Method for calculating magnetic field of single-rotor magnetic pendulum type mechanical antenna

Abstract

The invention discloses a method for calculating a magnetic field of a single-rotor magnetic pendulum type mechanical antenna. The method comprises the following steps of: calculating a torque generated by a stator magnetic field to a rotor, a torque generated by a coil magnetic field to the rotor and a friction torque generated by a bearing to the rotor in the single-rotor magnetic pendulum type mechanical antenna by using virtual magnetic charges; according to the torque generated by the stator magnetic field to the rotor, the torque generated by the coil magnetic field to the rotor and the friction torque generated by the bearing to the rotor, establishing a kinetic model of the rotor in the single-rotor magnetic pendulum mechanical antenna; and calculating the radiation magnetic field of the single-rotor magnetic pendulum type mechanical antenna by combining the magnetic field model of the magnetic dipole in the motion state with the kinetic model of the rotor. Establishing a dynamic model of the rotor, and providing a solving method for a radiation magnetic field of the single-rotor magnetic pendulum type mechanical antenna; according to the method, the radiation magnetic field space distribution of the single-rotor magnetic pendulum type mechanical antenna can be analyzed, the influence of the size and the structure of the single-rotor magnetic pendulum type mechanical antenna on the radiation magnetic field can be accurately analyzed, and the structural design of the antenna can be optimized.

Description

Technical Field

[0001] The invention belongs to the technical field of low-frequency communications, and in particular relates to a method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna. Background Art

[0002] Low-frequency electromagnetic waves have good penetration and play an extremely important role in long-distance and cross-medium communications. However, traditional antennas have low radiation efficiency, often occupy a large area, and the transmission system requires megawatts of power.

[0003] As a new antenna structure, the single-rotor magnetic pendulum mechanical antenna drives the rotor permanent magnet to swing through the magnetic field force, thereby emitting electromagnetic wave signals, which effectively overcomes the shortcomings of traditional antennas. It not only realizes the miniaturization of the antenna, but also can use the resonance effect to improve the radiation power and efficiency of the antenna. Therefore, accurately calculating the magnetic field of the single-rotor magnetic pendulum mechanical antenna is of great significance for mastering the radiation characteristics of the antenna and realizing the miniaturization of the antenna. Summary of the invention

[0004] The purpose of the present invention is to solve the above technical problems and to provide a single-rotor magnetic pendulum mechanical antenna magnetic field calculation method for accurately calculating the magnetic field distribution of the single-rotor magnetic pendulum mechanical antenna in space.

[0005] To achieve the above object, the present invention provides a method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna, which is as follows:

[0006] S1) using virtual magnetic charge to calculate the torque generated by the stator magnetic field on the rotor in a single-rotor magnetic pendulum mechanical antenna;

[0007] The virtual magnetic charge is used to calculate the torque generated by the coil magnetic field on the rotor in a single-rotor magnetic pendulum mechanical antenna.

[0008] The friction torque generated by the bearing on the rotor in a single-rotor magnetic pendulum mechanical antenna is calculated using virtual magnetic charge.

[0009] S2) establishing a dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna according to the torque generated by the stator magnetic field on the rotor, the torque generated by the coil magnetic field on the rotor, and the friction torque generated by the bearing on the rotor calculated in step S1);

[0010] S3) The swing angle θ of the rotor permanent magnet is analyzed by using the magnetic field model of the magnetic dipole in motion and the dynamic model of the rotor r Compute the radiated magnetic field of a single-rotor magnetic pendulum mechanical antenna.

[0011] Furthermore, in step S1), the torque generated by the stator magnetic field on the rotor is:

[0012]

[0013] T sx is the magnetic field component H of the stator permanent magnet sx The torque on the rotor, T sz is the magnetic field component H of the stator permanent magnet sz Torque on the rotor, T sxs It is T sx The amplitude, T szs It is T sz The amplitude of , t is the time, μ0 is the magnetic permeability in vacuum, M r is the magnetization intensity of the rotor permanent magnet, R r is the radius of the rotor permanent magnet, H r is the height of the rotor permanent magnet, θ r is the swing angle of the rotor permanent magnet, ξ and h are the integral variables introduced by the area element.

[0014] Furthermore, in step S1), the torque generated by the coil magnetic field on the rotor is:

[0015]

[0016] T cx is the magnetic field component H of the coil cxm The torque on the rotor, T cz is the magnetic field component H of the coil czm Torque on the rotor, T cxc It is T cx The amplitude, T czc It is T cz The amplitude of , f is the current frequency of the coil.

