阅读说明：本技术 一种磁力耦合器最大轴向力计算方法 (A kind of magnetic coupling maximum axial force calculation method ) 是由 刘巍 罗唯奇 程习康 刘思彤 张洋 贾振元 于 2019-08-08 设计创作，主要内容包括：本发明一种磁力耦合器最大轴向力计算方法属于磁力传动技术领域,涉及一种磁力耦合器最大轴向力计算方法。该方法基于高斯点处磁场测量,对磁力耦合器最大轴向力进行计算。利用磁力耦合器内部磁场分布的镜像规律及磁力耦合器内部磁场分布的周期性和对称性,对磁场区域进行分区,通过传统电磁动力理论公式及高精度的高斯型求积计算方法,结合有限点实测的磁感应强度数据,计算单个子区的最大轴向力,进而对耦合器的最大轴向力进行计算。该方法将电磁动力学和数值分析计算相结合,在避免传统电磁动力理论空间不均匀量的复杂多维积分计算的同时,保留了其精确度高的优点。在工程应用中具有较好的实用性,操作方便,计算简单。(A kind of magnetic coupling maximum axial force calculation method of the present invention belongs to technical field of magnetic transmission, is related to a kind of magnetic coupling maximum axial force calculation method.This method is based on magnetic-field measurement at Gauss point, calculates magnetic coupling maximum axial force.Utilize the mirror image rule of magnetic coupling internal magnetic field distribution and the periodicity and symmetry of the distribution of magnetic coupling internal magnetic field, subregion is carried out to field region, pass through traditional electromagnetic power theoretical formula and high-precision Gaussian type quadrature calculation method, the magnetic induction intensity data surveyed in conjunction with finite point, the maximum axial force of single sub-district is calculated, and then the maximum axial force of coupler is calculated.This method combines electromagnetic dynamics and numerical analysis, while avoiding traditional electromagnetic power theoretical space uneven amounts of complex multi-dimensional integral calculation, remains the high advantage of its accuracy.There is preferable practicability in engineer application, it is easy to operate, it calculates simple.)

1. a kind of magnetic coupling maximum axial force calculation method, characterized in that this method utilizes magnetic coupling internal magnetic field The mirror image rule of distribution, it is theoretical and high-precision by traditional electromagnetic power in conjunction with the magnetic induction intensity data that finite point is surveyed Numerical computation method calculates the maximum axial force of coupler, and specific step is as follows for calculation method:

The first step, the key parameter for determining magnetic coupling, build magnetic coupling experiment porch；

The key parameter of permanent magnetic coupling: the internal diameter r of copper dish (3) is determined first₁, outer diameter R₁, trapezoidal permanent magnet (5) length is l, Upper bottom width is a, and lower bottom width is b, the internal diameter r of permanent magnet holding tray (6)₂, outer diameter R₂；The quantity p of permanent magnet (5), and magnetic coupling The permanent magnet (5) of device needs the pole N, the pole S to be alternately arranged, and the minimum stroke of speed adjusting gear mover (7) is g_min, range g_max；

Parameter builds magnetic coupling experiment porch after determining, after speed adjusting gear pedestal (12) are fixed with bolt (13), is packed into Output shaft (11), speed adjusting gear pedestal (12) one end are covered with sealing cover (10), and the other end fills speed adjusting gear stator (8), speed regulation Mechanism mover (7) and speed adjusting gear stator (8) form relative motion using the principle of slide way mechanism, will equipped with input shaft (23) and The bearing block (22) of dynamometry probe (9) is fixed on bearing block base (25) with screw (15), and input shaft axle sleeve (1) is mounted in On input shaft (23), while motor (20) electricity consumption machine bolt (24) being fixed on motor base (19)；

