Vibration isolation rate calculation, regulation and control method and system for rigidity-variable magnetic torsional vibration buffer

Abstract

The invention belongs to the technical field of mechanical transmission systems, and particularly discloses a method and a system for calculating, regulating and controlling the vibration isolation rate of a rigidity-variable magnetic torsional vibration buffer, and the method comprises the following steps: obtaining a real-time working condition, modeling a single permanent magnet magnetic field by adopting an equivalent magnetic charge method, and calculating the vibration isolation rate of the rigidity-variable magnetic torsional vibration buffer; a magnetic block negative stiffness model and a spring torsion sheet positive stiffness model of the annular Halbach array are constructed, the total coupling stiffness is calculated, the vibration isolation effect of the magnetic torsional vibration buffer is solved, vibration suppression effects and resonance interval distribution under different working conditions are obtained, and based on the vibration isolation effect of the magnetic torsional vibration buffer, the vibration suppression effect of the magnetic torsional vibration buffer is calculated. The gap adjustable mechanism adjusts the rigidity of the spring torsion sheet and the gap of the magnetic ring in real time. By the adoption of the technical scheme, the gap between the inner magnetic ring and the outer magnetic ring is flexibly set according to multi-working-condition requirements, so that applicability and reliability are improved, and low-frequency torsional vibration is effectively restrained while efficient torque transmission is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical transmission systems, and relates to a method and system for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness. Background Art

[0002] As the power of mechanical transmission systems continues to increase, torsional vibrations are increasingly impacting the performance and service life of high-power devices. In transmission components like gearboxes, low-frequency torsional vibrations often lead to unstable operation, increased energy loss, and component fatigue failure. To suppress these low-frequency torsional vibrations, magnetic dampers, with their contactless torque transmission and excellent vibration isolation properties, have become a highly sought-after innovative solution.

[0003] However, existing magnetic dampers typically utilize fixed magnets or traditional magnetic circuit designs, making it difficult to achieve both high torque transmission and broadband vibration suppression. Furthermore, the rigidity and torque characteristics of existing magnetic dampers are often difficult to adjust due to the fixed permanent magnet arrangement. This results in significant damping effectiveness under varying loads and rotational frequencies.

[0004] In recent years, the Halbach magnetic array, proposed for its advantages in low-frequency vibration isolation, can achieve significant negative stiffness characteristics through optimized magnetization arrangement. However, once the magnets are magnetized, their characteristics are difficult to change, making them insufficient for handling variable working conditions and high load conditions. In addition, the coupling method between positive stiffness elements such as spring torsion plates and the negative stiffness of the Halbach array also determines the overall mechanical properties of the buffer. When the two are connected in parallel, quasi-zero stiffness can be formed, which theoretically significantly reduces the torsional vibration resonance frequency. However, how to accurately calculate and flexibly control the gap between the magnetic rings and the stiffness ratio remains a difficult problem facing current research and application; most solutions cannot maintain high torque transmission while taking into account excellent vibration reduction performance in the low-frequency band.

[0005] To this end, a comprehensive approach that combines variable stiffness design with multi-condition adaptability at the modeling and algorithm levels is crucial. On the one hand, a magneto-elastic coupling stiffness calculation model is needed to rapidly evaluate the torque transmission capacity and vibration suppression potential under varying magnetic ring gaps, loads, and frequencies. On the other hand, due to the significant nonlinearity of the coupling between the Halbach array's magnetic force and the spring torsion plate, traditional linearization methods lack accuracy under wide-range excitation or strong nonlinear conditions. Therefore, appropriate dynamic analysis methods must be employed to evaluate the buffer's response characteristics and vibration reduction effectiveness under actual operating conditions, targeting nonlinear torsional vibration excitation.

[0006] To address the above challenges, there is an urgent need for a variable-stiffness magnetic torsional vibration damper that can maintain high torque transmission efficiency while providing broadband vibration suppression capabilities under multiple operating conditions. Of particular concern is how to accurately describe the coupling between the negative-stiffness Halbach magnetic array and the positive-stiffness spring torsion plate at the modeling and calculation levels, solve their response characteristics and torsional vibration suppression effects under torsional vibration excitation, and combine them with adjustable mechanisms to achieve dynamic regulation of the magnetic ring gap. If a comprehensive magnetic-elastic coupling stiffness calculation method can be established, and a gap adjustment process is proposed based on this, it will hopefully provide a more flexible, efficient, and universal solution for vibration suppression under multiple operating conditions. Summary of the Invention

[0007] The purpose of the present invention is to provide a method and system for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness, so as to solve the problems of insufficient high torque, low frequency vibration isolation and multi-working condition adaptability of the current magnetic buffer.

[0008] To achieve the above objectives, the basic solution of the present invention is: a method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness, comprising the following steps:

[0009] S1, obtain real-time working conditions;

[0010] S2, the magnetic torsional vibration damper uses a circular Halbach array magnet block and uses the equivalent magnetic charge method to model the magnetic field of a single permanent magnet;

[0011] Based on the established magnetic field model of a single permanent magnet, the negative stiffness model of the annular Halbach array magnetic block and the positive stiffness model of the spring torsion plate were constructed, and the total coupling stiffness was calculated to obtain the torque transmission capacity.

[0012] S3, using the harmonic balance method, solve the vibration isolation effect of the magnetic torsional vibration buffer, and obtain the vibration suppression effect and resonance range distribution under different working conditions;

[0013] S4, determining whether the torque transmission capability and the low-frequency vibration suppression effect both meet the preset requirements; if so, executing step S1; otherwise, executing step S5;

[0014] S5, based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustable mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time, and returns to step S2.

[0015] The working principle and beneficial effects of this basic solution are as follows: This technical solution constructs a negative stiffness model based on the Halbach magnetic array and a positive stiffness model of the spring torsion plate, derives the torque-angle relationship and coupling stiffness formula of the magnetic torsional vibration buffer, uses the harmonic balance method to solve its vibration isolation effect, and combines the gap adjustable mechanism to achieve real-time adjustment of the stiffness and torque transmission characteristics.

