CN113944713B - Method for increasing magnetic force of permanent magnet spring - Google Patents

Method for increasing magnetic force of permanent magnet spring Download PDF

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CN113944713B
CN113944713B CN202111110168.4A CN202111110168A CN113944713B CN 113944713 B CN113944713 B CN 113944713B CN 202111110168 A CN202111110168 A CN 202111110168A CN 113944713 B CN113944713 B CN 113944713B
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permanent magnet
attraction
magnetic force
repulsion
area
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CN113944713A (en
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朱晨航
张晨晨
孟彬
衡垚圳
徐豪
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Zhejiang University of Technology ZJUT
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Zhejiang University of Technology ZJUT
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F6/00—Magnetic springs; Fluid magnetic springs, i.e. magnetic spring combined with a fluid
    • F16F6/005—Magnetic springs; Fluid magnetic springs, i.e. magnetic spring combined with a fluid using permanent magnets only
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2222/00—Special physical effects, e.g. nature of damping effects
    • F16F2222/06—Magnetic or electromagnetic
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16F—SPRINGS; SHOCK-ABSORBERS; MEANS FOR DAMPING VIBRATION
    • F16F2228/00—Functional characteristics, e.g. variability, frequency-dependence
    • F16F2228/06—Stiffness

Abstract

A method for increasing the magnetic force of a permanent magnet spring comprises the following steps: step 1, expressing the magnetic force between two permanent magnets as an explicit type of a known function through numerical calculation software; step 2, calculating fixed permanent magnets and permanent magnets in any shapes based on analytical models of longitudinal magnetic force between two permanent magnets in any shapesBetween infinitesimal F z Discrete coordinates of relative position of = 0; step 3, connecting the discrete coordinates to establish an attraction-repulsion boundary line of the fixed permanent magnet, and further drawing a repulsion area and an attraction area; step 4, determining the design range of the moving permanent magnet through the repulsion region and the attraction region; and 5, determining the shape of the moving permanent magnet when the magnetic force is maximum according to the attraction-repulsion boundary line, the attraction-repulsion area and the design range in the step. The method has the advantages that the repulsion area and the attraction area for fixing the permanent magnet are drawn, and the areas provide important references for solving the problems of small volume, maximum bearing capacity, stability, optimal design range determination and the like.

Description

Method for increasing magnetic force of permanent magnet spring
Technical Field
The invention belongs to the technical field of machinery and mechanics, and relates to a method for increasing the magnetic force of a permanent magnet spring.
Technical Field
Compared with the traditional mechanical spring, the permanent magnet spring has the advantages of no mechanical contact, no abrasion, no friction, good stability and the like, and the permanent magnet spring does not relate to fatigue failure in a magnetic field, so that the permanent magnet spring has almost unlimited service life. These characteristics are of great significance in improving vibration and noise of equipment, reducing energy consumption, prolonging service life and improving durability.
Because the rare earth permanent magnet resource is a non-renewable strategic resource, the method has important significance for the effective utilization of permanent magnet energy and the research of small volume. In order to increase the stiffness of the permanent magnet spring in a limited volume, the following three methods are generally used: 1) A hybrid magnetic spring. The permanent magnet spring can be combined with an electromagnet to control the stiffness, and although the design has more flexibility, the electromagnet with high power consumption, expensive sensors and controllers make the control complex and the volume larger. 2) Halbach array. The Halbach array is a very effective method for improving the maximum bearing capacity and rigidity of the magnetic spring, but the method inevitably has the problems of complex structure, great optimization difficulty and instability. 3) A differential spring structure. The differential permanent magnet spring has the advantages of simple manufacture, high reliability, large rigidity, linearity of a force-displacement curve close to a balance position and the like. However, almost all current differential permanent magnet springs use permanent magnet rings with rectangular cross-sections, and there is little research on more meaningful shapes.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides a method for increasing the magnetic force of a permanent magnet spring, which can improve the rigidity of the permanent magnet spring in a limited volume and save non-renewable rare earth permanent magnet resources.
