Calculation method for magnetic field of birotor magnetic pendulum type mechanical antenna

Abstract

The invention discloses a method for calculating a magnetic field of a double-rotor magnetic pendulum type mechanical antenna. Calculating the torque generated by a stator magnetic field to the double rotors, the torque generated by a coil magnetic field to the double rotors, the friction torque generated by a bearing to the double rotors, the torque generated by a second rotor magnetic field to the first rotor and the torque generated by the first rotor magnetic field to the second rotor in the double-rotor magnetic pendulum type mechanical antenna; establishing a dynamical model of double rotors in the double-rotor magnetic pendulum type mechanical antenna according to the torque; and calculating the radiation magnetic field of the double-rotor magnetic pendulum type mechanical antenna by using the double-rotor dynamic model. Establishing a dynamic model of the double rotors, and providing a solving method for a radiation magnetic field of the double-rotor magnetic pendulum type mechanical antenna; according to the method, the radiation magnetic field space distribution of the double-rotor magnetic pendulum type mechanical antenna can be analyzed, the influence of the size and the structure of the double-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 communication, and in particular relates to a method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna. Background Art

[0002] Low-frequency electromagnetic waves play a vital role in long-distance and cross-media information transmission due to their excellent penetration ability. However, traditional antennas have certain limitations in radiation efficiency, resulting in large antenna sizes, and in order to achieve effective communication effects, the transmission system often needs to consume a lot of power.

[0003] The dual-rotor magnetic pendulum mechanical antenna drives the two rotor permanent magnets to swing periodically through the magnetic field force, thereby generating electromagnetic wave signals, which not only effectively overcomes the limitations of the radiation efficiency of traditional antennas, but also realizes the miniaturization of the antenna. The working principle of the dual-rotor magnetic pendulum mechanical antenna is based on the interaction between the magnetic field and the two permanent magnet rotors. When the rotor swings, it will excite an alternating magnetic field in the surrounding space, and then propagate electromagnetic waves outward. Through structural design, the antenna can resonate at a specific frequency, thereby significantly improving the radiation power and efficiency. This feature enables the dual-rotor magnetic pendulum mechanical antenna to provide radiation performance comparable to that of traditional large antennas while maintaining a compact size. Therefore, accurately calculating the magnetic field of the dual-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 method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna, which is used to calculate the magnetic field distribution of the dual-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 dual-rotor magnetic pendulum mechanical antenna, comprising two identical first rotors and second rotors. The method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna is specifically as follows:

[0006] S1) Calculate the torque generated by the stator magnetic field on the dual rotors in the dual rotor magnetic pendulum mechanical antenna;

[0007] Calculate the torque generated by the coil magnetic field on the dual rotors in the dual rotor magnetic pendulum mechanical antenna;

[0008] Calculate the friction torque generated by the bearings on the dual rotors in the dual-rotor magnetic pendulum mechanical antenna;

[0009] Calculate the torque generated by the magnetic field of the second rotor on the first rotor and the torque generated by the magnetic field of the first rotor on the second rotor in the dual-rotor magnetic swing mechanical antenna;

[0010] S2) establishing a dynamic model of the dual rotors in the dual rotor magnetic pendulum mechanical antenna according to the torque generated by the stator magnetic field on the dual rotors, the torque generated by the coil magnetic field on the dual rotors, the friction torque generated by the bearings on the dual rotors, and the torque generated by the rotor magnetic field on the other rotor calculated in step S1);

[0011] S3) The angle θ of the dual rotor permanent magnet swing analyzed by the dual rotor dynamics model r1 and θ r2 Calculate the radiated magnetic field of a dual-rotor magnetic pendulum mechanical antenna.

[0012] Furthermore, in step S1), the torque generated by the stator magnetic field on the dual rotors is:

[0013] T s1 (t)=(T sz -T sx )sinθ r1 (t)

[0014] T s2 (t)=(T sz -T sx )sinθ r2 (t)

[0015] T s1 is the torque generated by the stator magnetic field on the first rotor, T s2 is the torque generated by the stator magnetic field on the second rotor, T sx and T sz is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure, θ r1 is the swing angle of the first rotor at time t, θ r2 is the swing angle of the second rotor at time t.

[0016] Furthermore, in step S1), the torque generated by the coil magnetic field on the dual rotor is:

[0017] T c1 =(T cz -T cx )cosθ r1 (t)sin(2πft)

[0018] T c2 =(T cz -T cx )cosθ r2 (t)sin(2πft)

[0019] T c1 is the torque generated by the coil magnetic field on the first rotor, T c2 is the torque generated by the coil magnetic field on the second rotor, T cx and T czis a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure, and f is the current frequency of the coil.