[0016] Compared to traditional dampers, the calculation method proposed in this paper effectively suppresses low-frequency torsional vibrations while ensuring efficient torque transmission. It also allows for flexible adjustment of the gap between the inner and outer magnetic rings to meet diverse operating conditions, improving applicability and reliability. This method offers a simple structure and convenient installation, significantly expanding the application range of magnetic torsional vibration dampers.

[0017] Furthermore, in step S2, the method of modeling the magnetic field of a single permanent magnet using the equivalent magnetic charge method is:

[0018] For each permanent magnet, derive the permanent magnet infinitesimal element P(r1,θ s ,z1) the magnetic field intensity distribution model for any point M in space, where r1,θ s , z1 is the coordinate parameter of the infinitesimal element P in the cylindrical coordinate system;

[0019] The magnetic field intensity H in the torsional direction of a single sector-shaped arc permanent magnet is obtained by integral calculation θ (r,θ,z):

[0020]

[0021] Among them, r, θ, z are the coordinate parameters of the cylindrical coordinate system; H θ (r,θ,z) is the tangential magnetic field strength of the permanent magnet element P at any point M in space; dσ v * The basic volume expression of the volume density of the arc permanent magnet is μ0 is the magnetic permeability of vacuum; r in1 is the inner radius of the magnetic block; r out1 is the outer radius of the magnetic block; θ1 is the initial angle of the magnetic block; θ2 is the end angle of the magnetic block; h is the top surface height of the magnetic block; is the space vector from the infinitesimal element P to the point M, is the θ-axis unit vector of the cylindrical coordinate system;

[0022] During operation, the inner and outer sector arc magnetic blocks of the Halbach array magnetic ring interact with each other. In magnetic charge theory, radially polarized sector arc permanent magnets are classified as non-uniformly magnetized. The inner and outer arc surfaces of each magnetic block carry a positive and negative magnetic pole surface density, while the internal arc volume of the magnetic block also has a magnetic pole volume density. Tangentially polarized sector arc permanent magnets are considered to be in a uniform magnetization state, that is, the two sides of the magnetic block carry a positive and negative magnetic charge respectively.

[0023] Based on H θ (r,θ,z) and torque dT=r×dF, considering that each radially polarized magnetic block has three magnetic charge distributions, nine corresponding interaction forces will be generated, and the torque T between the radial-radial polarized magnetic blocks is derived. RR:

[0024]

[0025] Among them, B r is the polarization intensity of the permanent magnet, 1 and 2 represent the subscripts of the outer and inner permanent magnets; r in1 is the inner radius of the outer ring magnet; r out1 is the outer radius of the outer ring magnet; θ b1 The initial angle of the outer ring magnet; θ e1 The end angle of the inner circle magnet; r in2 is the inner radius of the inner circle magnet; r out2 is the outer radius of the inner circle magnet; θ b2 The initial angle of the inner ring magnet; θ e2 The end angle of the inner circle magnet; f 1～9 are the expressions of the nine interaction forces between radial-radial polarized magnetic blocks; r1, θ1, z1, r2, θ2, and z2 are the three directional independent variables of the inner and outer ring magnetic blocks in the cylindrical coordinate system respectively;

[0026] Torque T between tangential-tangential polarized magnets AA The calculation formula consists of four quadruple integrals, and the torque T between the radial-tangential polarized magnets is AR It is formed by four quadruple integrals and two quintuple integrals.

[0027] Magnetic field modeling is based on the equivalent magnetic charge method, which is simple to operate and easy to use.

[0028] Furthermore, the negative stiffness model of the annular Halbach array magnetic block and the positive stiffness model of the spring torsion plate are constructed, and the method for calculating the total coupling stiffness is as follows:

[0029] The magnetic torsional vibration damper of the annular Halbach array is composed of three magnetization methods: radial-radial polarized magnet pairs, radial-tangential magnet pairs, and tangential-tangential polarized magnet pairs. Therefore, to solve the magnetic torque transmission capacity T(Δθ) of the annular Halbach array, it is only necessary to superimpose the torques generated by the three magnet pairs:

[0030]

[0031] Where i and j are sum index variables, representing the positions of the inner and outer ring magnets in the magnetic ring; N2 is the number of magnets in the Halbach magnetic ring; Δθ is the relative rotation angle of the magnetic ring; T AA is the torque between the tangential-tangential polarized magnets, T AR is the torque between the radial-tangential polarized magnets, T RR is the torque between radial-radial polarized magnets, T RA is the torque between the tangentially-radially polarized magnets;

[0032] The function relationship between the magnetic torque and the angle when the inner and outer rings of the Halbach magnetic ring produce relative rotation is calculated, and the magnetic torsional stiffness K of the Halbach array is obtained by derivation. m (θ):

[0033]

[0034] The spring torsion plate connects the active rotor and the driven rotor, and has a positive torsional stiffness K r , then by the material mechanics method, it is simplified into a cantilever beam model, and the deflection and transmission torque T of the inner and outer rotors under the relative rotation angle θ are derived. r Relationship, we get:

[0035]

[0036] Where n is the number of spring torsion pieces; E is the elastic modulus of the spring torsion piece; L f is the length of the spring torsion; b is the width of the spring torsion, t is the thickness of the spring torsion, I f is the section inertia moment of the spring torsion piece around the central axis of the section, θ is the relative rotation angle between the active and passive rotors; the torsional stiffness K of the spring torsion piece r Expressed as:

[0037]

[0038] After connecting the negative stiffness annular Halbach array magnetic block and the positive stiffness spring torsion piece in parallel, the total coupling stiffness K(θ)=K r +K m (θ).

[0039] At the initial equilibrium position, if the negative stiffness of the annular Halbach array magnet and the positive stiffness of the spring torsion plate cancel each other out, a quasi-zero stiffness characteristic can be achieved, effectively reducing the torsional resonance frequency and enhancing the vibration reduction capability in the low-frequency band.

