A multi-layer coaxial direct-drive motor transmission system optimization method

Abstract

The present disclosure relates to the field of direct-drive VICTS antenna motor design optimization, and specifically to a multi-layer coaxial direct-drive motor transmission system optimization method, the method comprising the following steps: systematically modeling the multi-layer coaxial direct-drive motor, the multi-layer coaxial direct-drive motor comprising: a plurality of motor layers with rotating support thin-walled rings, a plurality of balls and ball cages; based on the Euler-Bernoulli beam hypothesis, using the Lagrange equation modeling method, the resonance frequency of the rotating support thin-walled ring is obtained; based on the rotation frequency, the number of balls, the diameter of the rotating support thin-walled ring and the contact angle of the ball bearing of the multi-layer coaxial direct-drive motor, the excitation frequency of the ball revolution on the plurality of motor layers is calculated; based on the required rotation speed of the plurality of motor layers and the support stiffness and excitation frequency, the number of balls and the cross-sectional parameters of the rotating support thin-walled ring are optimized; based on the Fourier transform of the periodic magnetic field distribution, the magnetic field periodic distribution of the adjacent two layers of motor rotors is optimized, and the problem of interlayer magnetic field force disturbance is overcome. The present disclosure significantly improves the dynamic response capability of each layer of motor rotors.

Description

Technical Field

[0001] The present disclosure relates to the field of direct-drive VICTS antenna motor design optimization, and in particular to a multi-layer coaxial direct-drive motor transmission system optimization method. Background Art

[0002] Traditional VICTS satellite antennas usually use a multi-layer coaxial large-diameter transmission method, which relies on ordinary servo motors and drives large disks (rings) through mechanical transmission methods such as synchronous belts or gears. However, this method has obvious defects, such as low accuracy, insufficient rigidity, and high noise during operation. These problems limit the application of traditional antennas in scenarios with high performance requirements.

[0003] With the continuous development of low-orbit satellite constellations in the future, higher requirements are placed on the beam switching speed of the moving antenna, reaching 1000° / s. Although the prior patent (ZL202110938550.8) has proposed a multi-layer large hollow direct-drive motor suitable for VICTS moving satellite antennas and improved the problems of traditional technologies to a certain extent, there are still some key technical challenges.

[0004] Although the coaxial multi-layer direct-drive motor in the prior patent uses multi-layer rotating supports to achieve independent movement of the multi-layer direct-drive motor, and designs a permanent magnetic field on the outside of the rotating support to form the rotor structure of the direct-drive motor, and uses high-precision ceramic balls for interlayer isolation, under a 48V driving voltage, the maximum speed of each layer of the motor can only reach 300° / s, which is far from meeting the 1000° / s beam switching speed required for low-orbit satellite applications.

[0005] In addition, the direct-drive motor of the prior patent has other problems, including resistance fluctuations caused by mutual interference of magnetic fields between layers, vibration caused by high-speed movement of interlayer isolation balls, and low vibration modes caused by the thin-walled circular ring structure design of the rotating support, which may cause mechanism vibration and noise during high-speed operation.

[0006] In addition to the above-mentioned major technical problems, the coaxial multi-layer direct-drive motor in the prior patent also has problems such as overall heavy weight, which to some extent limits its use in certain specific applications.

[0007] In summary, the existing transmission technology for antennas in motion cannot meet the needs of future low-orbit satellite constellations for high-speed beam switching, and has obvious deficiencies in mechanical performance and vibration control. Summary of the invention

[0008] The present disclosure provides a multi-layer coaxial direct-drive motor transmission system optimization method, which can solve at least one of the problems mentioned in the background technology. To solve the above technical problems, the present disclosure provides the following technical solutions:

[0009] As one aspect of an embodiment of the present disclosure, a method for optimizing a multi-layer coaxial direct-drive motor transmission system is provided, comprising the following steps:

[0010] A system model is performed on the multi-layer coaxial direct-drive motor, wherein the multi-layer coaxial direct-drive motor comprises: a plurality of motor layers with rotating support thin-walled circular rings, a plurality of balls and a ball cage;

[0011] Based on the Euler-Bernoulli beam hypothesis, the resonant frequency of the rotating supported thin-walled ring is obtained using the Lagrange equation modeling method.