[0020] Furthermore, in step S1), the friction torque generated by the bearing on the dual rotor is:

[0021] T b =μFR r

[0022] 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 a single rotor and g is the acceleration due to gravity.

[0023] Furthermore, in step S1), the torque generated by the second rotor magnetic field on the first rotor and the torque generated by the first rotor magnetic field on the second rotor are:

[0024] T r1 =T rz (θ r1 ,θ r2 )-T rx (θ r1 ,θ r2 )

[0025] T r2 =T rz (θ r2 ,θ r1 )-T rx (θ r2 ,θ r1 )

[0026] T r1 is the torque generated by the second rotor magnetic field on the first rotor, T r2 is the torque generated by the magnetic field of the first rotor on the second rotor, T rx and T rz It is a function related to the swing angle of the dual rotors in the dual-rotor magnetic pendulum mechanical antenna.

[0027] Furthermore, in the step S2), the dynamic model of the rotor in the dual-rotor magnetic swing type mechanical antenna is established as follows:

[0028]

[0029]

[0030] is the angular velocity of the first rotor, is the angular velocity of the second rotor, is the angular acceleration of the first rotor, is the angular acceleration of the second rotor, I r =mr R r 2 / 2 is the moment of inertia of a single rotor, is the sign function of the first rotor angular velocity, is the sign function of the second rotor angular velocity, R r is the radius of a single rotor;

[0031] Furthermore, in the step S3), the swing angle θ of the dual rotor permanent magnets is analyzed by using the dynamic model of the dual rotors. r1 and θ r2 Calculation of the radiated magnetic field of a dual-rotor magnetic pendulum mechanical antenna for:

[0032]

[0033] is the magnetic field function of the rotor, x, y, z are the coordinates of the spatial field point on the X, Y, and Z axes;

[0034] The swing angle of the dual rotor permanent magnets is θ r1 and θ r2 The dual-rotor dynamics model constructed according to step S2) is solved by the Runge-Kutta method to obtain an analytical solution.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention proposes a calculation method for the radiated magnetic field of a dual-rotor magnetic pendulum mechanical antenna by establishing a dynamic model of the dual rotors in the dual-rotor magnetic pendulum mechanical antenna; the present invention can solve the spatial distribution characteristics of the radiated magnetic field of the dual-rotor magnetic pendulum mechanical antenna, and can analyze the influence of the structure of the dual-rotor magnetic pendulum mechanical antenna on the radiated magnetic field of the antenna, thereby providing an optimization basis for the antenna structure design. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1a , 1b It is a schematic diagram of a dual-rotor magnetic pendulum mechanical antenna;

[0038] Figure 2a This is the time domain diagram of the magnetic field of the dual-rotor magnetic pendulum mechanical antenna;

[0039] Figure 2b This is the frequency domain diagram of the magnetic field of the dual-rotor magnetic pendulum mechanical antenna. DETAILED DESCRIPTION

[0040] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0041] The following is a detailed introduction to the embodiments of the present invention:

[0042] 1) Calculation method of the torque generated by the stator magnetic field on the dual rotors in the dual-rotor magnetic swing mechanical antenna:

[0043] The rotors of the dual-rotor magnetic pendulum mechanical antenna are two cylindrical permanent magnets placed along the Y axis. The radius of the two rotors is R r , the length is H r , the magnetization intensity is M r , are radially magnetized along the X-axis direction, and the center distance between the two rotors is D rr The motion of both rotors is single-degree-of-freedom swing, and the swing angle at time t is denoted as θ r1 (t) and θ r2 (t), such as Figure 1a , 1b shown.

[0044] The stator of the dual-rotor magnetic pendulum mechanical antenna is a rectangular permanent magnet located on both sides of the rotor. The two stators are placed symmetrically along the X axis, and the dimensions of the stator along the X axis, Y axis and Z axis are all L. s , D s and H s , the magnetization intensity is M s , magnetized along the X-axis direction, the center distance between the two stators is D ss ,like Figure 1a , 1b shown.

[0045] The stator magnetic field torques on the first rotor and the second rotor of the dual-rotor magnetic pendulum mechanical antenna at time t are T s1 and T s2 :

[0046]

[0047] In the formula, θ r1 is the swing angle of the first rotor at time t, θ r2 is the swing angle of the second rotor at time t;

[0048] Parameter T sx and T sz is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure:

[0049]

[0050] Where μ0=4π×10 -7 N / A 2 is the magnetic permeability in vacuum, ξ and h are the angle and length parameters of the integral differential element, H sx and H sz They are the X-axis component and Z-axis component of the stator magnetic field generated in space by the stator structure in the mechanical antenna:

[0051]

[0052] Where x, y, z are the coordinates of the field point on the X, Y, and Z axes, 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:

[0053]

[0054] 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:

[0055]

[0056] Here, the function sgn(x) is the sign function.