[0040] Furthermore, in step S3, the harmonic balance method is used to solve the vibration isolation effect of the magnetic torsional vibration buffer. The specific steps are as follows:

[0041] The magnetic torsional vibration damper and shafting system is modeled as a nonlinear vibration equation system with coupled stiffness and damping:

[0042]

[0043] Among them, J D is the moment of inertia of the rotor on the input shaft side; θ D is the input shaft rotation angle; c is the damping coefficient; J L is the moment of inertia of the rotor on the output shaft side; θ Lis the output shaft rotation angle; T(θ) is the torque transmitted by the magnetic buffer; T d is the amplitude of the driving torque disturbance component; ω is the angular velocity of the driving torque; α is the phase difference; t is the thickness of the spring torsion plate, and θ is the relative rotation angle between the active and passive rotors;

[0044] After normalization, the formula is simplified to:

[0045]

[0046] make

[0047]

[0048] The formula is simplified to:

[0049]

[0050] make

[0051]

[0052] Then, taking the external excitation torque as input, the dimensionless dynamic equation of the system is expressed as:

[0053]

[0054] The parameters in the formula are dimensionless expressions, where is the system torsion angle variable; ζ is the system damping; t0 is the torsional amplitude; δ k is the fitting coefficient of harmonics, k is the index symbol of the summation formula; β is the system vibration frequency parameter; γ is the dimensionless reference θ; a k is the fitting coefficient of the total restoring torque; τ is the time variable; ω n Frequency parameter constructed for the intermediate variable; K r is the torsional stiffness of the spring torsion plate, n is the number of spring torsion plates; T0, J, t d To calculate and derive intermediate variables, for The second derivative of

[0055] Assume that the solution of the dynamic equation of the coupling is for:

[0056]

[0057] Where, φ is the simple harmonic amplitude;

[0058] Perform Fourier or polynomial expansion on the nonlinear stiffness term to obtain the steady-state response equations:

[0059]

[0060] The iterative algorithm is used to numerically solve the response amplitude t of the magnetic torsional vibration buffer at each excitation frequency. b And the torsional vibration transmissibility T:

[0061]

[0062] in, Under the premise of ensuring the accuracy of the solution, the sixth-order polynomial is used for approximate fitting.

[0063] Under torsional vibration excitation, nonlinear dynamic algorithms such as the harmonic balance method are used to accurately evaluate the system's vibration response and vibration reduction effect.

[0064] Furthermore, based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustable mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time. The specific steps are as follows:

[0065] Based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustment mechanism controls the gap change between the inner and outer rings, adjusts the magnetic force distribution of the annular Halbach array magnet block and affects the negative stiffness characteristics, achieving the buffer coupling static drive torque M(θ) = K r θ+M m Dynamic regulation of (θ), where K r is the torsional stiffness of the spring torsion plate, θ is the relative rotation angle between the active and passive rotors, M m (θ) is the torque transmitted by the magnetic ring.

[0066] The gap adjustable mechanism controls the change in the gap between the inner and outer rings, thereby adjusting the magnetic force distribution of the Haier Shell magnetic ring and affecting the negative stiffness characteristics, realizing dynamic adjustment of the buffer coupling static driving torque.

[0067] The present invention also provides a vibration isolation rate calculation and control system for a magnetic torsional vibration buffer with variable stiffness, comprising a magnetic torsional vibration buffer, a gap adjustable mechanism, and a processing mechanism;

[0068] The magnetic torsional vibration buffer is connected to the gap adjustable mechanism, and the processing mechanism is connected to the magnetic torsional vibration buffer and the gap adjustable mechanism. The processing mechanism executes the method described in the present invention, calculates the vibration isolation rate of the magnetic torsional vibration buffer, and controls the gap adjustable mechanism to adjust the stiffness and torque transmission characteristics of the magnetic torsional vibration buffer in real time.

[0069] This system, based on the coupling theory of Haier Shell magnetic rings and spring torsion plates, systematically proposes equivalent magnetic charge modeling, inter-magnetic torque and stiffness calculations, harmonic balance dynamics solutions, and gap adjustment mechanism design and operation procedures. Through a comprehensive multi-faceted technical solution, the buffer effectively reduces low-frequency vibration amplitude while ensuring high torque transmission. It can flexibly adapt to operating conditions with varying load levels and excitation frequencies, demonstrating significant application value in suppressing torsional vibration in high-power transmission systems.

[0070] Furthermore, the magnetic torsional vibration buffer includes a passive rotor, a flange, a load end, an inner ring permanent magnet block, an outer ring permanent magnet block, a spring torsion plate, an end cover, an active rotor, an input shaft and an output shaft;

[0071] The passive rotor is connected to the output shaft through a flange and coupled to the load end;

[0072] The inner ring permanent magnet blocks are embedded in the active rotor, while the outer ring permanent magnet blocks are assembled in the wedge-shaped slider of the gap adjustable mechanism;

[0073] The end cover is connected to the active rotor, and a gap is retained between the passive rotor and the active rotor. The active rotor is connected to the input shaft and plays the role of the driving end.

[0074] The spring torsion plate connects the driving rotor and the driven rotor to provide positive torsional stiffness.

[0075] The magnetic torsional vibration damper has a simple structure and can significantly improve the versatility and vibration reduction effect of the magnetic torsional vibration damper under multi-load and multi-band vibration conditions.

[0076] Furthermore, the gap adjustable mechanism includes a frameless motor, a spiral groove, a claw plate, a wedge-shaped slider, a return spring and a positioning pin;

[0077] One end of the frameless motor is fixed to the passive rotor, and the other end is connected to the spiral groove to control the rotation of the spiral groove;

[0078] The latch at one end of the claw disc is embedded in the spiral groove, converting the rotational motion of the spiral groove into radial expansion and contraction of the claw disc;

[0079] The wedge-shaped slider contacts the claw plate in a friction sliding manner, and under the action of the return spring and the positioning pin, the position control during the working process is achieved;

[0080] The spiral groove is driven to rotate by a frameless motor, causing the claw plate to produce axial displacement, which in turn pushes the wedge-shaped slider to slide smoothly in the radial direction.