Copper dish (3) are mounted on copper dish mounting disc (2), while permanent magnet (5) being fitted into permanent magnet holding tray (6), with forever Magnet cover board (4) covers tightly fixation；Copper dish mounting disc (2) and permanent magnet holding tray (6) are installed by fixing screws (14) respectively On input shaft axle sleeve (1) and speed adjusting gear mover (7)；By adjusting between bearing block base (25) and speed adjusting gear pedestal (12) Distance, adjust the air gap of copper dish (3) and permanent magnet holding tray (6) to the minimum stroke g of speed adjusting gear mover (7)_min, it is used in combination Bolt of lower base (16) fixed bearing block pedestal (25), with shaft coupling (17) by the axis of motor (20) and input shaft (being connected) 23, and It is fixed motor base (19) with motor base bolt (18), the output end of dynamometry probe (9) is connect with oscillograph (21)；Extremely This, the building of magnetic coupling axial force calculating system is completed；

Second step establishes polar coordinate system, carries out subregion to field region；

For the plane locating for copper dish (3) surface using copper dish (3) center of circle as origin o, it is from inside to outside pros that horizontal direction, which is polar axis or, To establishing polar coordinate system；It, will forever according to the parameters such as copper dish (3) size, permanent magnet holding tray (6) size, permanent magnet (5) quantity Corresponding region of the magnet holding tray (6) on coordinate plane is divided into p sub-regions, respectively number be 1,2,3 ..., p, with permanent magnetism Body (5) quantity is corresponding, the intermediate point coordinate (r of sub-district_p,θ_p) calculated by formula (1)；

Wherein, θ_pFor the polar polar angle of intermediate point of sub-district, r_pFor the polar polar diameter of intermediate point of sub-district, θ_p1、θ_p2For son The polar equation on the area boundary Liang Ge, i are sub-district number, and p is the quantity of permanent magnet (5)；

Third step chooses a certain sub-district, calculates Gauss point and respective coordinates, solves integral coefficient；

The maximum axial force of magnetic coupling occurs proper in the magnetic pole and copper dish (3) eddy region magnetic pole of permanent magnet holding tray (6) At the time of being overlapped opposite well, at this point, using the mirror image rule of magnetic coupling internal magnetic field distribution, it can be by the vortex of copper dish (3) Region is approximately the mirror image of permanent magnet (5)；The periodicity being distributed by magnetic coupling internal magnetic field is with symmetry it is found that Bu Tong sub The magnetic field strength in area is essentially identical, and the big small amount of axial force generated is of substantially equal, and the calculating of magnetic coupling axial force is turned It is changed to the axial force for calculating any sub-district；Some optional sub-district, calculates the big of the sub-district axial force by integral formula (2) It is small；

Wherein, axial force of the F between copper dish (3) and permanent magnet holding tray (6), μ₀For space permeability, s is selected sub-district area Domain, B are the magnetic field strength in the sub-district region；

Due to the inhomogeneities of magnetic coupling internal magnetic field distribution, direct solution formula (2) is extremely difficult, can pass through formula (3) quadrature formulas of Gauss type with 2n-1 algebraic accuracy is converted by formula (2) and then solve the size of axial force；

Wherein, s is selected sub-district region, and B is the magnetic field strength in the sub-district region, r₂、R₂Respectively permanent magnet holding tray 6 is interior Diameter and outer diameter, θ₁、θ₂Respectively polar polar angle of the front and back boundary line of the sub-district, A_i、A_jRespectively Radial Integrals coefficient and Circumferential integral coefficient, B (r_i,θ_j) it is Gauss point respective coordinates (r_i,θ_j) at magnitude of field intensity, i is the volume of radial Gauss point Number, j is the number of circumferential Gauss point, and n is the number of the Gauss point of the quadrature formulas of Gauss type；Using the intermediate point of the sub-district as base Standard can calculate Gauss point by formula (4)；

Wherein, n is the number of the Gauss point of the quadrature formulas of Gauss type, xⁿFor the substrate of the quadrature formulas of Gauss type, μ_nIt is asked for Gaussian The substrate inner product of product formula, the solution that formula (4) solves are Gauss point；The respective coordinates of Gauss point are found out by formula (5)；

Wherein, r_nFor the corresponding polar diameter of n-th of Gauss point, θ_nFor the corresponding polar angle of n-th of Gauss point, r₂、R₂Respectively forever The internal diameter and outer diameter of magnet holding tray (6), θ₁、θ₂Respectively polar polar angle of the front and back boundary line of the sub-district, x_nIt is n-th A Gauss point；Since integral formula is double integral, the corresponding polar diameter of Gauss point and polar angle combination of two can obtain n²A pole is sat Scale value；Integral coefficient A_iIt is solved by formula (6)；

