A Calculation Method of Magnetic Damping for a Permanent Magnet Coupling with Hysteresis Loop Energy Conservation

Abstract

The present invention belongs to the technical field of permanent magnet magnetic drive, and discloses a method for calculating the magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation. This method uses a three-dimensional magnetic force equivalent model of the permanent magnet coupling, applies an external force to the inner rotor to cause forced vibration, calculates the torque values of the inner rotor and the outer rotor of the permanent magnet coupling at different times respectively, forms a hysteresis loop curve of the torque value changing with the angular displacement at different times, and calculates the area enclosed by the hysteresis loop according to the ellipse area formula, that is, the energy dissipated due to magnetic damping within one vibration cycle of the permanent magnet coupling. According to the energy conservation effect, the magnetic damping of the permanent magnet coupling can be inversely calculated, accurately obtaining its dynamic behavior characteristics, providing a strong theoretical support for the analysis of the transmission performance of the permanent magnet coupling, and it is a calculation method with universality and practical application value.

Description

Technical Field

[0001] The present invention belongs to the technical field of permanent magnet magnetic drive, and relates to a calculation method of magnetic damping for a permanent magnet coupling with hysteresis loop energy conservation. Background Art

[0002] Underwater deep submersibles, underwater thrusters, navigators, etc. are the core equipment of major projects in China's marine field. Such equipment often operates under extremely harsh working conditions such as strong impact, high air pressure, strong load, and low temperature, which puts relatively strict requirements on the stable operation of the equipment. As a connecting component between the power source and the load, the coupling is used to transmit torque and thus achieve the transmission of equipment power, and is widely used in major engineering equipment. The traditional mechanical coupling uses a contact method for power transmission, and has disadvantages such as serious wear, large vibration, high centering accuracy, and difficult maintenance during operation. The permanent magnet coupling is a non-contact power transmission component that can isolate vibration from the power source, and has advantages such as overload protection, simple maintenance, low centering requirements, and high stability, and can effectively reduce the vibration transmission between the power source and the load. However, when the permanent magnet of the permanent magnet coupling moves in the magnetic field, an induced current will be generated, causing it to be affected by the Ampere force, and then generating electromagnetic damping, which is dissipated in the form of heat energy. Its dynamic characteristics are extremely complex. If the influence of magnetic damping on the permanent magnet coupling itself is ignored, it is contrary to the real physical phenomenon, and the dynamic behavior characteristics cannot be accurately obtained, thus affecting the research on the transmission performance. Therefore, developing a calculation method of magnetic damping for a permanent magnet coupling with hysteresis loop energy conservation is of great significance for the performance analysis of the permanent magnet coupling.

[0003] Regarding the calculation problem of magnetic damping of the permanent magnet coupling, Zhou Jinhua, Chen Jian, etc. proposed a magnet damping mechanism in "A Magnet Damper Mechanism" (CN 115800626 A) for linkage with the motor in the electric tailgate system of an automobile. The end face polarities of the soft magnetic ring and the strong magnetic ring are set to be opposite to generate an attractive force, enhance the radial torque, and improve the damping effect. This method analyzes the importance of magnetic damping in the whole mechanism, but does not study the calculation of magnetic damping and cannot provide an accurate magnetic damping value. Regarding the calculation problem of magnetic damping of the permanent magnet coupling, Zhang Guoyuan et al. from Xidian University published an article "Dynamic Characteristics of Misaligned Gear Coupling - Bearing - Rotor System" in the second issue of the Journal of Aerospace Power in 2022, constructed a calculation model of the stiffness and damping of the gear coupling and a solution model of additional forces and torques, and analyzed the influence laws of misalignment parameters on the critical speed, vibration response, etc., providing theoretical guidance for the stable operation of the shafting rotor system. This method can effectively analyze the influence laws of misalignment factors on the dynamic performance of the rotor. However, this method is only applicable to the damping generated by friction factors and cannot calculate the magnetic damping of the permanent magnet coupling.

[0004] Therefore, a method for calculating the magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation has important guiding significance for the research of permanent magnet magnetic drive technology. Summary of the Invention

[0005] In order to make up for the defects of the prior art, the present invention invents a method for calculating the magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation. The purpose is to fully consider the energy dissipated by the permanent magnet coupling within one vibration cycle, calculate the magnetic damping of the permanent magnet coupling by using the hysteresis loop energy conservation method, and provide important theoretical support for the analysis of the transmission performance of the permanent magnet coupling. This method is based on the three-dimensional magnetic force calculation model of the permanent magnet coupling, uses dynamic meshing to set the rotation domain of the inner rotor, sets the rotation type and angular velocity value, simulates the dynamic operation behavior of the permanent magnet coupling, and then obtains the torque value of the permanent magnet coupling at different times, and calculates the energy dissipated by the magnetic damping through the hysteresis loop curve, and finally realizes the calculation of the magnetic damping of the permanent magnet coupling.