[0081] The gap adjustable mechanism controls the gap change between the inner and outer rings, thereby adjusting the magnetic force distribution of the Haier Shell magnetic ring and affecting the negative stiffness characteristics, achieving the buffer coupling static driving torque M(θ)=Kr θ+M m Dynamic adjustment of (θ). BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 It is a structural schematic diagram of the vibration isolation rate calculation and control system of the magnetic torsional vibration buffer with variable stiffness of the present invention;

[0083] Figure 2 Schematic diagram of the polarization structure of the Halbach array of the vibration isolation rate calculation and control system of the magnetic torsional vibration buffer with variable stiffness of the present invention;

[0084] Figure 3 It is a structural schematic diagram of a magnetic field intensity distribution model of a method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness according to the present invention;

[0085] Figure 4 It is a structural schematic diagram of a radial-radial polarization action model of the vibration isolation rate calculation and control method of the magnetic torsional vibration buffer with variable stiffness of the present invention;

[0086] Figure 5 It is a structural schematic diagram of a tangential-tangential polarization action model of the vibration isolation rate calculation and control method of the magnetic torsional vibration buffer with variable stiffness of the present invention;

[0087] Figure 6 It is a structural schematic diagram of a radial-tangential polarization action model of the vibration isolation rate calculation and control method of the magnetic torsional vibration buffer with variable stiffness of the present invention;

[0088] Figure 7 The present invention is a schematic diagram of the operation flow of the gap adjustable mechanism of the vibration isolation rate calculation and control method of the magnetic torsional vibration buffer with variable stiffness.

[0089] The figure marks in the drawings of the specification include: passive rotor 1, wedge-shaped slider 2, positioning pin 3, return spring 4, load end 5, frameless motor 6, claw plate 7, spiral groove 8, inner ring permanent magnet block 9, outer ring permanent magnet block 10, spring torsion piece 11, end cover 12, flange 13, first bolt 14, second bolt 15, active rotor 16, drive end 17, bearing 18, input shaft 19, output shaft 20. DETAILED DESCRIPTION

[0090] The following describes embodiments of the present invention in detail. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended only to explain the present invention and are not to be construed as limiting the present invention.

[0091] In the description of the present invention, it should be understood that the terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0092] In the description of the present invention, unless otherwise specified and limited, it should be noted that the terms "installed", "connected" and "connected" should be understood in a broad sense. For example, it can be a mechanical connection or an electrical connection, or it can be the internal communication between two components. It can be a direct connection or an indirect connection through an intermediate medium. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to the specific circumstances.

[0093] The present invention discloses a method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness, which realizes torque transmission and low-frequency torsional vibration suppression under variable working conditions. Based on the traditional quasi-zero stiffness device scheme, the design and related calculation methods of a variable stiffness magnetic torsional vibration buffer are proposed. It not only includes the analysis and control mechanism of the buffer stiffness and torque output, but also uses nonlinear dynamic algorithms such as the harmonic balance method under torsional vibration excitation to accurately evaluate the vibration response and vibration reduction effect of the system. This method provides more reliable and flexible technical support for subsequent high-power or high-variable load transmission systems, and also opens up new directions for the theory and application of broadband torsional vibration suppression.

[0094] The method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness includes the following steps:

[0095] S1, obtains real-time operating conditions; obtains the system load size based on the rated operating conditions, calculates the corresponding rotational frequency and meshing frequency based on the rotational speed, and monitors the real-time torsional vibration phase angle and acceleration of the shaft system through the torsional vibration sensor.

[0096] S2, the magnetic torsional vibration damper uses a circular Halbach array magnet block and uses the equivalent magnetic charge method to model the magnetic field of a single permanent magnet;

[0097] Based on the established magnetic field model of a single permanent magnet, the negative stiffness model of the annular Halbach array magnetic block and the positive stiffness model of the spring torsion plate were constructed, and the total coupling stiffness was calculated to obtain the torque transmission capacity.

[0098] S3, using the harmonic balance method, solve the vibration isolation effect of the magnetic torsional vibration buffer, and obtain the vibration suppression effect and resonance range distribution under different working conditions;

[0099] S4, determining whether the torque transmission capability and the low-frequency vibration suppression effect both meet the preset requirements; if so, executing step S1; otherwise, executing step S5;

[0100] The maximum torque transfer capacity within the torsional vibration buffer's operating area is calculated through modeling to determine whether the load torque transfer requirements are met. The system dynamics equations are solved using the harmonic balance method to obtain the torsional vibration buffer transfer rate curve, which is used to determine whether the system operating frequency and excitation frequency are within the buffer's vibration suppression frequency range.

[0101] S5, based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustable mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time (such as Figure 7 and returns to step S2.

[0102] The frameless motor rotates to control the radial expansion and contraction of the claw disc, driving the outer ring slider to move radially to adjust the gap between the active and passive rotors; the gap is increased when the torque transmission capacity needs to be increased, and the gap is reduced when the low-frequency vibration suppression effect needs to be obtained.

[0103] The stiffness of the spring torsion plate remains unchanged. The frameless motor rotates to push the claw plate to slide, adjust the gap between the magnetic rings, adjust the stiffness of the Halbach magnetic ring, and then adjust the coupling stiffness of the torsional vibration buffer in real time.