Wherein, μ_n-1For the substrate inner product of the quadrature formulas of Gauss type, x_iFor i-th of Gauss point, A_iFor the corresponding product of i-th of Gauss point Divide coefficient, Radial Integrals coefficient and circumferential integral coefficient army are calculated using the formula, therefore the two numerical value is equal；

Magnetic field strength at sub-district Gauss point respective coordinates selected by 4th step, measurement calculates axial force；

Default relative error requires to be no more than ε；The n Gauss point found out by formula (4) is each in the circumferential direction and radial direction of selected areas There are n corresponding polar diameters and n corresponding polar angles, the total n of combination of two²A polar coordinates point, the corresponding n of n Gauss point of measurement²It is a Field strength values at polar coordinates point, in conjunction with boundary before and after integral coefficient, the internal-and external diameter of permanent magnet holding tray (6), selected sub-district Polar angle calculates the axial force F of the sub-district using formula (3)_sub, maximum total axial force is by formula (7) calculating；

F_total=pF_sub (7)

Wherein, F_totalFor maximum total axial force, F_subFor the maximum axial force of sub-district, p is the quantity of permanent magnet (5)；Total axial force After calculating, axial force can be measured by the dynamometry probe (9) installed on bearing block (22), with F_totalIt compares, relatively Error is Δ, if error is less than default accuracy value ε, calculated result is qualified, otherwise improves the algebra essence of the quadrature formulas of Gauss type The repetition third step of angle value, until all block results are qualified.

Technical field

The invention belongs to magnetic coupling technical fields, are related to a kind of magnetic coupling maximum axial force calculation method.

Background technique

Drive technology is most important in the fields such as petroleum, mining industry, electric power.Magnetic coupling because its strong antijamming capability, The features such as energy-saving effect is good, stability is high is applied in the Important Projects scene such as oil exploration, ore extraction, electricity generation Extensively.In transmission process, the axial force generated inside magnetic coupling can be acted directly on the bearing of speed adjusting gear, work as institute When being exceeded tolerance range by axial force, the bearing of speed adjusting gear easily fails, and then leads to coupler unstability.In speed adjusting gear axis During holding type selecting, the accurate calculating of the axial force of magnetic coupling is extremely crucial.However, the axial direction of magnetic coupling at this stage There are still computational accuracies and the incompatible problem of computation complexity for the calculation method of power, i.e. the precision to guarantee calculation method, Its calculating process can be very many and diverse or can not calculate at all；If using simplified formula to reduce computation complexity, computational accuracy Just it is unable to get guarantee, practical value is limited.Therefore the accurate efficient calculating of the axial force of magnetic coupling can be high for coupler Reliability design provides most important theories support.

For the Axial Force Calculating of magnetic coupling, Wang Peng of Dalian University Of Communications et al. is in 2018 in " Machine Design With production " the 10th phase of volume 332 delivered article " cage-type rotor asynchronous magnetic coupler Analysis of Axial ", and it is different to cage-type rotor Step magnetic coupling is studied carefully, and obtains mirror image rule of the permanent magnet in ferromagnet by current mirror method, and according to equivalent Magnetic charge theory derives the equivalent model of magnetized spot axial force；Magnetic then is cut to cage item according to the electromagnetic nature of line current The magnetic field that sense line generates is analyzed, and the axial force of cage-type rotor asynchronous magnetic coupler is calculated.Exciting current is produced in text Raw induction level reduces computation complexity as constant to simplify integral process.However the permanent magnetism of magnetic coupling The magnetic induction intensity of the exciting current generated in body magnetic induction intensity and its operational process is not equally distributed in space, and It is to show the feature that central magnetic induction intensity is high, edge magnetic induction intensity is low.Only by the calculated results and finite element in text Simulation result comparison, limited reliability.Therefore a kind of accurate efficient calculation method of the axial force of magnetic coupling is provided very It is necessary.