[0017] Furthermore, in step S1), the friction torque generated by the bearing on the rotor is:

[0018] T b =μFR r

[0019] μ is the friction coefficient of the bearing; F is the load on the bearing, F = m r g,m r is the mass of the rotor and g is the acceleration due to gravity.

[0020] Furthermore, in the step S2), the dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna is established as follows:

[0021]

[0022] is the angular velocity of the rotor, is the angular acceleration of the rotor, k = (T sxs -Tszs ) / I r is the equivalent stiffness, T f =T b / I r is the equivalent friction torque, F=(T czc -T cxc ) / I r is the equivalent exciting force, I r =m r R r 2 / 2 is the moment of inertia of the rotor, is a sign function.

[0023] Furthermore, in the step S3), the radiated magnetic field of the single-rotor magnetic pendulum mechanical antenna is calculated using the magnetic field model of the magnetic dipole in motion as follows:

[0024]

[0025] V r is the volume of the rotor permanent magnet, x p ,y p ,z p is the location of the field point, is the distance from the field point to the origin, is the unit direction vector along the X, Y, and Z axes;

[0026] The angle of the rotor permanent magnet swing is θ r The rotor dynamics model constructed according to step S2) is solved by using the Runge-Kutta method to obtain an analytical solution.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention provides a method for solving the radiation magnetic field of a single-rotor magnetic pendulum mechanical antenna by establishing a dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna; the present invention can analyze the spatial distribution of the radiation magnetic field of the single-rotor magnetic pendulum mechanical antenna, and can accurately analyze the influence of the size and structure of the single-rotor magnetic pendulum mechanical antenna on the radiation magnetic field, which is helpful to optimize the structural design of the antenna. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a schematic diagram of a single-rotor magnetic pendulum mechanical antenna;

[0029] Figure 2 for Figure 1 Schematic diagram of the principle;

[0030] Figure 3a , 3b This is a schematic diagram of the rotor force in a single-rotor magnetic pendulum mechanical antenna;

[0031] Figure 4 It is a schematic diagram of the moving magnetic dipole and the position of the field point;

[0032] Figure 5a This is the time domain diagram of the magnetic field of a single-rotor magnetic pendulum mechanical antenna;

[0033] Figure 5b This is the frequency domain diagram of the magnetic field of a single-rotor magnetic pendulum mechanical antenna. DETAILED DESCRIPTION

[0034] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0035] The following is a detailed introduction to the embodiments of the present invention:

[0036] 1) Calculation method of the torque generated by the stator magnetic field on the rotor in a single-rotor magnetic swing mechanical antenna:

[0037] One of the core components of the magnetic pendulum mechanical antenna is a cylindrical permanent magnet rotor placed along the Y axis, with a radius of R. r , length is H r The magnetization intensity of the rotor is M r , radial magnetization along the X-axis direction, thus generating a magnetic field in space. The motion of the rotor is a single-degree-of-freedom swing, and the swing angle at time t is recorded as θ r (t). As an important component of the mechanical antenna, the stator has dimensions of 2L along the X-axis, Y-axis, and Z-axis. s , 2D s , 2H s , the two stators are placed symmetrically along the X axis, with a center distance of 2D ss , the stator magnetization intensity is M s , magnetized along the X-axis direction, the two stators will generate a stable background magnetic field near the rotor, such as Figure 1 , Figure 2 shown.

[0038] Assuming the rotor is uniformly magnetized, the rotor volume magnetic charge density is Surface magnetic charge density of the rotor in is the unit normal vector of the rotor surface, is the magnetization intensity vector of the permanent magnet; since the rotor is perpendicular to the Y axis, the surface magnetic charge density σ of the rotor on its two circular surfaces S = 0. The magnetic charge of the rotor is mainly distributed on the cylindrical surface, and the surface magnetic charge density can be expressed as in is the angle between the area element and the magnetization direction of the rotor, such as Figure 3a shown.

[0039] Take the area element at the symmetrical position on the rotor cylindrical surface is the radian of the area element, dh is the height of the area element, and the magnetic charges of the area element are:

[0040]

[0041] Where the magnetic charge dq m The unit is A·m. The area elements at the symmetrical positions are positive and negative magnetic charges, forming a pair of magnetic dipoles, as shown in Figure 3(b). The magnitude of the magnetic dipole moment is:

[0042]

[0043] The unit of magnetic dipole moment is A·m 2 , the direction is

[0044] Stator magnetic field component H sx The angle between the magnetic dipole moment dm is The magnetic dipole is subject to a torque dT sx (t); stator magnetic field component H sz The angle between the magnetic dipole moment dm is The magnetic dipole is subject to a torque dT sz (t).

