle belt plate, and the height of the cube is not less than 10 times of the size of the opening;
step 102: applying a potential of 10V to the upper horizontal metal plate and the lower horizontal metal plate of the cubic model, and applying a potential of 0V to the middle perforated metal plate;
step 103: the dielectric material is set to be vacuum in the cubic model, namely the relative dielectric constant is 1;
the step 3 also comprises a step of determining an electric field intensity observation range suitable for calculation, and the step comprises the following steps:
step 301: determining the one-dimensional maximum size of the opening, defining the one-dimensional maximum size as the distance between two farthest points on the geometric figure of the opening, and taking 5 times of the one-dimensional maximum size as the lower limit of the electric field intensity observation distance in the step 3;
step 302: the shield depth is determined as the distance between the surface of the shield opening and its parallel opposing surface, and half the shield depth is taken as the upper limit of the observed distance of the electric field strength in step 3.
In the step 4, the exponential fitting of the electric field strength and the distance between the measuring point and the hole center is carried out, and in the Bethe theory, the relation between the equivalent electric dipole moment of the opening and the electric polarization coefficient is that P is α0E0ezWherein α is the electric polarization coefficient, E0The difference of the electric field intensity of two sides when the hole plane is not opened; namely, the field intensity on the central axis of the opening is expressed as the field intensity of the electric dipole along the direction of the electric dipole moment; the electric field intensity of a pair of electric dipoles with electric dipole moment P along the direction of the electric dipole moment is easily calculated by Coulomb's law
Where z is the distance of the observation point to the center of the electric dipole,0the dielectric constant of the vacuum is shown, and z is the distance from an observation point to the center of the electric dipole; obtaining the relationship between the electric polarization coefficient of the opening to be measured and the magnitude of the observed field intensity according to the two formulas,
comparing the equation with the fitting equation in step 4 can obtain the electric polarization coefficient.
The method has the advantages that the calculation of the electric polarization coefficient of the opening of the perforated shield is not limited to the gentle rigidity of the shape of the opening, and the electric polarization coefficient of the opening can be accurately obtained in a perforated shield model with a limited size.
Drawings
Fig. 1 is a simulation model diagram.
FIG. 2 shows the fitting result of the electric field intensity and the observed distance in the calculation of the circular hole electric polarization coefficient.
FIG. 3 shows the fitting result of the electric field intensity and the observed distance in the calculation of the electric polarization coefficient of the square hole.
Fig. 4 is a cross-hole shape.
FIG. 5 shows the fitting result of the electric field intensity and the observation distance in the calculation of the electric polarization coefficient of the cross-shaped hole.
Detailed Description
The invention provides a method for extracting an electric polarization coefficient of a small hole, which is a simulation method based on electrostatic field conditions, and is characterized in that electric field distribution in a shielding body with holes is obtained by utilizing electromagnetic field numerical calculation software, and the electric polarization coefficient of an opening with any shape is reversely deduced according to the electric field strength result at a proper position; the method specifically comprises the following steps:
step 1: creating a perforated shield model in electromagnetic field numerical calculation software, and applying material properties and boundary conditions;
step 2: calculating the electric field intensity on the central axis of the opening in the shield body through software, and subtracting the uniform electric field intensity between the plates from the electric field intensity to obtain the electric field intensity related to the small hole, wherein the uniform electric field intensity between the plates is equal to the potential difference between the upper or lower polar plate and the middle polar plate/the distance between the upper or lower polar plate and the middle polar plate;
and step 3: taking the result of the electric field intensity related to the small hole obtained in the step 2 at a certain distance from the center of the opening as the electric field intensity suitable for calculation;
and 4, step 4: and (4) performing exponential fitting on the electric field intensity suitable for calculation obtained in the step (3) and the distance between the measuring point and the center of the hole, and obtaining the electric polarization coefficient of the small hole by using the fitted coefficient.
The preferred embodiments will be described in detail below with reference to the accompanying drawings.