[0104] In a preferred embodiment of the present invention, in step S2, the method for modeling the magnetic field of a single permanent magnet using the equivalent magnetic charge method is:

[0105] For each permanent magnet, derive the permanent magnet infinitesimal element P(r1,θ s ,z1) The magnetic field intensity distribution model for any point M in space is as follows: Figure 3 As shown, where r1,θ s , z1 is the coordinate parameter of the infinitesimal element P in the cylindrical coordinate system;

[0106] The magnetic field intensity H in the torsional direction of a single sector-shaped arc permanent magnet is obtained by integral calculation θ (r,θ,z):

[0107]

[0108] Among them, r, θ, z are the coordinate parameters of the cylindrical coordinate system; H θ (r,θ,z) is the tangential magnetic field strength of the permanent magnet element P at any point M in space; dσ v * The basic volume expression of the volume density of the arc permanent magnet is μ0 is the magnetic permeability of vacuum; r in1 is the inner radius of the magnetic block; r out1is the outer radius of the magnetic block; θ1 is the initial angle of the magnetic block; θ2 is the end angle of the magnetic block; h is the top surface height of the magnetic block; is the space vector from the infinitesimal element P to the point M, is the θ-axis unit vector of the cylindrical coordinate system;

[0109] During the operation of the Halbach array magnetic ring, the fan-shaped arc magnetic blocks in the inner and outer rings interact with each other. The basic interaction situations can be divided into three types. The interaction model of the polarized magnetic blocks is as follows: Figure 4 、 Figure 5 、 Figure 6 shown.

[0110] The radially polarized sector-shaped arc permanent magnet belongs to non-uniform magnetization in magnetic charge theory. The inner and outer arc surfaces of each magnetic block have a positive and negative magnetic pole surface density, and the inner arc volume of the magnetic block also has a magnetic pole volume density.

[0111] The tangentially polarized sector arc permanent magnet is considered to be in a uniform magnetization state, that is, the two sides of the magnetic block carry a positive and a negative magnetic charge respectively;

[0112] Based on H θ (r,θ,z) and the torque calculation formula dT=r×dF, considering that each radially polarized magnetic block has three magnetic charge distributions, nine corresponding interaction forces will be generated, and the torque T between the radial-radial polarized magnetic blocks can be derived. RR :

[0113]

[0114] Among them, B r is the polarization intensity of the permanent magnet, 1 and 2 represent the subscripts of the outer and inner permanent magnets; r in1 is the inner radius of the outer ring magnet; r out1 is the outer radius of the outer ring magnet; θ b1 The initial angle of the outer ring magnet; θ e1 The end angle of the inner circle magnet; r in2 is the inner radius of the inner circle magnet; r out2 is the outer radius of the inner circle magnet; θ b2 The initial angle of the inner ring magnet; θ e2 The end angle of the inner circle magnet; f 1～9 are the expressions of the nine interaction forces between radial-radial polarized magnetic blocks; r1, θ1, z1, r2, θ2, and z2 are the three directional independent variables of the inner and outer ring magnetic blocks in the cylindrical coordinate system respectively;

[0115] Similarly, the torque T between the tangential-tangential polarized magnets AA The calculation formula consists of four quadruple integrals, and the torque T between the radial-tangential polarized magnets isAR It is formed by four quadruple integrals and two quintuple integrals.

[0116] In a preferred embodiment of the present invention, the negative stiffness model of the annular Halbach array magnetic block and the positive stiffness model of the spring torsion plate are constructed, and the method for calculating the total coupling stiffness is as follows:

[0117] The magnetic torsional vibration damper of the annular Halbach array is composed of three magnetization methods: radial-radial polarized magnet pairs, radial-tangential magnet pairs, and tangential-tangential polarized magnet pairs. Therefore, to solve the magnetic torque transmission capacity T(Δθ) of the annular Halbach array, it is only necessary to superimpose the torques generated by the three magnet pairs:

[0118]

[0119] Where i and j are sum index variables, representing the positions of the inner and outer ring magnets in the magnetic ring; N2 is the number of magnets in the Halbach magnetic ring; Δθ is the relative rotation angle of the magnetic ring; T AA is the torque between the tangential-tangential polarized magnets, T AR is the torque between the radial-tangential polarized magnets, T RR is the torque between radial-radial polarized magnets, T RA is the torque between the tangentially-radially polarized magnets;

[0120] The function relationship between the magnetic torque and the angle when the inner and outer rings of the Halbach magnetic ring produce relative rotation is calculated, and the magnetic torsional stiffness K of the Halbach array is obtained by derivation. m (θ):

[0121]

[0122] The spring torsion plate connects the active rotor and the driven rotor, and has a positive torsional stiffness K r , then by the material mechanics method, it is simplified into a cantilever beam model, and the deflection and transmission torque T of the inner and outer rotors under the relative rotation angle θ are derived. r Relationship, we get:

[0123]

[0124] Where n is the number of spring torsion pieces; E is the elastic modulus of the spring torsion piece; L f is the length of the spring torsion; b is the width of the spring torsion, t is the thickness of the spring torsion, I f is the section inertia moment of the spring torsion piece around the central axis of the section, θ is the relative rotation angle between the active and passive rotors; the torsional stiffness K of the spring torsion piece r Expressed as:

[0125]

[0126] After connecting the negative stiffness annular Halbach array magnetic block and the positive stiffness spring torsion piece in parallel, the total coupling stiffness K(θ)=K r +K m At the initial equilibrium position, if the two values ​​cancel each other out, a quasi-zero stiffness characteristic can be achieved, effectively reducing the torsional resonance frequency and enhancing the vibration reduction capability in the low-frequency band.