[0045]

[0046] In the formula is the magnetic dipole moment vector, and is the stator magnetic field component H sx and H sz vector, μ0=4π×10 - 7 N / A 2 is the magnetic permeability in vacuum, the torque dT sx The positive direction is clockwise, and the torque dT sz The positive direction is counterclockwise.

[0047] The background magnetic field generated by the stator structure in the antenna in space is:

[0048]

[0049] Where x, y, z are the positions of the spatial field points, and the auxiliary function f(x, y, z, L s ,D s ,H s ) and g(x,y,z,L s ,D s ,H s ) is defined as:

[0050]

[0051] The auxiliary function Γ(x,y,z,L s ,D s ,H s ) and Φ(x,y,z,L s ,D s ,H s ) is defined as:

[0052]

[0053] The function sgn(x) is a sign function.

[0054] Combined with formula (3) and (4), when the rotor swing angle is θ r At (t), the rotor is in the stator magnetic field component H sx The torque on is:

[0055]

[0056] Among them, the parameter T sxs and T sxc for:

[0057]

[0058] The parameters ξ and h are integral variables introduced by the area element, and the parameters The purpose of parameter transformation is to transform the variable θ in formula (7) r Separate from the integral to facilitate subsequent processing of the integral. At this time, the parameter T in formula (7) sxs and T sxc It has nothing to do with the time variable, but only with the antenna structure. sx (R r cosξ,h,R r sinξ) is an even function of the variable ξ, with parameter T sxc = 0, the torque (7) can be further simplified to:

[0059] T sx (t) = T sxs sinθ r (t) (9)

[0060] Similarly, when the rotor swings at an angle of θ r At (t), the rotor is in the stator magnetic field H sz The torque on is:

[0061]

[0062] Among them, the parameter T szs and T szc for:

[0063]

[0064] Due to the magnetic field H sz (R r cosξ,h,R r sinξ) is an odd function of the variable ξ, with parameter T szc = 0, the moment (10) is further simplified to:

[0065] T sz (t) = T szs sinθ r (t) (12)

[0066] 2) Calculation method of the torque generated by the coil magnetic field on the rotor in a single-rotor magnetic pendulum mechanical antenna:

[0067] In order to simplify the model, the article ignores the influence of coil height and thickness and assumes that the coil is concentrated in the XOY plane and the size is -L c ≤x≤L c , -D c ≤y≤D c , the number of turns is N c .

[0068] A sinusoidal current I flows through the coil. c , the current frequency is f. According to the Biot-Savart law, the magnetic field generated by the coil in space P(x,y,z) is for:

[0069]

[0070] In the formula is the current element, r c is the distance from the current element to point P, is the unit direction vector from the current element to point P. Ignoring the influence of the coil corners, the coil magnetic field can be regarded as the resultant magnetic field of four straight wires.

[0071]

[0072] Where H cxm ,H cym ,H czm The amplitude of the magnetic field generated by the coil along the X-axis, Y-axis, and Z-axis. ± ,y ± , α ± , β ± , for:

[0073]

[0074] right Figure 3b The magnetic dipole in the coil generates a magnetic field H cx The angle between (t) and the magnetic dipole moment dm(t) is The magnetic dipole is subject to a torque dT cx (t); the magnetic field H generated by the coil cz The angle between (t) and the magnetic dipole moment dm(t) is The magnetic dipole is subject to a torque dT cz (t).

[0075]

[0076] Where torque dT cx The positive direction of (t) is clockwise, and the torque dT cz The positive direction of (t) is counterclockwise.

[0077] When the rotor angle is θ r At (t), the rotor is in the magnetic field H cx The moment in (t) is:

[0078]

[0079] Among them, the parameter T cxs and T cxc for:

[0080]

[0081] in Due to the magnetic field H cxm (R r cosξ,h,R r sinξ) is an odd function of the variable ξ, with parameter T cxs = 0, the torque (17) is further simplified to:

[0082] T cx (t) = T cxc cosθ r (t)sin(2πft) (19)

[0083] Similarly, the rotor is in the magnetic field H cz The torque on is:

[0084]

[0085] Among them, the parameter T czs and T czc for:

[0086]

[0087] Due to the magnetic field Hczm (R r cosξ,h,R r sinξ) is an even function of the variable ξ, and the integral T czs = 0, the moment (20) is further simplified to:

[0088] T cz (t) = T czc cosθ r (t)sin(2πft) (22)