The technical scheme adopted by the invention is as follows: a method for increasing the magnetic force of a permanent magnet spring comprises the following steps:
and step 1, expressing the longitudinal magnetic force between two permanent magnet micro-elements as an explicit expression of a known function through numerical calculation software. Because the magnetic force of the permanent magnet follows the superposition principle, the permanent magnet in any shape can be regarded as a combination of numerous permanent magnet microelements theoretically, so that the longitudinal magnetic force between two permanent magnets in any shape can be calculated through the following analytical model:
Figure BDA0003270306690000011
wherein l is the length of the permanent magnet, B 1 、B 2 Respectively, permanent magnet infinitesimal ds 1 And ds 2 Residual magnetic induction intensity of 0 Is a vacuum permeability, ds 1 、ds 2 Respectively the cross-sectional areas of the two permanent magnet infinitesimal. r is ds 1 And ds 2 Theta is the included angle between the straight line r and the positive direction of the x abscissa, and alpha and beta are the magnetic induction intensity B respectively 1 、B 2 The angle to the positive direction of the x-axis of the abscissa.
Step 2, calculating F between the fixed permanent magnet in any shape and the permanent magnet infinitesimal based on the analytic model of the longitudinal magnetic force between the two permanent magnets in any shape z Discrete coordinates of relative position of =0.
And 3, connecting the discrete coordinates to establish an attraction-repulsion boundary line of the fixed permanent magnet, and further drawing a repulsion area and an attraction area.
And 4, determining the design range of the moving permanent magnet through the repelling area and the attracting area.
And 5, determining the shape of the moving permanent magnet when the magnetic force is maximum according to the attraction-repulsion boundary line, the repulsion area, the attraction area and the design range in the steps.
The invention has the beneficial effects that the attraction-repulsion boundary line of the permanent magnet is provided, the repulsion area and the attraction area of the fixed permanent magnet are drawn, and the areas provide important references for solving the problems of small volume, maximum bearing capacity, stability, determination of the optimization design range and the like. Compared with the traditional permanent magnet spring with a rectangular section, the permanent magnet spring designed by the method has the advantages that:
1) And (4) small volume. The volume of the permanent magnet spring is effectively reduced, so that the permanent magnet spring has larger volume force and is particularly suitable for special fields of space flight and aviation, high speed, ultra-pure and the like.
2) The optimization is convenient. The effective magnetic force and the stable position of the permanent magnet spring are determined, the optimal design range of the permanent magnet spring is narrowed, and the design efficiency of the spring is improved.
3) High rigidity. The permanent magnet spring ensures that only repulsive force is applied between the two permanent magnets, and effectively improves the rigidity and the bearing capacity of the permanent magnet spring.
4) Is environment-friendly. Reduces the waste of the non-renewable rare earth permanent magnet resource and has obvious environmental protection effect.
5) Simple structure and low cost. Need not to use electro-magnet, controller to carry out auxiliary control, need not to use halbach array, remain the light and handy simple characteristic of traditional spring.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a permanent magnet element according to the method of the present invention.
Fig. 3 is a schematic diagram of the position coordinates of the attraction-repulsion boundary line of a single fixed permanent magnet ring of method embodiment 1 of the present invention.
Fig. 4a is a schematic diagram of the repulsive and attractive zones between a single fixed permanent magnet ring and a downward-charged permanent magnet micro element according to embodiment 1 of the method of the present invention.
Fig. 4b is a schematic diagram of the repulsive and attractive zones between a single fixed permanent magnet ring and the left-charged permanent magnet micro-elements according to embodiment 1 of the method of the present invention.
Fig. 4c is a schematic diagram of the repulsive area and attractive area between a single fixed permanent magnet ring and an upward-magnetizing permanent magnet micro element in embodiment 1 of the method of the present invention.
Fig. 4d is a schematic diagram of the repulsive and attractive areas between a single fixed permanent magnet ring and the rightward magnetized permanent magnet micro-elements according to embodiment 1 of the method of the present invention.
Fig. 5 is a schematic diagram of the position coordinates of the attraction-repulsion boundary line of two fixed permanent magnet rings according to embodiment 2 of the method of the present invention.
Fig. 6a is a schematic diagram of the equilibrium state of two fixed permanent magnet rings in embodiment 2 of the method of the present invention.
Fig. 6b is a schematic diagram of the moving state of two fixed permanent magnet rings in embodiment 2 of the method of the present invention.
Fig. 6c is a partially enlarged schematic view of two fixed permanent magnet rings according to embodiment 2 of the method of the present invention.
Detailed Description
The technical scheme of the invention is clearly and completely described in the following with reference to the attached drawings.