Summary of the invention

The present invention has invented a kind of calculating side of magnetic coupling maximum axial force to make up the defect of the prior art Method.The purpose is to the mirror image being distributed based on magnetic coupling internal magnetic field rules, in conjunction with traditional electromagnetic theory and high-precision number Value calculating method calculates the maximum axial force of coupler, as magnetic coupling speed adjusting gear bearing type selecting and coupling Clutch structure High Reliability Design provides important technology support.This method combines electromagnetic dynamics and numerical analysis, While avoiding traditional electromagnetic power theoretical space uneven amounts of complex multi-dimensional integral calculation, it is high to remain its accuracy Advantage has preferable practicability in engineer application, easy to operate, calculates simple.

The technical solution adopted by the present invention is that a kind of calculation method of magnetic coupling axial force, characterized in that this method Using the mirror image rule of magnetic coupling internal magnetic field distribution, pass through traditional electromagnetic power theory and high-precision numerical value calculating side Method, in conjunction with finite point survey magnetic induction intensity data, the maximum axial force of coupler is calculated, calculation method it is specific Steps are as follows:

The first step, the key parameter for determining magnetic coupling, build magnetic coupling experiment porch.

The key parameter of permanent magnetic coupling: the internal diameter r of copper dish 3 is determined first₁, outer diameter R₁, trapezoidal 5 length of permanent magnet is l, Upper bottom width is a, and lower bottom width is b, the internal diameter r of permanent magnet holding tray 6₂, outer diameter R₂, the quantity p of permanent magnet 5, and magnetic coupling Permanent magnet 5 needs the pole N, the pole S to be alternately arranged, and the minimum stroke of speed adjusting gear mover 7 is g_min, range g_max；

Parameter builds magnetic coupling experiment porch after determining, after speed adjusting gear pedestal 12 is fixed with bolt 13, is packed into Output shaft 11,12 one end sealing cover 10 of speed adjusting gear pedestal cover, and the other end fills speed adjusting gear stator 8, speed adjusting gear mover 7 Relative motion is formed using the principle of slide way mechanism with speed adjusting gear stator 8, by the bearing equipped with input shaft 23 and dynamometry probe 9 Seat 22 is fixed on bearing block base 25 with screw 15, and by input shaft axle sleeve 1 on input shaft 23, while motor 20 being used Motor bolt 24 is fixed on motor base 19；

Copper dish 3 are mounted in copper dish mounting disc 2, while permanent magnet 5 being fitted into permanent magnet holding tray 6, use permanent magnet Cover board 4 covers tightly fixation；Copper dish mounting disc 2 and permanent magnet holding tray 6 are mounted on input shaft axle sleeve 1 by fixing screws 14 respectively On speed adjusting gear mover 7；By adjusting the distance between bearing block base 25 and speed adjusting gear pedestal 12, copper dish 3 and forever are adjusted The air gap of magnet holding tray 6 to speed adjusting gear mover 7 minimum stroke g_min, and with 16 fixed bearing block pedestal 25 of bolt of lower base, The axis of motor 20 is connected with input shaft 23 with shaft coupling 17, and is fixed on motor base 19 with motor base bolt 18, it will The output end of dynamometry probe 9 is connect with oscillograph 21；So far, the building of magnetic coupling axial force calculating system is completed；

Second step establishes polar coordinate system, carries out subregion to field region.

For the plane locating for 3 surface of copper dish using 3 center of circle of copper dish as origin o, it is from inside to outside pros that horizontal direction, which is polar axis or, To establishing polar coordinate system；According to the parameters such as 3 size of copper dish, 6 size of permanent magnet holding tray, 5 quantity of permanent magnet, permanent magnet is put Set corresponding region of the disk 6 on coordinate plane and be divided into p sub-regions, respectively number be 1,2,3 ..., p, with 5 quantity phase of permanent magnet It is corresponding, the intermediate point coordinate (r of sub-district_p,θ_p) calculated by formula (1)；

Wherein, θ_pFor the polar polar angle of intermediate point of sub-district, r_pFor the polar polar diameter of intermediate point of sub-district, θ_p1、θ_p2 For the polar equation on two boundaries of sub-district, i is sub-district number, and p is the quantity of permanent magnet 5.