[0127] In a preferred embodiment of the present invention, in step S3, the vibration isolation effect of the magnetic torsional vibration buffer is solved using the harmonic balance method for external torsional vibration excitation, and the specific steps are as follows:

[0128] The magnetic torsional vibration damper and shafting system is modeled as a nonlinear vibration equation system with coupled stiffness and damping:

[0129]

[0130] Among them, J D is the moment of inertia of the rotor on the input shaft side; θ D is the input shaft rotation angle; c is the damping coefficient; J L is the moment of inertia of the rotor on the output shaft side; θ L is the output shaft rotation angle; T(θ) is the torque transmitted by the magnetic buffer; T d is the amplitude of the driving torque disturbance component; ω is the angular velocity of the driving torque; α is the phase difference; t is the thickness of the spring torsion plate, and θ is the relative rotation angle between the active and passive rotors;

[0131] After normalization, the formula is simplified to:

[0132]

[0133] make

[0134]

[0135] The formula is simplified to:

[0136]

[0137] make

[0138]

[0139] Then, taking the external excitation torque as input, the dimensionless dynamic equation of the system is expressed as:

[0140]

[0141] The parameters in the formula are dimensionless expressions, where is the system torsion angle variable; ζ is the system damping; t0 is the torsional amplitude; δ k is the fitting coefficient of harmonics, k is the index symbol of the summation formula; β is the system vibration frequency parameter; γ is the dimensionless reference θ; a k is the fitting coefficient of the total restoring torque; τ is the time variable; ω n Frequency parameter constructed for the intermediate variable; K r is the torsional stiffness of the spring torsion plate, n is the number of spring torsion plates; T0, J, t d To calculate and derive intermediate variables, for The second derivative of

[0142] Assume that the solution of the dynamic equation of the coupling is:

[0143]

[0144] Where, φ is the simple harmonic amplitude;

[0145] Perform Fourier or polynomial expansion on the nonlinear stiffness term to obtain the steady-state response equations:

[0146]

[0147] The iterative algorithm is used to numerically solve the response amplitude t of the magnetic torsional vibration buffer at each excitation frequency. b And the torsional vibration transmissibility T:

[0148]

[0149] in, Under the premise of ensuring the accuracy of the solution, the sixth-order polynomial is used for approximate fitting.

[0150] In a preferred embodiment of the present invention, based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustable mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time. The specific steps are as follows:

[0151] Based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustment mechanism controls the gap change between the inner and outer rings, adjusts the magnetic force distribution of the annular Halbach array magnet block and affects the negative stiffness characteristics, achieving the buffer coupling static drive torque M(θ) = K r θ+M m Dynamic adjustment of (θ), where K r is the torsional stiffness of the spring torsion plate, θ is the relative rotation angle between the active and passive rotors, M m (θ) is the torque transmitted by the magnetic ring.

[0152] The present invention also provides a magnetic torsional vibration buffer with variable stiffness for calculating and controlling the vibration isolation rate, such as Figure 1 As shown, it includes a magnetic torsional vibration buffer, a gap adjustable mechanism and a processing mechanism.

[0153] The magnetic torsional vibration buffer is connected to the gap adjustable mechanism, and the processing mechanism is connected to the magnetic torsional vibration buffer and the gap adjustable mechanism. The processing mechanism executes the method described in the present invention, calculates the vibration isolation rate of the magnetic torsional vibration buffer, and controls the gap adjustable mechanism to adjust the stiffness and torque transmission characteristics of the magnetic torsional vibration buffer in real time.

[0154] This system, based on the coupling theory of Haier Shell magnetic rings and spring torsion plates 11, systematically proposes equivalent magnetic charge modeling, inter-magnetic torque and stiffness calculations, harmonic balance dynamics solutions, and gap adjustment mechanism design and operation procedures. Through a comprehensive multi-faceted technical solution, the buffer effectively reduces low-frequency vibration amplitude while ensuring high torque transmission. It can flexibly adapt to operating conditions with varying load levels and excitation frequencies, demonstrating significant application value in suppressing torsional vibration in high-power transmission systems.

[0155] In a preferred embodiment of the present invention, the magnetic torsional vibration buffer includes a passive rotor 1, a flange 13, a load end 5, an inner ring permanent magnet block 9, an outer ring permanent magnet block 10, a spring torsion plate 11, an end cover 12, an active rotor 16, an input shaft 19 and an output shaft 20.

[0156] The passive rotor 1 is connected to the output shaft 20 via a flange 13 and coupled to the load end 5. The flange 13 is connected to the passive rotor 1 via a second bolt 15. The inner ring permanent magnet block 9 is embedded in the active rotor 16, while the outer ring permanent magnet block 10 is assembled in the wedge-shaped slider 2 of the gap adjustable mechanism.

[0157] The end cover 12 is connected to the active rotor 16 by a first bolt 14, and a gap is retained between the passive rotor 1 and the active rotor 16. The active rotor 16 is connected to the input shaft 19 and serves as the driving end 17.

[0158] The spring torsion plate 11 connects the active rotor 16 and the driven rotor, providing positive torsional stiffness. When connected in parallel, the two form a quasi-zero stiffness characteristic, enabling broadband torsional vibration suppression in the low-frequency band. The input shaft 19 is connected to the bearing 18.

[0159] In a preferred embodiment of the present invention, the gap adjustable mechanism includes a frameless motor 6, a spiral groove 8, a claw disk 7, a wedge-shaped slider 2, a reset spring 4 and a positioning pin 3. One end of the frameless motor 6 is fixed to the passive rotor 1, and the other end is tightly connected to the spiral groove 8 to control the rotation of the spiral groove 8. The pin at one end of the claw disk 7 is embedded in the spiral groove 8, converting the rotational motion of the spiral groove 8 into radial expansion and contraction of the claw disk 7. The wedge-shaped slider 2 contacts the claw disk 7 in a frictional sliding manner, and under the action of the reset spring 4 and the positioning pin 3, position control is achieved during the working process. The spiral groove 8 is driven to rotate by the frameless motor 6, and the claw disk 7 produces axial displacement, which then pushes the wedge-shaped slider 2 to slide smoothly in the radial direction.

[0160] In order to obtain a stronger magnetic field distribution in a limited size, the present invention adopts a ring-shaped Halbach array and uses Figure 2 The polarization direction and initial position are arranged in the manner shown, that is, the radial polarization and tangential polarization of the annular magnetic block are periodically alternately distributed to obtain significant negative stiffness characteristics.

[0161] The present invention combines the aforementioned coupling stiffness formula and the analysis results of the harmonic balance method, and in practical applications can automatically adjust the gap according to real-time working conditions (load size, vibration frequency, etc.).