Example 1
Referring to fig. 1-4 d, flow charts of the present invention are shown. The detailed steps are as follows:
step 1, because the magnetic force of the permanent magnet follows the superposition principle, theoretically, two parallel permanent magnets in any shape can be regarded as two permanent magnet micro-elements IPM-1 and IPM-2 in an infinite graph 2 to be combined, so the z-direction magnetic force between two permanent magnets in any shape can be calculated through the following analytical model:
Figure BDA0003270306690000031
the above equation is subjected to integral expansion in numerical calculation software to obtain the explicit expression of the known function. Wherein l is the length of the permanent magnet, B 1 、B 2 The residual magnetic induction, mu, of the two permanent magnet infinitesimal 1, 2 respectively 0 Is vacuum magnetConductivity, ds 1 、ds 2 The cross-sectional areas of the permanent magnet micro-elements 1 and 2, respectively. r is ds 1 And ds 2 Theta is the included angle between the straight line r and the positive direction of the x abscissa, and alpha and beta are respectively the magnetic induction intensity B 1 、B 2 The angle is from the positive direction of the x-axis of the abscissa.
Step 2, as shown in FIG. 3, based on the analytic model of the magnetic force between the two permanent magnets, F between the PM-1 of the fixed permanent magnet and the IPM of the permanent magnet micro-element can be calculated through numerical calculation software z Discrete coordinates of relative position of =0, where (x) 1 ,z 1 ),(x 2 ,z 2 ),……，(x n ,z n ) Is the discrete coordinate of IPM close to the outer diameter, (x) 1 ’,z 1 ’),(x 2 ’,z 2 ’),……，(x n ’,z n ') is the discrete coordinates of the IPM near the inner diameter. In fig. 2, the rectangular section permanent magnet ring PM-1 is magnetized upwards, and the large number of permanent magnet micro-elements IPM above the permanent magnet ring are magnetized downwards. The cross section sizes of the permanent magnet rings PM-1 are a and b, and the cross section size of the permanent magnet micro element IPM is far smaller than that of the permanent magnet rings PM-1, and can be 0.01mm multiplied by 0.01mm.
Step 3, as shown in fig. 4a, the discrete coordinates of these IPMs are connected to establish four attraction-repulsion boundary lines of PM-1, which enclose three zones. The IPM is then placed into these three regions to determine the force direction of the permanent magnet in these regions. In FIG. 4a, IPM is placed in the middle region, and the force acting between IPM and PM-1 can be calculated as repulsive force by numerical calculation software. Similarly, the force acting between the PM-1 when IPM is placed in the left zone and the right zone is the suction force. The repulsive and attractive zones of PM-1 in fig. 4a are finally determined. In FIG. 4a, the blank area above PM-1 represents a repulsive force area, i.e. the acting force of the permanent magnet and PM-1 in the z direction in this area is repulsive force; the scattered point area above PM-1 represents an attraction area, namely the action force of the permanent magnet and PM-1 in the z direction in the area is an attraction force.
Step 4, as shown in fig. 4a, it is clear whether any shape of permanent magnet completely repels, completely attracts, or mixes with PM-1 through the repelling and attracting areas. The maximum radial dimension of PM-2 is determined according to the particular required clearance, space, stroke as shown in fig. 4a, and the subsequent design of PM-2 is performed within the maximum radial dimension. If the permanent magnet spring is structurally optimized, the range of the permanent magnet PM-2 is inevitably smaller than the maximum radial dimension of the PM-2, so that the optimization search time is greatly shortened, and the design efficiency is improved.
Step 5, FIG. 4a, PM-2 is completely in the repulsive zone, and therefore is subjected to only upward repulsive force F 1 Under the same gap, the repulsion force of the isosceles trapezoid PM-2 is larger. If both corners of PM-2 are complemented, PM-2 will have an attractive force F 2 This may lead to a situation where the total repulsive force is reduced although the volume of the permanent magnet is increased. Therefore, the shape can be selected to replace a permanent magnet ring with a rectangular cross section so as to achieve the purpose of increasing the magnetic force of the permanent magnet.
