CN110188418A - A kind of permanent-magnet coupler transmitting torque calculation method - Google Patents

A kind of permanent-magnet coupler transmitting torque calculation method Download PDF

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CN110188418A
CN110188418A CN201910398885.8A CN201910398885A CN110188418A CN 110188418 A CN110188418 A CN 110188418A CN 201910398885 A CN201910398885 A CN 201910398885A CN 110188418 A CN110188418 A CN 110188418A
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magnetic
permanent
magnet
flux
conductor disc
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CN110188418B (en
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刘巍
程习康
刘思彤
罗唯奇
张洋
周志龙
逯永康
贾振元
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Dalian University of Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K49/00—Dynamo-electric clutches; Dynamo-electric brakes
    • H02K49/02—Dynamo-electric clutches; Dynamo-electric brakes of the asynchronous induction type
    • H02K49/04—Dynamo-electric clutches; Dynamo-electric brakes of the asynchronous induction type of the eddy-current hysteresis type
    • H02K49/046—Dynamo-electric clutches; Dynamo-electric brakes of the asynchronous induction type of the eddy-current hysteresis type with an axial airgap
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K49/00—Dynamo-electric clutches; Dynamo-electric brakes
    • H02K49/10—Dynamo-electric clutches; Dynamo-electric brakes of the permanent-magnet type
    • H02K49/102—Magnetic gearings, i.e. assembly of gears, linear or rotary, by which motion is magnetically transferred without physical contact
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02K—DYNAMO-ELECTRIC MACHINES
    • H02K49/00—Dynamo-electric clutches; Dynamo-electric brakes
    • H02K49/10—Dynamo-electric clutches; Dynamo-electric brakes of the permanent-magnet type
    • H02K49/104—Magnetic couplings consisting of only two coaxial rotary elements, i.e. the driving element and the driven element
    • H02K49/108—Magnetic couplings consisting of only two coaxial rotary elements, i.e. the driving element and the driven element with an axial air gap

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  • Pure & Applied Mathematics (AREA)
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  • Computational Mathematics (AREA)
  • Dynamo-Electric Clutches, Dynamo-Electric Brakes (AREA)

Abstract

A kind of permanent-magnet coupler transmitting torque calculation method of the present invention belongs to permanent magnet transmission technical field, is related to a kind of permanent-magnet coupler transmitting torque calculation method.Fan-shaped eddy region is equivalent calculates conductor disk area totality eddy-current loss power according to Faraday's electromagnetic induction law at circle by produced in conductor disc first for this method.Further according to the topological structure of permanent-magnet coupler, establish comprising main flux, leakage magnetic flux, useful flux and the magnetomotive magnetic circuit equivalent model of induction.According to the design size of permanent-magnet coupler, permanent magnet magnetic kinetic potential, eddy region induction magnetomotive force, main flux magnetic resistance, leakage magnetic flux magnetic resistance are calculated.In conjunction with Kirchhoff's first law, effective magnetic induction intensity across conductor disc is calculated.The transmitting torque for calculating permanent-magnet coupler, compares with the result of finite element method.This method is a kind of calculation method with practical implementation value, and method is simple, and computational efficiency is high, and time cost is low.