[0162] If insufficient torque transfer capacity or poor low-frequency vibration suppression is detected, the negative stiffness ratio is adjusted by appropriately increasing or decreasing the magnetic ring gap. This, combined with the stiffness of the spring torsion plate 11, creates a coupling stiffness curve that meets the current requirements. This control process can be iterated multiple times until the damper performance indicators (such as torsional vibration transmissibility and static torque output) reach the expected range.

[0163] Based on the coupling theory of Haier Shell magnetic rings and spring torsion plates, this invention systematically proposes equivalent magnetic charge modeling, inter-magnetic torque and stiffness calculations, harmonic balance dynamics solutions, and gap adjustment mechanism design and operation procedures. Through this multi-faceted, integrated technical solution, the buffer effectively reduces low-frequency vibration amplitude while ensuring high torque transmission. It can flexibly adapt to operating conditions with varying load levels and excitation frequencies, demonstrating significant application value in suppressing torsional vibration in high-power transmission systems.

[0164] Throughout this specification, reference to terms such as "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" means that a specific feature, structure, material, or characteristic described in conjunction with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0165] While embodiments of the present invention 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 invention, and that the scope of the invention is defined by the claims and their equivalents.

Claims

1. A method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration buffer with variable stiffness, characterized in that: The steps include: S1, obtain real-time working conditions; S2, the magnetic torsional vibration damper uses a circular Halbach array magnet block and uses the equivalent magnetic charge method to model the magnetic field of a single permanent magnet; Based on the established magnetic field model of a single permanent magnet, the negative stiffness model of the annular Halbach array magnetic block and the positive stiffness model of the spring torsion plate were constructed, and the total coupling stiffness was calculated to obtain the torque transmission capacity. S3, using the harmonic balance method, solve the vibration isolation effect of the magnetic torsional vibration buffer, and obtain the vibration suppression effect and resonance range distribution under different working conditions; S4, determining whether the torque transmission capability and the low-frequency vibration suppression effect both meet the preset requirements; if so, executing step S1; otherwise, executing step S5; S5, based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustable mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time, and returns to step S2.

2. The method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration damper with variable stiffness according to claim 1, wherein: In step S2, the method of modeling the magnetic field of a single permanent magnet using the equivalent magnetic charge method is: For each permanent magnet, derive the permanent magnet infinitesimal element P(r1,θ s ,z1) the magnetic field intensity distribution model for any point M in space, where r1,θ s , z1 is the coordinate parameter of the infinitesimal element P in the cylindrical coordinate system; The magnetic field intensity H in the torsional direction of a single sector-shaped arc permanent magnet is obtained by integral calculation θ (r,θ,z): Among them, r, θ, z are the coordinate parameters of the cylindrical coordinate system; H θ (r,θ,z) is the tangential magnetic field strength of the permanent magnet element P at any point M in space; The basic volume expression of the volume density of the arc permanent magnet is μ0 is the magnetic permeability of vacuum; r in1 is the inner radius of the magnetic block; r out1 is the outer radius of the magnetic block; θ1 is the initial angle of the magnetic block; θ2 is the end angle of the magnetic block; h is the top surface height of the magnetic block; is the space vector from the infinitesimal element P to the point M, is the θ-axis unit vector of the cylindrical coordinate system; During operation, the inner and outer sector arc magnetic blocks of the Halbach array magnetic ring interact with each other. In magnetic charge theory, radially polarized sector arc permanent magnets are classified as non-uniformly magnetized. The inner and outer arc surfaces of each magnetic block carry a positive and negative magnetic pole surface density, while the internal arc volume of the magnetic block also has a magnetic pole volume density. Tangentially polarized sector arc permanent magnets are considered to be in a uniform magnetization state, that is, the two sides of the magnetic block carry a positive and negative magnetic charge respectively. Based on H θ (r,θ,z) and torque dT=r×dF, considering that each radially polarized magnetic block has three magnetic charge distributions, nine corresponding interaction forces will be generated, and the torque T between the radial-radial polarized magnetic blocks is derived. RR : Among them, B r is the polarization intensity of the permanent magnet, 1 and 2 represent the subscripts of the outer and inner permanent magnets; r in1 is the inner radius of the outer ring magnet; r out1 is the outer radius of the outer ring magnet; θ b1 Initial angle of the outer ring magnet; θ e1 The end angle of the inner circle magnet; r in2 is the inner radius of the inner circle magnet; r out2 is the outer radius of the inner circle magnet; θ b2 The initial angle of the inner ring magnet; θ e2 The end angle of the inner circle magnet; f 1～9 are the expressions of the nine interaction forces between radial-radial polarized magnetic blocks; r1, θ1, z1, r2, θ2, and z2 are the three directional independent variables of the inner and outer ring magnetic blocks in the cylindrical coordinate system respectively; Torque T between tangential-tangential polarized magnets AA The calculation formula consists of four quadruple integrals, and the torque T between the radial-tangential polarized magnets is AR It is formed by four quadruple integrals and two quintuple integrals.

3. The method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration damper with variable stiffness according to claim 1, wherein: The method for constructing the negative stiffness model of the ring-shaped Halbach array magnetic block and the positive stiffness model of the spring torsion plate and calculating the total coupling stiffness is as follows: The magnetic torsional vibration damper of the annular Halbach array is composed of three magnetization methods: radial-radial polarized magnet pairs, radial-tangential magnet pairs, and tangential-tangential polarized magnet pairs. Therefore, to solve the magnetic torque transmission capacity T(Δθ) of the annular Halbach array, it is only necessary to superimpose the torques generated by the three magnet pairs: Where i and j are sum index variables, representing the positions of the inner and outer ring magnets in the magnetic ring; N2 is the number of magnets in the Halbach magnetic ring; Δθ is the relative rotation angle of the magnetic ring; T AA is the torque between the tangential-tangential polarized magnets, T AR is the torque between the radial-tangential polarized magnets, T RR is the torque between radial-radial polarized magnets, T RA is the torque between the tangentially-radially polarized magnets; The function relationship between the magnetic torque and the angle when the inner and outer rings of the Halbach magnetic ring produce relative rotation is calculated, and the magnetic torsional stiffness K of the Halbach array is obtained by derivation. m (θ): The spring torsion plate connects the active rotor and the driven rotor, and has a positive torsional stiffness K r , then by the material mechanics method, it is simplified into a cantilever beam model, and the deflection and transmission torque T of the inner and outer rotors under the relative rotation angle θ are derived. r Relationship, we get: Where n is the number of spring torsion pieces; E is the elastic modulus of the spring torsion piece; L f is the length of the spring torsion; b is the width of the spring torsion, t is the thickness of the spring torsion, I f is the section inertia moment of the spring torsion piece around the central axis of the section, θ is the relative rotation angle between the active and passive rotors; the torsional stiffness K of the spring torsion piece r Expressed as: After connecting the negative stiffness annular Halbach array magnetic block and the positive stiffness spring torsion piece in parallel, the total coupling stiffness K(θ)=K r +K m (θ).