[0006] The technical solution of the present invention:

[0007] A method for calculating the magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation, which establishes a three-dimensional magnetic force equivalent model of the permanent magnet coupling, calculates the Lorentz force received by the permanent magnet coupling by using the Lorentz force equation, and calculates the torque values of the inner rotor and the outer rotor of the permanent magnet coupling at different times respectively, forms a hysteresis loop curve of the torque value changing with the angular displacement at different times, and calculates the area enclosed by the hysteresis loop according to the ellipse area formula, that is, the energy dissipated by the magnetic damping, and the magnetic damping of the permanent magnet coupling can be inversely calculated according to the energy conservation effect, and its dynamic behavior characteristics can be accurately obtained, providing strong theoretical support for the analysis of the transmission performance of the permanent magnet coupling; the specific steps are as follows:

[0008] The first step is to determine the key parameters of the permanent magnet coupling and calculate the torque values of the inner and outer rotors

[0009] First, determine the key parameters of the permanent magnet coupling: the outer diameter of the inner rotor hub 3 of the permanent magnet coupling is r1, the inner diameter of the outer rotor hub 5 is r2, the number of pole pairs of the inner rotor permanent magnet 2 and the outer rotor permanent magnet 6 is p, the thickness of the permanent magnet is h, the length is a, the width of the upper bottom surface is b1, the width of the lower bottom surface is b2, the relative rotation angle of the inner and outer rotors is θ, the permanent magnets are arranged alternately with N and S poles along the circumference, and the number of pole pairs is even;

[0010] Next, calculate the torque values of the inner and outer rotors of the permanent magnet coupling: Since the permanent magnet coupling is a periodically symmetric structure, to improve the calculation efficiency, the interaction between a pair of magnetic steels of the inner and outer rotors can be analyzed. Establish a three-dimensional magnetic force equivalent model for a pair of magnetic steels of the inner and outer rotors of the permanent magnet coupling, and set the number of sectors z in the sector symmetry. The number of sectors z is the number of pole pairs p of the magnetic steels of the inner and outer rotors. Complete the torque analysis of the entire structure of the permanent magnet coupling through anti-periodicity; the force exerted on a moving magnetic charge in a magnetic field, that is, the Lorentz force, is calculated by the formula:

[0011] F = q(E + v×B) (1)

[0012] where F is the Lorentz force exerted on the moving magnetic charge, B is the magnetic induction intensity at the location of the magnetic charge, q is the charge quantity of the moving magnetic charge, v is the velocity of the moving charge, and E is the electric field intensity.

[0013] Then the resultant force F of the p pairs of magnetic steels of the permanent magnet coupling p The calculation formula is expressed as:

[0014] F p = p·F(2)

[0015] The calculation formulas for the torque T1 of the inner rotor and the torque T2 of the outer rotor of the permanent magnet coupling are expressed as:

[0016] T1 = F p ·r1(3)

[0017] T2 = F p ·r2(4)

[0018] Using the three-dimensional magnetic force equivalent model of a pair of magnetic steels of the inner and outer rotors of the permanent magnet coupling, set the inner rotor as the rotating domain by using dynamic meshing, and given the initial angle α0 and the angular velocity ω to make it rotate relative to the outer rotor, calculate the torque values of the inner and outer rotors at different times.

[0019] That is, the calculation of the torque values of the inner and outer rotors of the permanent magnet coupling is completed above.

[0020] Step 2: Calculate the energy dissipated by the permanent magnet coupling

[0021] Set the boundary condition of the outer rotor of the permanent magnet coupling as a fixed constraint, apply an external force that changes with time t to the inner rotor, the permanent magnet coupling will generate damped forced vibration, and the established differential equation is expressed as:

[0022]

[0023] where m is the mass of the permanent magnet coupling, c is the damping of the permanent magnet coupling, k is the stiffness of the permanent magnet coupling, x, They are the displacement, velocity, and acceleration of the permanent magnet coupling respectively. F0 is the external force applied to the inner rotor, and ω is the angular velocity of the inner rotor rotation.