[0089] 3) Calculation method of friction torque generated by bearing on rotor in single-rotor magnetic pendulum mechanical antenna

[0090] During the operation of the mechanical antenna, it will be affected by the friction torque caused by the bearing. The friction torque acts as a damper to suppress the swing of the rotor, which will affect the swing amplitude of the rotor and the characteristic frequency of the system swing. Therefore, it is very important to analyze the influence of the friction torque on the rotor motion. The rotor is supported by bearings at both ends, and friction will be generated in the bearings when the rotor rotates. The bearing friction torque is:

[0091] T b =μFR r (twenty three)

[0092] Where μ is the friction coefficient of the bearing; F is the load on the bearing, F = m r g,m r =ρ r πR r 2 H r is the rotor mass, ρ r is the rotor density.

[0093] 4) Establish the dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna

[0094] The rotor is subjected to torque T sx (t), T sz (t), T cx (t) and T cz (t) acts, the rotor moves under the action of the resultant torque, and the differential equation of the rotor force is:

[0095]

[0096] Where k = (T sxs -T szs ) / I r is the equivalent stiffness, T f =T b / I r is the equivalent friction torque, F=(T czc -T cxc) / I r is the equivalent exciting force, I r =m r R r 2 / 2 is the moment of inertia of the rotor, is a sign function, is the angular velocity of the rotor, is the angular acceleration of the rotor. The Runge-Kutta method is used to solve equation (24) to obtain the swing angle θ of the rotor permanent magnet: r .

[0097] 5) Calculation method of the magnetic field radiated by a single-rotor magnetic pendulum mechanical antenna

[0098] The rotor will generate an alternating electromagnetic field in space during its movement, thereby transmitting signals to the outside. Therefore, it is particularly important to study the electromagnetic field model of the rotor movement. Based on the solved analytical solution of the rotor motion and the magnetic field model of the magnetic dipole in the moving state, the magnetic field model of the rotor in the moving state was constructed. Figure 4 In the coordinate system shown, the rotor axis is placed along the Y axis, and two magnetic charge elements ±q are selected at symmetrical positions on the cylindrical surface with a height of h. m It forms a magnetic dipole, the angle between the magnetic dipole and the X-axis is θ, and the angle between the magnetic dipole and the Y-axis is φ.

[0099] against Figure 4 The coordinate system shown, the transformation relationship from the rectangular coordinate system to the spherical coordinate system is:

[0100]

[0101] In the formula is the distance in spherical coordinates, R r is the rotor radius. The magnetic charge of the rotor is concentrated on the cylindrical surface in the form of a magnetic dipole. When the rotor moves, the magnetic dipole will move in the same way. The magnetic field model of the magnetic dipole in motion is:

[0102]

[0103] The subscript τ in the formula indicates that the parameter in the formula is the time of magnetic dipole movement, that is, the moment when the electromagnetic wave is generated, τ = tR / c, t is the time when the electromagnetic wave reaches the field point, and hysteresis occurs at the receiving point due to the influence of the receiving distance; c = 3×10 8 m / s is the speed of light; R is the distance from the center of the magnetic dipole to the field point; is the unit direction vector of the distance from the magnetic dipole to the field point; is the magnetic dipole moment vector of the magnetic dipole; the parameter is the velocity of the magnetic dipole at time τ.

[0104] Combined with the actual situation, the following simplifications are made to formula (26):

[0105] (1) The electromagnetic wave propagates at the speed of light, and the time delay caused by the distance between the receiving point and the transmitting point can be ignored, τ≈t;

[0106] (2) The rotational speed of the rotor is much smaller than the speed of light, v<<c, so the parameter

[0107] (3) The size of the rotor is relatively small compared to the distance of the field point. Ignoring the size effect of the rotor, R can be approximated as the distance r from the origin to the field point, and n can be approximated as the unit distance vector from the origin to the field point

[0108] At this time, formula (26) will be simplified to:

[0109]

[0110] where In formula (27), the first term of the magnetic field is inversely proportional to r 3 and dominates in the near field region; the second term is inversely proportional to r 2 and dominates in the intermediate field region; the third term is inversely proportional to r and dominates in the far field region.