Third step chooses a certain sub-district, calculates Gauss point and respective coordinates, solves integral coefficient.

The maximum axial force of magnetic coupling occurs proper in the magnetic pole and 3 eddy region magnetic pole of copper dish of permanent magnet holding tray 6 At the time of being overlapped opposite well, at this point, using the mirror image rule of magnetic coupling internal magnetic field distribution, it can be by the vortex of copper dish 3 Domain is approximately the mirror image of permanent magnet 5.The periodicity and symmetry that be distributed by magnetic coupling internal magnetic field are it is found that different sub-districts Magnetic field strength is essentially identical, and the big small amount of axial force generated is of substantially equal, therefore can be by the calculating of magnetic coupling axial force Be converted to the axial force for calculating any sub-district.Some optional sub-district, can calculate the sub-district axial force by integral formula (2) Size.

Wherein, axial force of the F between copper dish 3 and permanent magnet holding tray 6, μ₀For space permeability, s is selected sub-district area Domain, B are the magnetic field strength in the sub-district region.

Due to the inhomogeneities of magnetic coupling internal magnetic field distribution, direct solution formula 2 is extremely difficult, can pass through formula (3) quadrature formulas of Gauss type with 2n-1 algebraic accuracy is converted by formula (2) and then solve the size of axial force.

Wherein, s is selected sub-district region, and B is the magnetic field strength in the sub-district region, r₂、R₂Respectively permanent magnet holding tray 6 Internal diameter and outer diameter, θ₁、θ₂Respectively polar polar angle of the front and back boundary line of the sub-district, A_i、A_jRespectively Radial Integrals system Several and circumferential integral coefficient, B (r_i,θ_j) it is Gauss point respective coordinates (r_i,θ_j) at magnitude of field intensity, i is radial Gauss point Number, j is the number of circumferential Gauss point, and n is the number of the Gauss point of the quadrature formulas of Gauss type.It is with the intermediate point of the sub-district Benchmark can calculate Gauss point by formula (4).

Wherein, n is the number of the Gauss point of the quadrature formulas of Gauss type, xⁿFor the substrate of the quadrature formulas of Gauss type, μ_nFor Gauss The substrate inner product of type quadrature formula, the solution that formula (4) solves are Gauss point.The respective coordinates of Gauss point are found out by formula (5).

Wherein, r_nFor the corresponding polar diameter of n-th of Gauss point, θ_nFor the corresponding polar angle of n-th of Gauss point, r₂、R₂Respectively For the internal diameter and outer diameter of permanent magnet holding tray 6, θ₁、θ₂Respectively polar polar angle of the front and back boundary line of the sub-district, x_nIt is N Gauss point.Since integral formula is double integral, the corresponding polar diameter of Gauss point and polar angle combination of two can obtain n²A pole is sat Scale value.Integral coefficient A_iIt is solved by formula (6).

Wherein, μ_n-1For the substrate inner product of the quadrature formulas of Gauss type, x_iFor i-th of Gauss point, A_iIt is corresponding for i-th of Gauss point Integral coefficient, Radial Integrals coefficient and circumferential integral coefficient army are using formula calculating, therefore the two numerical value is equal.

Magnetic field strength at sub-district Gauss point respective coordinates selected by 4th step, measurement calculates axial force.

Default relative error requires to be no more than ε.Circumferential direction and diameter of the n Gauss point found out by formula (4) in selected areas To respectively having n corresponding polar diameters and n corresponding polar angles, the total n of combination of two²A polar coordinates point, n Gauss point of measurement are corresponding n²Field strength values at a polar coordinates point, in conjunction with integral coefficient, the internal-and external diameter of permanent magnet holding tray 6, selected sub-district front and rear side Boundary's polar angle calculates the axial force F of the sub-district using formula (3)_sub, maximum total axial force is by formula (7) calculating.

F_total=pF_sub (7)

Wherein, F_totalFor maximum total axial force, F_subFor the maximum axial force of sub-district, p is the quantity of permanent magnet 5.Line shaft to After power is calculated, axial force can be measured by the dynamometry probe 9 installed on bearing block 22, with F_totalIt compares, it is opposite to miss Difference is Δ, if error is less than default accuracy value ε, calculated result is qualified, otherwise improves the algebraic accuracy of the quadrature formulas of Gauss type The repetition third step of value, until all block results are qualified.