[0012] Calculate the excitation frequency of the ball revolution on multiple motor layers based on the rotation frequency of the multi-layer coaxial direct-drive motor, the number of balls, the diameter of the rotating support thin-walled ring, and the contact angle of the ball bearing;

[0013] The number of balls and the cross-sectional parameters of the thin-walled ring of the rotating support are optimized based on the required rotational speed of multiple motor layers as well as the support stiffness and excitation frequency.

[0014] Optionally, based on the Euler-Bernoulli beam hypothesis, a Lagrange equation modeling method is used to obtain a calculation method for the resonance frequency of the ring structure, and the process includes calculating the following expression:

[0015]

[0016]

[0017] make have to:

[0018] B1B4-B2B3=0 (1)

[0019] B5B3-B6B7=0 (2)

[0020] Where E is the elastic modulus of the material, I i is the area moment of inertia about the z-axis; I o is the area moment of inertia about the x-axis; I p is the polar area moment of inertia around the y-axis; R is the radius of the ring; p is the material density; G is the shear modulus; A is the cross-sectional area of ​​the ring; Ω is the rotation speed of the ring; n is the model order;

[0021] Substituting the above parameters into formula (1) and formula (2), we can get the resonant frequency ω corresponding to different orders n: n ; Take n=2, corresponding to the lowest resonant frequency.

[0022] Optionally, when the number of motor layers is 4, the excitation frequency of each layer due to the revolution of the ball is:

[0023]

[0024] f 1c ~f 4c Corresponding to the ball revolution frequency of the thin-walled ring of the four-layer coaxial direct-drive motor rotation support, where N b is the number of balls between every two layers, d is the ball diameter, D is the pitch circle diameter of the rotating support raceway, and α is the contact angle of the angular contact ball bearing.

[0025] Optionally, the multi-layer coaxial direct-drive motor transmission system optimization method also includes optimization of the inter-layer magnetic field force, wherein the multi-layer coaxial direct-drive motor includes a rotor with N and S alternating magnetic poles installed on the outer circle of a rotating support, which together with the stator part of the motor constitutes a drive motor.

[0026] Optionally, the optimization of the interlayer magnetic field force includes:

[0027] The interlayer magnetic field force is provided by the alternating magnetic field, and the Fourier series of the alternating magnetic field is expressed as:

[0028]

[0029] Among them, a0 is the amplitude coefficient of the DC component of the Fourier transform, a n and b n is the amplitude coefficient of the Fourier transform nth harmonic component; to eliminate the interlayer magnetic field force, it is necessary to:

[0030]

[0031] Among them, τ1 and τ2 represent the magnetic field period between two adjacent layers;

[0032] From formulas (7) and (8), we can obtain: τ2 = (2n+1)τ1 / 2, where n is a natural number.

[0033] Optionally, when n=0, τ2=τ1 / 2.

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present disclosure successfully optimizes the magnetic field force between adjacent layers of rotors of a multi-layer direct-drive motor in theory by introducing a magnetic field period optimization formula. This optimization effectively overcomes the problem of large inter-layer magnetic field force, significantly improves the dynamic response speed of each layer of motor rotors, and is more suitable for high-speed motion applications. By analyzing the resonant frequency of the thin-walled circular ring structure of each motor layer of a multi-layer coaxial direct-drive motor and the orbital excitation frequency of each layer of balls, a thin-walled circular ring optimization method and a ball quantity matching method under specific speed requirements are theoretically given, thereby optimizing the dynamic response capability of the multi-layer coaxial direct-drive motor to meet high-speed motion applications and reduce system resonance and noise. The present disclosure enables the multi-layer direct-drive motor transmission system to have dynamic response capabilities at a speed of 1000° / s. , meeting the requirements of beam switching speed for low-orbit satellite applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of a method for optimizing a multi-layer coaxial direct-drive motor transmission system in an embodiment of the present disclosure;

[0037] Figure 2 This is a structural diagram of a rotating support thin-walled circular ring included in a motor layer of a multi-layer coaxial direct-drive motor in the prior art;

[0038] Figure 3 2 is a diagram of the motor layer structure in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present disclosure to clearly and completely describe the technical solutions in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all of the embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present disclosure.