[0024] During the forced vibration of the inner rotor of the permanent magnet coupling, the energy input to the system by the externally applied force is dissipated by the damping of the permanent magnet coupling. The formula for calculating the energy dissipated by the damping within one cycle of forced vibration is expressed as:

[0025]

[0026] Among them, Q is the energy dissipated by the permanent magnet coupling, f is the damping force acting on the inner rotor, dx represents the differential of x, dt represents the differential of t, and x0 represents the amplitude of the inner rotor movement.

[0027] Step 3: Calculate the area enclosed by the hysteresis loop curve and back-calculate the magnetic damping value

[0028] The damping force acting on the inner rotor can be calculated from the damping and the velocity of the movement. The formula is expressed as:

[0029]

[0030] Among them, x(t) represents the displacement of the inner rotor changing with time, represents the velocity of the inner rotor changing with time.

[0031] From the above formula (7), we can obtain:

[0032]

[0033] The above formula (8) represents an ellipse equation, that is, the damping force and the displacement enclose an ellipse, namely the hysteresis loop curve.

[0034] According to the set angular velocity ω above, the angular displacement q of the inner rotor of the permanent magnet coupling at different times can be calculated. The calculation formula is expressed as:

[0035] q = ω·t (9)

[0036] In the first step, the torque values of the inner and outer rotors of the permanent magnet coupling at different times were calculated. Due to the existence of magnetic damping, the torque value of the inner rotor of the permanent magnet coupling decreases during the reciprocating operation. Similar to the analysis of the damping force and displacement, the angular displacement and torque value of the permanent magnet coupling at different times also enclose a hysteresis loop. The theoretical numerical calculation formula for the area S enclosed by the hysteresis loop curve is expressed as:

[0037] S = π×l×n (10)

[0038] Among them, l is the length of the major semi-axis of the ellipse, and n is the length of the minor semi-axis of the ellipse.

[0039] That is, the above completes the calculation of the hysteresis loop curve area.

[0040] Since the energy dissipated by the damping of the inner rotor of the permanent magnetic coupling during forced vibration is the area enclosed by the hysteresis loop, the magnetic damping value of the permanent magnetic coupling can be calculated by combining equations (6) and (10). The calculation formula is expressed as:

[0041]

[0042] That is, the above completes the calculation of the magnetic damping of the permanent magnet coupling.

[0043] The beneficial effect of the present invention is that a method for calculating the magnetic damping of a permanent magnet coupling based on the conservation of hysteresis loop energy is proposed, which can comprehensively analyze the change of the torque value with the angular displacement when the permanent magnet coupling generates forced vibration under the action of an external force, and use the hysteresis loop curve to calculate the energy dissipated by the permanent magnet coupling, and then accurately calculate the magnetic damping value of the permanent magnet coupling; this method accurately calculates the magnetic damping value of the permanent magnet coupling, helps to analyze its dynamic characteristics, accurately obtain its dynamic operating behavior, and provide strong theoretical support for the study of the transmission performance of the permanent magnet coupling. It is a universal analysis method. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The present invention is a flow chart of a method for calculating magnetic damping of a permanent magnetic coupling based on hysteresis loop energy conservation.

[0045] Figure 2 It is a schematic diagram of the permanent magnet coupling structure.

[0046] Figure 3 It is a hysteresis loop curve.

[0047] In the figure: 1-inner rotor end cover, 2-inner rotor magnet, 3-inner rotor hub, 4-outer rotor cover plate, 5-outer rotor hub, 6-outer rotor magnet, 7-inner rotor cover plate, 8-outer rotor end cover. Specific implementation plan

[0048] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0049] Example

[0050] A trapezoidal permanent magnet coupling with 16 pairs of magnetic poles is selected. An external force that varies with time is applied to the inner rotor to force it to vibrate. The torque values of the inner and outer rotors at different times are obtained, and the changes in torque under different angular displacements are analyzed. The energy dissipated by the permanent magnet coupling is calculated using the hysteresis loop curve, and then the magnetic damping value of the permanent magnet coupling is inversely calculated.