The beneficial effects of the invention are as follows permanent magnet magnetic inductions and its fortune that this method has fully considered magnetic coupling The magnetic induction intensity of the exciting current generated during row is not equally distributed in space, but shows central magnetic induction The feature that intensity is high, edge magnetic induction intensity is low improves the deficiency that tradition replaces whole audience magnetic field with average value.In addition, the party Method passes through biography in conjunction with the magnetic induction intensity data that finite point is surveyed using the mirror image rule of magnetic coupling internal magnetic field distribution System electromagnetic power theory and high-precision numerical computation method, calculate the axial force of coupler, are avoiding traditional electromagnetism While the uneven amounts of complex multi-dimensional integral calculation in dynamic Theory space, the high advantage of its accuracy is remained, this method exists There is preferable practicability in engineer application, it is easy to operate, it calculates simple.

Detailed description of the invention

Fig. 1 is a kind of magnetic coupling Axial Force Calculating method flow diagram.

Fig. 2 is the structural schematic diagram of magnetic coupling, and Fig. 3 is magnetic coupling axial force measuration experimental system schematic diagram. Wherein, 1- input shaft axle sleeve, 2- copper dish mounting disc, 3- copper dish, 4- permanent magnet cover board, 5- permanent magnet, 6- permanent magnet holding tray, 7- Speed adjusting gear mover, 8- speed adjusting gear stator, 9- dynamometry probe, 10- sealing cover, 11- output shaft, 12- speed adjusting gear pedestal, 13- bolt, 14- fixing screws, 15- screw, 16- bolt of lower base, 17- shaft coupling, 18- motor base bolt, 19- motor bottom Seat, 20- motor, 21- oscillograph, 22- bearing block, 23- input shaft, 24- motor bolt, 25- bearing block base.

Fig. 4 is polar coordinate system and subregion schematic diagram.Wherein, 1- sub-district 1,2- sub-district 2,3- sub-district 3,4- sub-district 4 Number, 5- sub-district 5,6- sub-district 6,7- sub-district 7,8- sub-district 8,9- sub-district 9,10- sub-district 10,11- sub-district 11, 12- sub-district 12, o point-origin, or- polar axis.

Specific embodiment

The embodiment of the present invention is further elaborated with technical solution with reference to the accompanying drawing.

Fig. 2 is the structural schematic diagram of magnetic coupling, and Fig. 3 is magnetic coupling axial force measuration experimental system schematic diagram. The present embodiment selects a rated speed 2400r/min, the single disc-type speed-regulating type magnetic coupler that magnet pairs are 6 pairs.

Fig. 1 is a kind of magnetic coupling Axial Force Calculating method flow diagram, and specific step is as follows for calculation method:

The first step, the key parameter for determining permanent magnetic coupling, build magnetic coupling experimental system

Firstly, determining the key parameter of magnetic coupling: the internal diameter r of copper dish 3₁=170mm, outer diameter R₁=335mm, permanent magnetism The internal diameter r of body holding tray 6₂=176mm, outer diameter R₂=330mm, trapezoidal 5 length of permanent magnet are l=50mm, and upper bottom is a=60mm, Bottom is b=40mm, and remanent magnetism is about B=0.65T, the quantity p=12 of permanent magnet 5, speed adjusting gear mover on permanent magnet holding tray 6 7 minimum stroke is g_min=10mm, range g_max=43mm.