For the attraction-repulsion boundary line, two points need to be noted: 1) The attraction-repulsion boundary line of PM-1 is not a straight line. 2) The attraction-repulsion boundary line of PM-1 is not constant but varies according to the variation of the magnetization direction of IPM. If the magnetization direction of PM-2 is changed to the horizontal left, as shown in FIG. 4b, the left side of PM-2 has a vertically downward force F 1 Right side with vertical upward force F 2 ，F 1 And F 2 The addition will result in a vertical direction magnetic force Fz =0. Suppose PM-2 is not a permanent magnet ring, but a single permanent magnet bar, F 1 And F 2 A couple may form causing PM-2 to rotate counter-clockwise and become very unstable. FIG. 4c is a schematic diagram of the repelling zone and the attracting zone between the PM-1 and the upward-magnetizing permanent magnet micro-element, and FIG. 4d is a schematic diagram of the repelling zone and the attracting zone between the PM-1 and the rightward-magnetizing permanent magnet micro-element. Fig. 4c and 4d are supplementary to facilitate understanding of the attraction-repulsion boundary lines in different charging directions.
Example 2
Referring to fig. 1 to 3, fig. 5 to 6c:
step 1, because the magnetic force of the permanent magnet follows the superposition principle, theoretically, two parallel permanent magnets in any shape can be regarded as two permanent magnet micro-elements IPM-1 and IPM-2 in an infinite graph 2 to be combined, so the z-direction magnetic force between two permanent magnets in any shape can be calculated through the following analytical model:
Figure BDA0003270306690000051
and (4) performing integral expansion on the above expression in numerical calculation software to obtain an explicit expression of the known function. Wherein l is the length of the permanent magnet, B 1 、B 2 The residual magnetic induction, mu, of the two permanent magnet infinitesimal 1, 2 respectively 0 Is a vacuum permeability, ds 1 、ds 2 The cross-sectional areas of the permanent magnet elements 1 and 2, respectively. r is ds 1 And ds 2 Theta is the included angle between the straight line r and the positive direction of the x abscissa, and alpha and beta are respectively the magnetic induction intensity B 1 、B 2 The angle is from the positive direction of the x-axis of the abscissa.
Step 2, as shown in FIG. 5, F between the PM-1 and PM-2 of the fixed permanent magnets and the permanent magnet micro-element IPM can be calculated through numerical calculation software z Discrete coordinates of relative position of =0. In FIG. 4, the magnetization direction of PM-1 and PM-2 is upward, and the magnetization direction of the permanent magnet micro-element IPM is downward, (x) 1 ,z 1 ),(x 2 ,z 2 ),……，(x 2n ,z 2n ) F being IPM close to outer diameter z Coordinates of =0, (x) 1 ’,z 1 ’),(x 2 ’,z 2 ’),……，(x 2n ’,z 2n ') IPM near the inner diameter F z Coordinates of =0.
And 3, connecting the discrete coordinates of the IPM to establish an attraction-repulsion boundary line of the PM-1 and the PM-2 as shown in FIG. 6a, and further obtaining a repulsion area and an attraction area of the PM-1 and the PM-2. In FIG. 6a, the blank area in the middle of PM-1 and PM-2 represents an upward repelling area, i.e. the permanent magnet in this area is upward to the total acting force direction of PM-1 and PM-2 in the z direction; the upper scatter plot of PM-1 represents the downward area, i.e., the area in which the total force of the permanent magnets and PM-1, PM-2 in the z-direction is directed downward.
Step 4, as shown in FIG. 6a, through the repelling and attracting regions, it is apparent whether any shape of permanent magnet is completely repelling, completely attracting, or mixed with PM-1 and PM-2, from which the maximum radial dimension of PM-3 can be determined, and subsequent design of PM-3 within the maximum radial dimension. If the structure of the permanent magnet spring is optimized, the range of the permanent magnet PM-3 is inevitably smaller than the maximum radial dimension, so that the optimization search time is greatly reduced, and the design efficiency is improved.
Step 5, as shown in FIG. 6a, the octagonal dynamic ring PM-3 is placed between the fixed rings PM-1 and PM-2, and since half of the dynamic ring is in the upward repulsive area and the other half is in the downward repulsive area, the PM-3 is still at the middle position. When PM-3 moves axially downwards as shown in FIG. 6b, the upward repulsive force area occupied by PM-3 is increased, and the downward repulsive force area is decreased, so that the upward repulsive force F borne by PM-3 is reduced 1 Increasing, downward repulsive force F 2 And decreases. The repulsive force of the octagonal shape of PM-3 in fig. 6b is larger at the same gap. 6b-6c, if the four corners of PM-3 are complemented, PM-3 will be subjected to an additional downward repulsive force F 2 This will result in a reduction of the total upward repulsive force, resulting in a waste of rare earth permanent magnetic material. Therefore, the octagonal permanent magnet ring can be used for replacing a permanent magnet ring with a rectangular cross section, so that the purpose of increasing the magnetic force of the permanent magnet is achieved.