[0051] Figure 1It is a flowchart of a calculation method for magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation. The specific steps of the calculation method are as follows:

[0052] First step: Determine the key parameters of the permanent magnet coupling and calculate the torque values of the inner and outer rotors

[0053] First, determine the key parameters of the permanent magnet coupling: Figure 2 It is a schematic structural diagram of the permanent magnet coupling. The inner diameter of the outer rotor hub 5 of the permanent magnet coupling is 70 mm, the outer diameter of the inner rotor hub 3 is 65 mm, the number of pole pairs of the inner rotor magnet 2 and the outer rotor magnet 6 is 16, the thickness of the magnet is 10 mm, the length is 40 mm, the width of the upper bottom surface is 10 mm, the width of the lower bottom surface is 15 mm, the relative rotation angle of the inner and outer rotors is 0°, and the magnets are arranged alternately with N and S poles along the circumference;

[0054] Secondly, calculate the torque values of the inner and outer rotors of the permanent magnet coupling: Since the permanent magnet coupling is a periodically symmetric structure, in order to improve the calculation efficiency, the interaction between a pair of magnets of the inner and outer rotors can be analyzed. Establish a three-dimensional magnetic force equivalent model for a pair of magnets of the inner and outer rotors of the permanent magnet coupling, and set the number of sectors to 16 in the sector symmetry to complete the torque analysis of the entire structure of the permanent magnet coupling through anti-periodicity; Use the three-dimensional magnetic force equivalent model of a pair of magnets of the inner and outer rotors of the permanent magnet coupling, set the inner rotor as the rotating domain by using dynamic meshing, and give an initial angle of 0.9° and an angular velocity of sin(20πt) to make it rotate relative to the outer rotor. According to the Lorentz force theorem, the Lorentz force F = 27.21 N is calculated by Equation (1); Then, the tangential resultant force F of 16 pairs of magnets is calculated by Equation (2) p = 435.36 N; Finally, the inner rotor torque T1 = 28.30 N·m is calculated by Equation (3), and the outer rotor torque T2 = 30.48 N·m is calculated by Equation (4), that is, the calculation of the torque values of the inner and outer rotors of the permanent magnet coupling is completed above.

[0055] Second step: Calculate the energy dissipated by the permanent magnet coupling

[0056] Set the boundary condition of the outer rotor of the permanent magnet coupling as a fixed constraint, apply an external force that changes with time t to the inner rotor, and the inner rotor of the permanent magnet coupling will generate damped forced vibration. During the forced vibration of the inner rotor, the energy input to the system by the external applied force is dissipated by the damping of the permanent magnet coupling. During one cycle of forced vibration, the angular displacement amplitude of the inner rotor movement is 2.78×10 -4 rad. Therefore, the energy E dissipated by the damping is E = 7.73×10 -8 πcω.

[0057] Third step: Calculate the area enclosed by the hysteresis loop curve and inversely calculate the magnetic damping value

[0058] In the first step, the torque values of the inner and outer rotors of the permanent magnet coupling are calculated. Due to the existence of magnetic damping, the torque value of the inner rotor of the permanent magnet coupling decreases during the reciprocating operation, and the angular displacement and torque value of the permanent magnet coupling at different times form a hysteresis loop, such as Figure 3 As shown, the length of the major axis of the ellipse is 1.3m, and the length of the minor axis is 5.56×10 -4 m, then the area of the hysteresis loop curve is S = 2.27 × 10 -3 m 2 .

[0059] That is, the above completes the calculation of the hysteresis loop curve area.

[0060] Since the energy dissipated by the damping of the inner rotor of the permanent magnet coupling during forced vibration is the area enclosed by the hysteresis loop, the magnetic damping value of the permanent magnet coupling can be calculated by combining equations (6) and (10), c = 414.01 N·m·s / rad.

[0061] That is, the above completes the calculation of the magnetic damping of the permanent magnet coupling.

[0062] This method uses the three-dimensional magnetic equivalent model of the permanent magnet coupling, applies external force to the inner rotor to force it to vibrate, and calculates the torque values of the inner rotor and the outer rotor of the permanent magnet coupling at different times, respectively, to form a hysteresis loop curve of the torque value changing with the angular displacement at different times, and calculates the area enclosed by the hysteresis loop according to the ellipse area formula, that is, the energy dissipated by the permanent magnet coupling due to magnetic damping in a vibration cycle. The magnetic damping of the permanent magnet coupling can be inversely calculated according to the energy conservation effect, and its dynamic behavior characteristics can be accurately obtained, providing strong theoretical support for the analysis of the transmission performance of the permanent magnet coupling. It is a calculation method with universal applicability and practical application value.