Example 1
The electric polarization coefficient of the circular hole is extracted. The specific execution steps are as follows:
step 1: creating a cubic model as shown in the attached figure 1, wherein the side length of an upper horizontal metal plate and a lower horizontal metal plate of the model is 1m, and the radius of a circular hole is 0.01 m; applying a potential of 10V to the upper and lower horizontal metal plates of the model, and applying a potential of 0V to the middle perforated metal plate; the dielectric material in the cube is set to vacuum, i.e., has a relative dielectric constant of 1.
Step 2: and calculating the electric field intensity on the central axis of the opening in the shield body by software, and subtracting the uniform electric field intensity between the plates by 20V/m.
And step 3: an observation distance suitable for calculation is determined. The one-dimensional maximum size of the round hole in the model is 0.02m in diameter, so the lower limit of the distance between the observation point and the center of the hole is 0.1 m. The shield depth is 0.5m, so the upper limit of the distance from the observation point to the center of the opening is 0.25 m.
And 4, step 4: and (3) performing exponential fitting on the electric field strength in the region determined in the step (3) and the observation distance to obtain a result as shown in the attached figure 2.
In the fitting process, y is defined as the electric field intensity on the central axis of the opening, z is the distance from the observation point to the center of the opening, and the fitting equation is E-azb. Wherein a is a system related to the electric polarization coefficient of the small holeThe number, b, represents the change in field strength with distance (b should be 3 theoretically, depending on the characteristics of the electric dipole.) the fitting results in a-8.524 × 10-6And b is-2.960, and the fitting coefficient is compared with the formula 1 to obtain α which is 1.338 × 10-6m3。
Because the electric polarization coefficient of the round hole has analytic calculation formula
r is the radius of the circular hole, so that the electric polarization coefficient of the circular hole in the model is 1.333 × 10-6m3. The result is similar to the result obtained by the method of the invention, and the error is not more than 0.5 percent.
Example 2
For the electric polarization coefficient of the square hole, the method can be adopted for extraction. The specific execution steps are as follows:
step 1: creating a cube model as shown in the attached drawing 1, wherein the side length of the cube is 1m, the hole formed in the middle plate is replaced by a square hole, and the side length is 0.02 m; applying a potential of 10V to the upper and lower horizontal metal plates of the model, and applying a potential of 0V to the middle perforated metal plate; the dielectric material in the cube is set to vacuum, i.e., has a relative dielectric constant of 1.
Step 2: and calculating the electric field intensity on the central axis of the opening in the shield body by software, and subtracting the uniform electric field intensity between the plates by 20V/m.
And step 3: an observation distance suitable for calculation is determined. The one-dimensional maximum size of the round hole in the model is 0.02m, so the lower limit of the distance between the observation point and the center of the hole is 0.1 m. The shield depth is 0.5m, so the upper limit of the distance from the observation point to the center of the opening is 0.25 m.
And 4, step 4: and (3) performing exponential fitting on the electric field strength in the region determined in the step (3) and the observation distance to obtain a result as shown in the attached figure 3.
Fitting results a-7.290 × 10-6And b is-2.950. comparing the fitting coefficient with the formula 1, α is 1.143 × 10-6m3。
Example 3
For the electric polarization coefficient of the cross-shaped hole, the method can be adopted for extraction. The specific execution steps are as follows:
step 1: creating a cube model shown in the attached drawing 1, wherein the side length of the cube is 1m, the opening of the middle plate is replaced by a cross-shaped hole shown in the attached drawing 4, and l is 0.01 m; applying a potential of 10V to the upper and lower horizontal metal plates of the model, and applying a potential of 0V to the middle perforated metal plate; the dielectric material in the cube is set to vacuum, i.e., has a relative dielectric constant of 1.
Step 2: and calculating the electric field intensity on the central axis of the opening in the shield body by software, and subtracting the uniform electric field intensity between the plates by 20V/m.
And step 3: an observation distance suitable for calculation is determined. The one-dimensional maximum size of the round hole in the model is 0.03m, so the lower limit of the distance between the observation point and the center of the opening is 0.15 m. The shield depth is 0.5m, so the upper limit of the distance from the observation point to the center of the opening is 0.25 m.