[0111] When in the near field range, only the first term in the radiation magnetic field needs to be considered. At this time, the magnetic field is simplified to:

[0112]

[0113] As Figure 4 shown, the magnetic charges at symmetric positions on the cylindrical surface form a magnetic dipole. The azimuth angle θ r of the magnetic dipole is the angle of the rotor swing, is the angle between the area element and the magnetization direction of the rotor. The magnetic dipole moment is:

[0114]

[0115] For the convenience of integral operation, we expand the electromagnetic field (28) in the rectangular coordinate system. Assuming the position of the field point is P(x p , y p , z p ), and the direction vector where is the unit direction vector of the X-axis, is the unit direction vector of the Z-axis; substituting formula (29) into the electromagnetic field formula (28), the magnetic field of the magnetic dipole in the near field range is obtained:

[0116]

[0117] By integrating formula (30), we can obtain the magnetic field of the rotor in the near field:

[0118]

[0119] See also Figure 5a , 5b , is the magnetic field signal captured by the magnetic field receiving device at a height of 50cm and the corresponding theoretical calculation result when an alternating current of 200Hz is applied to the excitation coil. At this time, the spatial magnetic field of the antenna is the superposition of the magnetic field generated by the rotor and the magnetic field of the coil. It can be seen that the experimental test results are consistent with the theoretical calculation results. At the same time, the spatial magnetic field is simple harmonic and consistent with the excitation coil frequency. Based on the experimental results, the frequency of the magnetic field can be changed by adjusting the frequency of the excitation coil, thereby achieving the purpose of extracting signals at the receiving end to transmit information.

Claims

1. A method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna, characterized in that: The magnetic field calculation method of the single-rotor magnetic pendulum mechanical antenna is specifically as follows: S1) using virtual magnetic charge to calculate the torque generated by the stator magnetic field on the rotor in a single-rotor magnetic pendulum mechanical antenna; The virtual magnetic charge is used to calculate the torque generated by the coil magnetic field on the rotor in a single-rotor magnetic pendulum mechanical antenna. The friction torque generated by the bearing on the rotor in a single-rotor magnetic pendulum mechanical antenna is calculated using virtual magnetic charge. S2) establishing a dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna according to the torque generated by the stator magnetic field on the rotor, the torque generated by the coil magnetic field on the rotor, and the friction torque generated by the bearing on the rotor calculated in step S1); S3) The swing angle θ of the rotor permanent magnet is analyzed by using the magnetic field model of the magnetic dipole in motion and the dynamic model of the rotor r Compute the radiated magnetic field of a single-rotor magnetic pendulum mechanical antenna.

2. The method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna according to claim 1, characterized in that: In step S1), the torque generated by the stator magnetic field on the rotor is: T sx is the magnetic field component H of the stator permanent magnet sx The torque on the rotor, T sz is the magnetic field component H of the stator permanent magnet sz Torque on the rotor, T sxs It is T sx The amplitude, T szs It is T sz The amplitude of , t is the time, μ0 is the magnetic permeability in vacuum, M r is the magnetization intensity of the rotor permanent magnet, R r is the radius of the rotor permanent magnet, H r is the height of the rotor permanent magnet, θ r is the swing angle of the rotor permanent magnet, ξ and h are the integral variables introduced by the area element.

3. The method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna according to claim 2, characterized in that: In step S1), the torque generated by the coil magnetic field on the rotor is: T cx is the magnetic field component H of the coil cxm The torque on the rotor, T cz is the magnetic field component H of the coil czm Torque on the rotor, T cxc It is T cx The amplitude, T czc It is T cz The amplitude of , f is the current frequency of the coil.

4. The method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna according to claim 3, characterized in that: The friction torque generated by the bearing on the rotor in step S1) is: T b =μFR r μ is the friction coefficient of the bearing; F is the load on the bearing, F = m r g,m r is the mass of the rotor and g is the acceleration due to gravity.

5. The method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna according to claim 4, characterized in that: In the step S2), the dynamic model of the rotor in the single-rotor magnetic pendulum mechanical antenna is established as follows: is the angular velocity of the rotor, is the angular acceleration of the rotor, k = (T sxs -T szs ) / I r is the equivalent stiffness, T f =T b / I r is the equivalent friction torque, F=(T czc -T cxc ) / I r is the equivalent exciting force, I r =m r R r 2 / 2 is the moment of inertia of the rotor, is a sign function.

6. The method for calculating the magnetic field of a single-rotor magnetic pendulum mechanical antenna according to claim 5, characterized in that: In the step S3), the radiated magnetic field of the single-rotor magnetic pendulum mechanical antenna is calculated using the magnetic field model of the magnetic dipole in motion as follows: V r is the volume of the rotor permanent magnet, x p ,y p ,z p is the location of the field point, is the distance from the field point to the origin, is the unit direction vector along the X, Y, and Z axes; The angle of the rotor permanent magnet swing is θ r The rotor dynamics model constructed according to step S2) is solved by using the Runge-Kutta method to obtain an analytical solution.

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