Claims

1. A calculation method for magnetic damping of a permanent magnet coupling with hysteresis loop energy conservation, characterized in that The steps are as follows: First step, determine the key parameters of the permanent magnet coupling and calculate the torque values of the inner and outer rotors. First, determine the key parameters of the permanent magnet coupling: The outer diameter of the inner rotor hub (3) of the permanent magnet coupling is r1, the inner diameter of the outer rotor hub (5) is r2, the number of pole pairs of the inner rotor permanent magnets (2) and the outer rotor permanent magnets (6) is p, the thickness of the permanent magnets is h, the length is a, the width of the upper bottom surface is b1, the width of the lower bottom surface is b2, the relative rotation angle between the inner and outer rotors is θ, the permanent magnets are arranged alternately with N and S poles along the circumference, and the number of pole pairs is an even number. Secondly, calculate the torque values of the inner and outer rotors of the permanent magnet coupling: Since the permanent magnet coupling is a periodically symmetric structure, in order to improve the calculation efficiency, the interaction between a pair of permanent magnets of the inner and outer rotors can be analyzed; establish a three-dimensional magnetic force equivalent model for a pair of permanent magnets of the inner and outer rotors of the permanent magnet coupling, and set the number of sectors z in the sector symmetry, where the number of sectors z is the number of pole pairs p of the inner and outer rotor permanent magnets, and complete the torque analysis of the entire structure of the permanent magnet coupling through anti-periodicity; the force exerted on a moving magnetic charge in a magnetic field, that is, the Lorentz force, is calculated by the formula: F = q(E + v×B) (1) where, F is the Lorentz force exerted on the moving magnetic charge, B is the magnetic induction intensity at the location of the magnetic charge, q is the charge quantity of the moving magnetic charge, v is the velocity of the moving charge, and E is the electric field intensity. Then the resultant force F of the permanent magnet coupling p on the permanent magnets p is expressed by the calculation formula as follows: F p = p·F (2) The calculation formulas for the inner rotor torque T1 and the outer rotor torque T2 of the permanent magnet coupling are expressed as: T1 = F p ·r1 (3) T2 = F p ·r2 (4) Using the three-dimensional magnetic force equivalent model of a pair of permanent magnets of the inner and outer rotors of the permanent magnet coupling, set the inner rotor as a rotating domain by using dynamic meshing, and give the initial angle α0 and the angular velocity ω to make it rotate relative to the outer rotor, and calculate the torque values of the inner and outer rotors at different times. That is, the calculation of the torque values of the inner and outer rotors of the permanent magnet coupling is completed. Second step, calculate the energy dissipated by the permanent magnet coupling. Set the boundary condition of the outer rotor of the permanent magnet coupling as a fixed constraint, apply an external force that changes with time t to the inner rotor, and the permanent magnet coupling will generate damped forced vibration. The established differential equation is expressed as: where m is the mass of the permanent magnet coupling, c is the damping of the permanent magnet coupling, k is the stiffness of the permanent magnet coupling, x, are respectively the displacement, velocity, and acceleration of the permanent magnet coupling, F0 is the external force applied to the inner rotor, and ω is the angular velocity of the inner rotor rotation; During the process of forced vibration of the inner rotor of the permanent magnet coupling, the energy input to the system by the external applied force is dissipated by the damping of the permanent magnet coupling. The calculation formula for the energy dissipated by the damping within one cycle of forced vibration is: where, Q is the energy dissipated by the permanent magnet coupling, f is the damping force received by the inner rotor, dx represents the differential of x, dt represents the differential of t, and x0 represents the amplitude of the inner rotor movement. Third step, calculate the area enclosed by the hysteresis loop curve and inversely calculate the magnetic damping value. The damping force received by the inner rotor is calculated by the damping and the velocity of the movement, and the formula is expressed as: where x(t) represents the displacement of the inner rotor varying with time, represents the speed of the inner rotor varying with time; From the above formula (7), we get: The above formula (8) represents an ellipse equation, that is, the damping force and the displacement enclose an ellipse, that is, the hysteresis loop curve. According to the set angular velocity ω, calculate the angular displacement q of the inner rotor of the permanent magnet coupling at different times, and the calculation formula is expressed as: q = ω·t (9) In the first step, the torque values of the inner and outer rotors of the permanent magnet coupling at different times are calculated. Due to the existence of magnetic damping, the torque value of the inner rotor of the permanent magnet coupling decreases during the reciprocating operation, and the angular displacement and torque value of the permanent magnet coupling at different times also form a hysteresis loop; the theoretical numerical calculation formula of the area S enclosed by the hysteresis loop curve is expressed as: S=π×l×n (10) Among them, l is the length of the major semi-axis of the ellipse, and n is the length of the minor semi-axis of the ellipse; That is to complete the calculation of the hysteresis loop curve area; Since the energy dissipated by the damping of the inner rotor of the permanent magnetic coupling during forced vibration is the area enclosed by the hysteresis loop, the magnetic damping value of the permanent magnetic coupling can be calculated by combining equations (6) and (10). The calculation formula is expressed as: That completes the calculation of the magnetic damping of the permanent magnet coupling.

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