[0040] In this embodiment, the multi-layer coaxial direct-drive motor in the prior patent (ZL202110938550.8) is used as the research object for analysis, and a multi-layer coaxial direct-drive motor transmission system optimization method is proposed, such as Figure 1 As shown, the following steps are included:

[0041] S10, performing system modeling on the multi-layer coaxial direct-drive motor, wherein the multi-layer coaxial direct-drive motor comprises: a plurality of motor layers having a rotating support thin-walled circular ring, a plurality of balls and a ball cage;

[0042] S20, based on the Euler-Bernoulli beam hypothesis, the resonant frequency of the rotating supported thin-walled ring is obtained using the Lagrange equation modeling method;

[0043] S30, calculating the excitation frequency of the ball revolution on multiple motor layers based on the rotation frequency of the multi-layer coaxial direct-drive motor, the number of balls, the diameter of the rotating support thin-walled ring, and the contact angle of the ball bearing;

[0044] S40, optimizing the number of balls and the cross-sectional parameters of the rotating support thin-walled ring based on the required rotational speeds of multiple motor layers, support stiffness, and excitation frequency.

[0045] Based on the above steps, the embodiment of the present disclosure analyzes the resonance frequency of the thin-walled circular ring structure of the rotor rotation support of each layer of the multi-layer coaxial direct-drive motor and the excitation frequency of multiple motor layers, and theoretically provides a thin-walled circular ring optimization method and a ball quantity matching method under specific speed requirements, thereby optimizing the dynamic response capability of the multi-layer direct-drive motor to meet high-speed motion applications and reduce system resonance and noise. The above steps will be described in detail below.

[0046] S10, performing system modeling on the multi-layer coaxial direct-drive motor, wherein the multi-layer coaxial direct-drive motor comprises: a plurality of motor layers having a rotating support thin-walled circular ring, a plurality of balls and a ball cage;

[0047] For example, Figure 2 As shown, the motor layer of the multi-layer coaxial direct-drive motor in the prior art (ZL202110938550.8) includes a rotating thin-walled circular ring structure, and the multiple motor layers include multiple rotating diameter thin-walled circular ring structures, and the multiple motor layers sequentially include a first motor layer, a second motor layer, a third motor layer and a top motor layer; a ball retainer and a plurality of balls, and the plurality of balls are accommodated between the ball retainers of two adjacent motor layers, and the above structure is systematically modeled.

[0048] S20, based on the Euler-Bernoulli beam hypothesis, the resonant frequency of the rotating supported thin-walled ring is obtained using the Lagrange equation modeling method;

[0049] Among them, based on the Euler-Bernoulli beam hypothesis, the Lagrange equation modeling method is used to obtain the calculation method of the resonance frequency of the ring structure, and the process includes calculating the following expressions:

[0050]

[0051] make have to:

[0052] B1B4-B2B3=0 (1)

[0053] B5B3-B6B7=0 (2)

[0054] Where E is the elastic modulus of the material, I i is the area moment of inertia about the z-axis; I ois the area moment of inertia about the x-axis; I p is the polar area moment of inertia around the y-axis; R is the radius of the ring; ρ is the material density; G is the shear modulus; A is the cross-sectional area of ​​the ring; Ω is the rotation speed of the ring; n is the model order;

[0055] Substituting the above parameters into formula (1) and formula (2), we can get the resonant frequency ω corresponding to different orders n: n ; Take n=2, corresponding to the lowest resonant frequency.