[0057] 2) Calculation method of the torque generated by the coil magnetic field on the dual rotors in the dual rotor magnetic pendulum mechanical antenna:

[0058] In order to simplify the model, the influence of coil height and thickness is ignored. It is assumed that the coil is concentrated in the XOY plane and the coil length is L. c , width D c , the number of turns is N c There is a sinusoidal current in the coil, and the current amplitude is I c , the current frequency is f.

[0059] The coil magnetic field torques on the first rotor and the second rotor of the dual-rotor magnetic pendulum mechanical antenna at time t are T c1 and T c2 :

[0060]

[0061] Where f is the current frequency of the coil;

[0062] Parameter T cx and T cz is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure:

[0063]

[0064] Where H cxm and H czmThey are the X-axis component and Z-axis component of the coil magnetic field generated by the coil in the mechanical antenna in space:

[0065]

[0066] The parameter x ± ,y ± ,α ± ,β ± ,ρ ± for:

[0067]

[0068] 3) Calculation method of the friction torque generated by the bearing on the dual rotors in the dual-rotor magnetic pendulum mechanical antenna

[0069] 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:

[0070] T b =μFR r (10)

[0071] 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 mass of a single rotor (i.e. the mass of the first rotor is equal to the mass of the second rotor, both are m r ), ρ r is the rotor density.

[0072] 4) Calculation method of the torque generated by the magnetic field of one rotor on the other rotor in a dual-rotor magnetic swing mechanical antenna:

[0073] The torque generated by the magnetic field of the second rotor on the first rotor and the torque generated by the magnetic field of the first rotor on the second rotor in the dual-rotor magnetic swing mechanical antenna are:

[0074]

[0075] In the formula, function T rx (θ r1 ,θ r2 ) and T rz (θ r1 ,θ r2 ) is a function related to the rotor swing angle:

[0076]

[0077] The parameter T rx1 ,T rx2 ,T rx3 ,T rx4 ,T rx5 ,T rx6 ,T rx7 ,T rz1 ,T rz2 ,T rz3 is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure:

[0078]

[0079] The auxiliary function H mx1 ,H mx2 ,H mz is a function related to the rotor magnetic field:

[0080]

[0081] The auxiliary function F 11 ,F 12 ,F2,F3 means:

[0082]

[0083] Where K(k 2 ), E(k 2 ) and Π(n,k 2 ) represent the complete elliptic integrals of the first, second, and third kind respectively:

[0084]

[0085] The parameters n, r 1,2 ,k 1,2 The meaning is:

[0086]

[0087] Where R is the distance from the infinitesimal element in the integral to the center of the other rotor:

[0088]

[0089] 5) Establish the dynamic model of the dual rotors in the dual rotor magnetic pendulum mechanical antenna

[0090] During the operation of the magnetic pendulum mechanical antenna, the rotor is subjected to the combined effects of the stator magnetic field torque, the coil magnetic field torque, the rotor magnetic field torque and the friction torque. Therefore, the dynamic equation of the rotor can be constructed:

[0091]

[0092] In the formula is the angular velocity of the first rotor, is the angular velocity of the second rotor, is the angular acceleration of the first rotor, is the angular acceleration of the second rotor, I r =m r R r 2 / 2 is the moment of inertia of a single rotor, is the sign function of the first rotor angular velocity, is the sign function of the second rotor angular velocity. The Runge-Kutta method is used to solve equation (19) to obtain the swing angle θ of the dual rotor permanent magnets: r1 and θ r2 .

[0093] 6) Calculation method of the magnetic field radiated by the dual-rotor magnetic pendulum mechanical antenna

[0094] The rotor of the magnetic pendulum mechanical antenna swings back and forth, generating an alternating electromagnetic field in space, which radiates outward. for:

[0095]

[0096] In the formula is the magnetic field function of the rotor:

[0097]

[0098] Where θ r is the angle of rotation of the rotor, is the rotor volume, is the distance from the field point to the origin.