4. The method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration damper with variable stiffness according to claim 1, wherein: In step S3, the harmonic balance method is used to solve the vibration isolation effect of the magnetic torsional vibration buffer. The specific steps are as follows: The magnetic torsional vibration damper and shafting system is modeled as a nonlinear vibration equation system with coupled stiffness and damping: Among them, J D is the moment of inertia of the rotor on the input shaft side; θ D is the input shaft rotation angle; c is the damping coefficient; J L is the moment of inertia of the rotor on the output shaft side; θ L is the output shaft rotation angle; T(θ) is the torque transmitted by the magnetic buffer; T d is the amplitude of the driving torque disturbance component; ω is the angular velocity of the driving torque; α is the phase difference; t is the thickness of the spring torsion plate, and θ is the relative rotation angle between the active and passive rotors; After normalization, the formula is simplified to: make The formula is simplified to: make Then, taking the external excitation torque as input, the dimensionless dynamic equation of the system is expressed as: The parameters in the formula are dimensionless expressions, where is the system torsion angle variable; ζ is the system damping; t0 is the torsional amplitude; δ k is the fitting coefficient of harmonics, k is the index symbol of the summation formula; β is the system vibration frequency parameter; γ is the dimensionless reference θ; a k is the fitting coefficient of the total restoring torque; τ is the time variable; ω n Frequency parameter constructed for the intermediate variable; K r is the torsional stiffness of the spring torsion plate, n is the number of spring torsion plates; T0, J, t d To calculate and derive intermediate variables, for The second derivative of Assume that the solution of the dynamic equation of the coupling is for: Where φ is the amplitude of the solution to the equation; Perform Fourier or polynomial expansion on the nonlinear stiffness term to obtain the steady-state response equations: The iterative algorithm is used to numerically solve the response amplitude t of the magnetic torsional vibration buffer at each excitation frequency. b And the torsional vibration transmissibility T: in, Under the premise of ensuring the accuracy of the solution, the sixth-order polynomial is used for approximate fitting.

5. The method for calculating and controlling the vibration isolation rate of a magnetic torsional vibration damper with variable stiffness according to claim 1, wherein: Based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustment mechanism adjusts the spring torsion plate stiffness and the magnetic ring gap in real time. The specific steps are as follows: Based on the vibration isolation effect of the magnetic torsional vibration buffer, the gap adjustment mechanism controls the gap change between the inner and outer rings, adjusts the magnetic force distribution of the annular Halbach array magnet block and affects the negative stiffness characteristics, achieving the buffer coupling static drive torque M(θ) = K r θ+M m Dynamic adjustment of (θ), where K r is the torsional stiffness of the spring torsion plate, θ is the relative rotation angle between the active and passive rotors, M m (θ) is the torque transmitted by the magnetic ring.

6. A vibration isolation rate calculation and control system for a magnetic torsional vibration buffer with variable stiffness, characterized in that: It includes a magnetic torsional vibration buffer, a gap adjustable mechanism and a processing mechanism; The magnetic torsional vibration buffer is connected to the gap adjustable mechanism, and the processing mechanism is connected to the magnetic torsional vibration buffer and the gap adjustable mechanism. The processing mechanism executes the method described in one of claims 1 to 5, calculates the vibration isolation rate of the magnetic torsional vibration buffer, and controls the gap adjustable mechanism to adjust the stiffness and torque transmission characteristics of the magnetic torsional vibration buffer in real time.

7. The vibration isolation rate calculation and control system of the variable stiffness magnetic torsional vibration buffer according to claim 6, characterized in that: The magnetic torsional vibration buffer includes a passive rotor, a flange, a load end, an inner ring permanent magnet block, an outer ring permanent magnet block, a spring torsion plate, an end cover, an active rotor, an input shaft and an output shaft; The passive rotor is connected to the output shaft through a flange and coupled to the load end; The inner ring permanent magnet blocks are embedded in the active rotor, while the outer ring permanent magnet blocks are assembled in the wedge-shaped slider of the gap adjustable mechanism; The end cover is connected to the active rotor, and a gap is retained between the passive rotor and the active rotor. The active rotor is connected to the input shaft and plays the role of the driving end. The spring torsion plate connects the driving rotor and the driven rotor to provide positive torsional stiffness.

8. The vibration isolation rate calculation and control system of the variable stiffness magnetic torsional vibration buffer according to claim 6, characterized in that: The gap adjustable mechanism includes a frameless motor, a spiral groove, a claw plate, a wedge-shaped slider, a return spring and a positioning pin; One end of the frameless motor is fixed to the passive rotor, and the other end is connected to the spiral groove to control the rotation of the spiral groove; The latch at one end of the claw disc is embedded in the spiral groove, converting the rotational motion of the spiral groove into radial expansion and contraction of the claw disc; The wedge-shaped slider contacts the claw plate in a friction sliding manner, and under the action of the return spring and the positioning pin, the position control during the working process is achieved; The spiral groove is driven to rotate by a frameless motor, causing the claw plate to produce axial displacement, which in turn pushes the wedge-shaped slider to slide smoothly in the radial direction.

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