The magnetic force increasing method can be used for a permanent magnet spring, and can also be used for permanent magnet elements such as a permanent magnet bearing, a permanent magnet guide rail, a permanent magnet coupler and the like.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (5)

1. A method for increasing the magnetic force of a permanent magnet spring comprises the following steps:
step 1, expressing the magnetic force between two permanent magnet elements as an explicit type of a known function through numerical calculation software; the longitudinal magnetic force between two permanent magnets of any shape is calculated by the following analytical model:
Figure FDA0003949549090000011
wherein l is the length of the permanent magnet, B 1 、B 2 Respectively, permanent magnet infinitesimal ds 1 And ds 2 Residual magnetic induction intensity of (u) 0 Is a vacuum permeability, ds 1 、ds 2 The cross section areas of the two permanent magnet microelements are respectively; r is ds 1 And ds 2 Theta is the included angle between the straight line r and the positive direction of the x abscissa, and alpha and beta are respectively the magnetic induction intensity B 1 、B 2 The included angle with the positive direction of the x-axis of the abscissa;
step 2, calculating F between the fixed permanent magnet in any shape and the permanent magnet infinitesimal based on the analytic model of the longitudinal magnetic force between the two permanent magnets in any shape z Discrete coordinates of relative position of = 0;
step 3, connecting the discrete coordinates to establish an attraction-repulsion boundary line of the fixed permanent magnet, and further drawing a repulsion area and an attraction area;
step 4, determining the design range of the moving permanent magnet through the repulsion region and the attraction region;
and 5, determining the shape of the moving permanent magnet when the magnetic force is maximum according to the attraction-repulsion boundary line, the repulsion area, the attraction area and the design range in the steps.
2. The method for increasing the magnetic force of a permanent magnet spring according to claim 1, wherein: step 2 further comprises calculating F between the fixed permanent magnet and the permanent magnet micro-element through numerical calculation software z Discrete coordinates of relative position of = 0; the section size of the permanent magnet element is far smaller than that of the fixed permanent magnet, and the value is 0.01mm multiplied by 0.01mm.
3. The method for increasing the magnetic force of a permanent magnet spring according to claim 1, wherein: step 3, further comprising the steps of connecting the discrete coordinates of all the permanent magnet micro-elements to establish attraction-repulsion boundary lines of the fixed permanent magnets, wherein all the attraction-repulsion boundary lines can enclose a plurality of areas; and placing the permanent magnet micro elements into the regions, and calculating whether the acting force between the permanent magnet micro elements and the fixed permanent magnet is an attractive force or a repulsive force through numerical calculation software so as to determine a repulsive region and an attractive region of the fixed permanent magnet.
4. The method for increasing the magnetic force of a permanent magnet spring according to claim 1, wherein: step 4 further comprises determining the maximum radial dimension of the moving permanent magnet according to the required gap, space and preset stroke between the specific moving permanent magnet and the fixed permanent magnet, and subsequent permanent magnet design or optimization is performed within the maximum radial dimension.
5. The method for increasing the magnetic force of a permanent magnet spring according to claim 1, wherein: step 5 further comprises: and determining the shape of the moving permanent magnet when the magnetic force is maximum according to the attraction-repulsion boundary line, the repulsion area and the attraction area, the design range, the specifically required gap, the space and the preset stroke obtained in the steps.
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WO2007131434A1 (en) * 2006-05-11 2007-11-22 Lu, Yumin Permanent magnetic force motor
CN104006078B (en) * 2014-05-07 2016-04-06 西安理工大学 Adopt the Halbach Permanent-magnet bearing that triangular-section permanent-magnetic clamp stacks
CN104712655A (en) * 2015-02-16 2015-06-17 西安理工大学 Magnetic force determination method of rectangular cross-section permanent magnet guide rails or bearings
CN112182844B (en) * 2020-09-04 2022-09-16 大连理工大学 Effective magnetic potential calculation method for permanent magnet magnetic coupler
CN112347627B (en) * 2020-10-28 2023-06-23 南京信息工程大学 Magnetic field calculation method for axial magnetic field hybrid excitation motor with asymmetric air gap structure
CN112737173B (en) * 2020-12-17 2022-06-07 天津工业大学 Magnetic field calculation method for segmented oblique pole surface-mounted permanent magnet motor

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