[0056] S30, calculating the excitation frequency of the ball revolution on multiple motor layers based on the rotation frequency of the multi-layer coaxial direct-drive motor, the number of balls, the diameter of the rotating support thin-walled ring, and the contact angle of the ball bearing;

[0057] like Figure 3 , the rotating thin-walled circular ring structure 1 of the motor layer is evenly distributed with balls 2 (such as steel balls or ceramic balls) above and below, so that the two adjacent motor layers can rotate relative to each other, similar to the bearing structure. Under appropriate preload, without considering ball slippage, the balls 2 revolve along the rotating support raceway on the rotating diameter supporting thin-walled circular ring structure and are accompanied by self-rotation, wherein the revolution forms a vibration excitation source for the rotating support raceway. When the motor layer is 4 layers, the excitation frequency of the ball revolution on each layer is:

[0058]

[0059] f 1c ~f 4c Corresponding to the ball revolution frequency of the thin-walled ring of the four-layer coaxial direct-drive motor rotation support, where N b is the number of balls between every two layers, d is the ball diameter, D is the pitch circle diameter of the rotating support raceway, and α is the contact angle of the angular contact ball bearing.

[0060] S40, optimizing the number of balls and the cross-sectional parameters of the rotating support thin-walled ring based on the required rotational speeds of multiple motor layers, support stiffness, and excitation frequency.

[0061] According to formulas (3) to (6) in S30, the rotation speed and number of balls of each layer and adjacent layers jointly determine the excitation frequency, so the number of balls can be optimized according to the rotation speed requirements of each layer and the resonance frequency of the corresponding layer calculated by formulas (1) and (2); further, the cross-sectional parameters of the thin-walled circular ring of the corresponding layer rotation support can be optimized according to the minimum required number of balls (determined by the support stiffness, not expanded here) and the rotation speed requirements of each layer (the radius of the circular ring is determined by the antenna RF characteristics, which is not a mechanical optimization parameter); the optimization goal is that the excitation frequency of the ball revolution on each layer is significantly lower than the lowest in-plane vibration mode and out-of-plane vibration mode of the corresponding layer. By analyzing the resonant frequency of the thin-walled circular ring structure of each motor layer of the multi-layer coaxial direct-drive motor and the excitation frequency of the ball revolution of each layer, a thin-walled circular ring optimization method and a ball number matching method under specific rotation speed requirements are theoretically given, thereby optimizing the dynamic response capability of the multi-layer coaxial direct-drive motor to meet high-speed motion applications and reduce system resonance and noise.

[0062] As an optional implementation, the multi-layer coaxial direct-drive motor transmission system optimization method also includes optimizing the inter-layer magnetic field force, wherein the multi-layer coaxial direct-drive motor includes a rotor with alternating magnetic poles of N and S phases mounted on the outer circle of the rotating support, which together with the stator part of the motor constitutes a drive motor. The leakage magnetic field of each layer will generate an attractive or repulsive force between the layers. If τ1 and τ2 are equal, the huge magnetic field force will cause the layers to be unable to move relative to each other.

[0063] As an optional implementation, the optimization of the interlayer magnetic field force includes:

[0064] The interlayer magnetic field force is provided by the alternating magnetic field. Since the alternating magnetic field is a periodic function, it can be expressed by the Fourier series as follows:

[0065]

[0066] Among them, a0 is the amplitude coefficient of the DC component of the Fourier transform, a n and b n is the amplitude coefficient of the Fourier transform nth harmonic component; to eliminate the interlayer magnetic field force, it is necessary to:

[0067]

[0068] Among them, τ1 and τ2 represent the magnetic field period between two adjacent layers;

[0069] From formulas (7) and (8), we can obtain τ2=(2n+1)τ1 / 2, where n is a natural number.

[0070] Preferably, when n=0, τ2=τ1 / 2.

[0071] According to the optimization method of the multi-layer coaxial direct-drive motor transmission system in this embodiment, one of the motor layers is selected for optimization design:

[0072] The material and optimized mechanical dimension parameters are as follows:

[0073] Variable Name Numeric density <![CDATA[7810Kg / m ^ 3]]> Elastic modulus E 2.16×10^11Pa Shear modulus G 8.307×10^10Pa Radius R 0.3867m Ring wall width b 0.0134m Ring wall thickness h 0.0177m

[0074] The calculated lowest in-plane resonance mode is about 58.1 Hz, and the lowest out-of-plane resonance frequency is about 72.1 Hz; under the rotation speed requirement of 1000° / s, the ball excitation frequency of the motor layer should be lower than 41 Hz (the lowest mode 58.1 / 1.4 is used as the safety frequency); it is concluded that when the motor layer is at 1000° / s, that is, when the relative rotation speed of the two adjacent motor layers reaches 2000° / s, the maximum number of balls is 10; in actual applications, during the maximum rotation speed movement of the beam switching of low-orbit satellites, the relative rotation speed of adjacent motor layers is zero, and in other scenarios, the relative rotation speed of adjacent motor layers is about 100° / s. At this time, the number of balls should be 97.