And 4, step 4: the electric field strength in the region determined in step 3 and the observation distance are subjected to exponential fitting, and the obtained result is shown in fig. 5.
Fitting results a-3.311 × 10-7B-2.915. comparing the fitting coefficient with formula 1, α -1.956 × 10-6m3。
Claims (3)
1. A method for extracting the electric polarization coefficient of a small hole is characterized by comprising the following steps: the method is a simulation method based on electrostatic field conditions, and utilizes electromagnetic field numerical calculation software to obtain electric field distribution in a shield with holes, further obtain an electric field strength result at a proper position, and reversely deduce the electric polarization coefficient of an opening with any shape; the method specifically comprises the following steps:
step 1: creating a perforated shield model in electromagnetic field numerical calculation software, and applying material properties and boundary conditions;
step 2: calculating the electric field intensity on the central axis of the opening in the shield body through software, and subtracting the uniform electric field intensity between the plates from the electric field intensity to obtain the electric field intensity related to the small hole, wherein the uniform electric field intensity between the plates is equal to the potential difference between the upper or lower polar plate and the middle polar plate/the distance between the upper or lower polar plate and the middle polar plate;
and step 3: taking the result of the electric field intensity related to the small hole obtained in the step 2 on the distance between the upper or lower polar plate and the middle polar plate from the center of the opening as the electric field intensity suitable for calculation;
and 4, step 4: performing exponential fitting on the electric field intensity suitable for calculation obtained in the step 3 and the distance between the measuring point and the hole center, defining E as the electric field intensity on the central axis of the hole, defining z as the distance between the observation point and the hole center, and defining a fitting equation as E-azbThe method comprises the steps of obtaining the electric polarization coefficient of the small hole by using the fitting coefficient a, obtaining the exponential fitting of the electric field intensity and the distance between a measuring point and the center of the hole by using the fitting coefficient a, and obtaining the relation between the equivalent electric dipole moment of the open hole and the electric polarization coefficient in the Bethe theory that the relation between the equivalent electric dipole moment of the open hole and the electric polarization coefficient is P- α0E0ezWherein α is the electric polarization coefficient, E0The difference of the electric field intensity of two sides when the hole plane is not opened; namely, the field intensity on the central axis of the opening is expressed as the field intensity of the electric dipole along the direction of the electric dipole moment; the electric field intensity of a pair of electric dipoles with electric dipole moment P along the direction of the electric dipole moment is easily calculated by Coulomb's law
Where z is the distance from the observation point to the center of the opening,0is a vacuum dielectric constant according to the above P- α0E0ezAnd
the second expression obtains the relationship between the electric polarization coefficient of the opening to be measured and the magnitude of the observed field intensity as the following expression,
compare the equation with the fitting equation E ═ azbAnd obtaining the electric polarization coefficient.
2. The method for extracting the electric polarization coefficient of the small hole according to claim 1, wherein: the establishment of the shielding body model with the holes in the step 1 comprises the following steps:
step 101: creating a cube model, wherein the upper surface and the lower surface of the cube are square, the side length of the cube is not less than 30 times of the size of the opening of the middle belt plate, and the height of the cube is not less than 10 times of the size of the opening;
step 102: applying a potential of 10V to the upper horizontal metal plate and the lower horizontal metal plate of the cubic model, and applying a potential of 0V to the middle perforated metal plate;
step 103: in the cubic model, the dielectric material is set to a vacuum, i.e., a relative dielectric constant is 1.
3. The method for extracting the electric polarization coefficient of the small hole according to claim 1, wherein: the step 3 also comprises a step of determining an electric field intensity observation range suitable for calculation, and the step comprises the following steps:
step 301: determining the one-dimensional maximum size of the opening, defining the one-dimensional maximum size as the distance between two farthest points on the geometric figure of the opening, and taking 5 times of the one-dimensional maximum size as the lower limit of the electric field intensity observation distance in the step 3;
step 302: the shield depth is determined as the distance between the surface of the shield opening and its parallel opposing surface, and half the shield depth is taken as the upper limit of the observed distance of the electric field strength in step 3.
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