Parameter builds magnetic coupling experiment porch after determining, after speed adjusting gear pedestal 12 is fixed with bolt 13, is packed into Output shaft 11,12 one end sealing cover 10 of speed adjusting gear pedestal cover, and the other end fills speed adjusting gear stator 8, speed adjusting gear mover 7 Relative motion is formed using the principle of slide way mechanism with speed adjusting gear stator 8, by the bearing equipped with input shaft 23 and dynamometry probe 9 Seat 22 is fixed on bearing block base 25 with screw 15, and by input shaft axle sleeve 1 on input shaft 23, while motor 20 being used Motor bolt 24 is fixed on motor base 19；

Copper dish 3 are mounted in copper dish mounting disc 2, while permanent magnet 5 being fitted into permanent magnet holding tray 6, use permanent magnet Cover board 4 covers tightly fixation；Copper dish mounting disc 2 and permanent magnet holding tray 6 are mounted on input shaft axle sleeve 1 by fixing screws 14 respectively On speed adjusting gear mover 7；By adjusting the distance between bearing block base 25 and speed adjusting gear pedestal 12, copper dish 3 and forever are adjusted The minimum stroke of the air gap of magnet holding tray 6 to speed adjusting gear mover 7 is used and with 16 fixed bearing block pedestal 25 of bolt of lower base The axis of motor 20 is connected by shaft coupling 17 with input shaft 23, and fixes motor base 19 with motor base bolt 18, and dynamometry is visited First 9 output end is connect with oscillograph 21；So far, the building of magnetic coupling axial force calculating system is completed, such as Fig. 3 institute Show.

Second step establishes polar coordinate system, carries out subregion to field region.

For the plane locating for 3 surface of copper dish using 3 center of circle of copper dish as origin o, it is from inside to outside pros that horizontal direction, which is polar axis or, To establishing polar coordinate system；According to the parameters such as 3 size of copper dish, 6 size of permanent magnet holding tray, 5 quantity of permanent magnet, permanent magnet is put Set corresponding region of the disk 6 on coordinate plane and be divided into 12 sub-regions, respectively number be 1,2,3 ..., 12, with 5 quantity of permanent magnet It is corresponding, the intermediate point coordinate of sub-district be respectively as follows: (310,0), (310,π)、

Third step chooses a certain sub-district, calculates Gauss point and respective coordinates, solves integral coefficient.

Select sub-district 1, the midpoint coordinates of the sub-district is (310,0), front and back boundary polar angle be respectively θ=π/12, θ=- π/ 12, n=3,2n-1=5 are taken, algebraic accuracy is selected as 5, and the Gaussian type quadrature with 5 algebraic accuracies can be calculated by formula (4) The Gauss point of formula.

3 Gauss points solved by the equation are as follows:x₂=0,9 calculated by formula (5) A Gauss point respective coordinates are as follows: (312.64, -0.203), (312.64,0), (312.64,0.203), (253, -0.203), (253,0),(253,0.203),(193.36,-0.203),(193.36,0),(193.36,0.203).It can be calculated by formula (6) Integral coefficient.

3 integral coefficients solved by the equation are as follows:

Magnetic field strength at sub-district Gauss point respective coordinates selected by 4th step, measurement calculates axial force.

Default relative error ε is no more than 0.5%, with gaussmeter measurement point (193.36, -0.203), (193.36,0), (193.36,0.203)、(253,-0.203)、(253,0)、(253,0.203)、(312.64,-0.203)、(312.64,0)、 Magnitude of field intensity at (312.64,0.203), result be respectively 90.66mT, 100.32mT, 90.80mT, 405.35mT, 647.95mT, 403.02mT, 315.05mT, 298.22mT, 314.68mT calculate the axial force F of the sub-district using formula (3)_sub =203.68N, total axial force F_total=12F_sub=2444.17N is measured by the dynamometry probe 9 installed on bearing block 22 Maximum axial force is 2436.27N, with F_totalCompare, relative error is Δ=0.324%, be less than default relative error ε= 0.5%, then calculated result is qualified.

This method is regular using the mirror image of magnetic coupling internal magnetic field distribution, theoretical and high-precision by traditional electromagnetic power The numerical computation method of degree calculates the maximum axial force of coupler, in conjunction with finite point survey magnetic induction intensity data, Traditional calculating methods are improved by the induction level inside magnetic coupling as constant, sacrifice computational accuracy to reduce The limitation of computation complexity.Avoiding the same of the uneven amounts of complex multi-dimensional integral calculation of traditional electromagnetic power theoretical space When, the high advantage of its accuracy is remained, is the calculation method that there is practical implementation to be worth.