[0075] According to the magnetic field period optimization formula, the magnetic field length periods of adjacent motor layers are 16 mm and 8 mm respectively;

[0076] Finally, the maximum speed of the motor layer's independent movement is 1000° / s, the positioning accuracy is 0.05°, the speed fluctuation is <±10%, and the inter-layer magnetic field force is almost zero, which has no effect on the motor rotation.

[0077] Although embodiments of the present disclosure have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present disclosure, and the scope of the present disclosure is defined by the appended claims and their equivalents.

Claims

1. A multi-layer coaxial direct-drive motor transmission system optimization method, characterized in that: The steps include: A system model is performed on the multi-layer coaxial direct-drive motor, wherein the multi-layer coaxial direct-drive motor comprises: a plurality of motor layers with rotating support thin-walled circular rings, a plurality of balls and a ball cage; Based on the Euler-Bernoulli beam hypothesis, the resonant frequency of the rotating supported thin-walled ring is obtained using the Lagrange equation modeling method. Calculate the excitation frequency of the ball revolution on multiple motor layers based on the rotation frequency of the multi-layer coaxial direct-drive motor, the number of balls, the diameter of the rotating support thin-walled ring, and the contact angle of the ball bearing; Optimize the number of balls and cross-sectional parameters of the rotating support thin-walled ring based on the required rotation speed of multiple motor layers, support stiffness and excitation frequency; Based on the Euler-Bernoulli beam hypothesis, the Lagrange equation modeling method is used to obtain the calculation method of the resonant frequency of the ring structure. The process includes calculating the following expressions: make have to: B1B4-B2B3=0 (1) B5B8-B6B7=0 (2) Where E is the elastic modulus of the material, I i is the area moment of inertia about the z-axis; I o is the area moment of inertia about the x-axis; I p is the polar area moment of inertia around the y-axis; R is the radius of the ring; ρ is the material density; G is the shear modulus; A is the cross-sectional area of ​​the ring; Ω is the rotation speed of the ring; n is the model order; Substituting the above parameters into formula (1) and formula (2), we can get the resonant frequency ω corresponding to different orders n: n ; Take n=2, corresponding to the lowest resonant frequency.

2. The multi-layer coaxial direct-drive motor transmission system optimization method according to claim 1, characterized in that: When the motor has 4 layers, the excitation frequency of each layer due to the revolution of the ball is: f 1c ~f 4c Corresponding to the ball revolution frequency of the thin-walled ring of the four-layer coaxial direct-drive motor rotation support, where N b is the number of balls between every two layers, d is the ball diameter, D is the pitch circle diameter of the rotating support raceway, and α is the contact angle of the angular contact ball bearing.

3. The multi-layer coaxial direct-drive motor transmission system optimization method according to claim 1, characterized in that: The multi-layer coaxial direct-drive motor transmission system optimization method also includes the optimization of the inter-layer magnetic field force, wherein the multi-layer coaxial direct-drive motor includes a rotor with N and S alternating magnetic poles installed on the outer circle of a rotating support, which together with the stator part of the motor constitutes a drive motor.

4. The multi-layer coaxial direct-drive motor transmission system optimization method according to claim 3, characterized in that: Optimization of interlayer magnetic field forces, including: The interlayer magnetic field force is provided by the alternating magnetic field, and the Fourier series of the alternating magnetic field is expressed as: To eliminate the magnetic field force between layers, you need to: Among them, τ1 and τ2 represent the magnetic field period between two adjacent layers; From formulas (7) and (8), we can obtain: τ2 = (2n+1)τ1 / 2, where n is a natural number.

5. The multi-layer coaxial direct-drive motor transmission system optimization method according to claim 4, characterized in that: When n=0, τ2=τ1 / 2.

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