[0099] See also Figure 2a , 2b , which is the magnetic field signal captured by the magnetic field receiving device placed at a height of 50 cm when an alternating current of 300 Hz is applied to the excitation coil, and the result calculated by the theoretical model. After filtering, the background magnetic field and high-frequency interference magnetic field are filtered out. At this time, the magnetic field of the antenna is the synthesis of the rotor magnetic field and the coil magnetic field, which enhances the radiation magnetic field strength of the antenna. Through time domain analysis, it is found that the magnetic field fluctuations obtained in the experiment have harmonic characteristics; further, through frequency domain analysis, it is found that the signal frequency obtained by theoretical calculation is consistent with the frequency of the experimental test. Based on the experimental results, the frequency of the radiated magnetic field is adjusted by changing the current 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 dual-rotor magnetic pendulum mechanical antenna, comprising two identical first rotors and a second rotor, characterized in that: The magnetic field calculation method of the dual-rotor magnetic pendulum mechanical antenna is specifically as follows: S1) Calculate the torque generated by the stator magnetic field on the dual rotors in the dual rotor magnetic pendulum mechanical antenna; Calculate the torque generated by the coil magnetic field on the dual rotors in the dual rotor magnetic pendulum mechanical antenna; Calculate the friction torque generated by the bearings on the dual rotors in the dual-rotor magnetic pendulum mechanical antenna; Calculate the torque generated by the magnetic field of the second rotor on the first rotor and the torque generated by the magnetic field of the first rotor on the second rotor in the dual-rotor magnetic swing mechanical antenna; S2) establishing a dynamic model of the dual rotors in the dual rotor magnetic pendulum mechanical antenna according to the torque generated by the stator magnetic field on the dual rotors, the torque generated by the coil magnetic field on the dual rotors, the friction torque generated by the bearings on the dual rotors, and the torque generated by the rotor magnetic field on the other rotor calculated in step S1); S3) The angle θ of the dual rotor permanent magnet swing analyzed by the dual rotor dynamics model r1 and θ r2 Calculate the radiated magnetic field of a dual-rotor magnetic pendulum mechanical antenna.

2. The method for calculating the magnetic field of a dual-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 dual rotor is: T s1 (t)=(T sz -T sx )sinθ r1 (t) T s2 (t)=(T sz -T sx )sinθ r2 (t) T s1 is the torque generated by the stator magnetic field on the first rotor, T s2 is the torque generated by the stator magnetic field on the second rotor, T sx and T sz is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure, θ r1 is the swing angle of the first rotor at time t, θ r2 is the swing angle of the second rotor at time t.

3. The method for calculating the magnetic field of a dual-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 dual rotor is: T c1 =(T cz -T cx )cosθ r1 (t)sin(2πft) T c2 =(T cz -T cx )cosθ r2 (t)sin(2πft) T c1 is the torque generated by the coil magnetic field on the first rotor, T c2 is the torque generated by the coil magnetic field on the second rotor, T cx and T cz is a coefficient related to the dual-rotor magnetic pendulum mechanical antenna structure, and f is the current frequency of the coil.

4. The method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna according to claim 3, characterized in that: The friction torque generated by the bearing on the dual 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 a single rotor and g is the acceleration due to gravity.

5. The method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna according to claim 4, characterized in that: In step S1), the torque generated by the second rotor magnetic field on the first rotor and the torque generated by the first rotor magnetic field on the second rotor: T r1 =T rz (i r1 ,i r2 )-T rx (i r1 ,i r2 ) T r2 =T rz (i r2 ,i r1 )-T rx (i r2 ,i r1 ) T r1 is the torque generated by the second rotor magnetic field on the first rotor, T r2 is the torque generated by the magnetic field of the first rotor on the second rotor, T rx and T rz It is a function related to the swing angle of the dual rotors in the dual-rotor magnetic pendulum mechanical antenna.

6. The method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna according to claim 5, characterized in that: In the step S2), the dynamic model of the rotor in the dual-rotor magnetic swing type mechanical antenna is established as follows: is the angular velocity of the first rotor, is the angular velocity of the second rotor, is the angular acceleration of the first rotor, is the angular acceleration of the second rotor, I r =m r R r 2 / 2 is the moment of inertia of a single rotor, is the sign function of the first rotor angular velocity, is the sign function of the second rotor angular velocity, R r is the radius of a single rotor.

7. The method for calculating the magnetic field of a dual-rotor magnetic pendulum mechanical antenna according to claim 6, characterized in that: In the step S3), the angle θ of the dual rotor permanent magnet swing is analyzed by the dynamic model of the dual rotor. r1 and θ r2 Calculation of the radiated magnetic field of a dual-rotor magnetic pendulum mechanical antenna for: is the magnetic field function of the rotor, x, y, z are the coordinates of the spatial field point on the X, Y, and Z axes; The swing angle of the dual rotor permanent magnets is θ r1 and θ r2 The dual-rotor dynamics model constructed according to step S2) is solved by the Runge-Kutta method to obtain an analytical solution.

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