Description

A kind of permanent-magnet coupler transmitting torque calculation method
Technical field
The invention belongs to permanent magnet transmission technical fields, are related to a kind of permanent-magnet coupler transmitting torque calculation method.
Background technique
With the continuous improvement of industrial level and scientific and technological strength, the national high-end equipment in Important Project field is to efficient, Gao Ke Higher demand is proposed by drive technology.Energy-efficient, environmental suitability is strong, speed regulation property because having for permanent magnet coupling drive technology Can good, smooth starting, the advantages such as overload protection, cost is low, vibration interference is small, be widely used in petroleum, chemical industry, coal The Important Projects such as charcoal, electric power field.Wherein, permanent-magnet coupler is the vital classification of permanent magnet coupling drive technology, transmitting Effective calculating of torque has important value to its own performance prediction and Optimal Structure Designing, is to guarantee heavy construction equipment just The important prerequisite often run.Permanent-magnet coupler transmitting torque Traditional calculating methods mainly include finite element method and Analytic Calculation Method.Finite element method computational accuracy is high, but modeling is complicated, it is long to calculate the time, particularly with especially complex Topological structure, change size and material property it is extremely inconvenient to design optimization.
For the calculating of permanent-magnet coupler transmitting torque, Chen Hongkui of China Coal Research Institute et al. was in 2017 years Article " the permanent-magnet coupler torque characteristics research based on Ansoft " has been delivered in " colliery engineering " the 3rd phase of volume 36, has been mentioned FEM calculation is carried out to permanent-magnet coupler with Ansof simulation software out, is made according to Theory of Electromagnetic Field and ignores leakage field It is assumed that obtaining the calculated result of transmitting torque by post-processing.But need first to carry out three-dimensional modeling with SolidWorks software, Pre-treatment number of grid is numerous and jumbled, and calculation method is complicated, and computational efficiency is low, and time cost is higher.
Summary of the invention
The present invention in order to overcome the drawbacks of the prior art, invents a kind of permanent-magnet coupler transmitting torque calculation method, The method improve the low defects of finite element method modeling complexity, computational efficiency, are based on permanent-magnet coupler topology knot Structure feature, building include main flux, leakage magnetic flux, useful flux and the magnetomotive magnetic circuit equivalent model of induction, establish magnetic circuit etc. Model equation is imitated, effective magnetic induction intensity across conductor disc is solved, analyzes to obtain permanent-magnet magnetic couple of force by analytical Calculation The result of clutch transmitting torque.This method is a kind of calculation method with practical implementation value.Calculation method is simple, meter High-efficient, time cost is low.
The technical solution adopted by the present invention is that a kind of permanent-magnet coupler transmits torque calculation method, characterized in that should Fan-shaped eddy region is equivalent is calculated at circle according to Faraday's electromagnetic induction law by produced in conductor disc first for method Conductor disk area totality eddy-current loss power；Then it according to the topological structure of permanent-magnet coupler, establishes comprising main flux, let out Leakage magnetic flux, useful flux and the magnetomotive magnetic circuit equivalent model of induction, and make corresponding simplification；According to permanent-magnet coupler Design size calculates permanent magnet magnetic kinetic potential, eddy region induction magnetomotive force, main flux magnetic resistance, leakage magnetic flux magnetic resistance, in conjunction with base That Hough First Law, calculates effective magnetic induction intensity across conductor disc；Finally, the biography of permanent-magnet coupler is calculated Pass torque；Specific step is as follows for calculation method:
The first step calculates conductor disk area totality eddy-current loss power
The equivalent eddy region of circle, permanent magnet axial charging, round equivalent eddy region are taken in conductor disc first Movement and cutting magnetic line in magnetic field, the variation across round equivalent eddy region magnetic flux follow following formula:
φ=BeSecosωt (1)
In formula (1), BeFor across effective magnetic induction intensity of round equivalent eddy region, t is time, SeIt is round equivalent The area of eddy region, and have:
Se=1.2 (a+b) L/2 (2)
And
The π p Δ n/60 of ω=2 (3)
In formula (2), a is the size of permanent magnet inward flange, and b is the outer peripheral size of permanent magnet, and L is permanent magnet radial edges Vertical dimension.
In formula (3), p is permanent magnet magnetic number of pole-pairs, slip of the Δ n between permanent magnetism body disc and conductor disc.
According to Faraday's electromagnetic induction law, the induced electromotive force E that the round equivalent eddy region of conductor disc generates is obtained are as follows:
Conductor disc totality eddy-current loss power PeAre as follows:
In formula (5), R is conductor disc equivalent resistance, and is had:
In formula (6), ρ is the resistivity of conductor disc, lcFor conductor disc thickness, μ0For space permeability, μrcFor conductor disc phase To magnetic conductivity.
Second step, the magnetic circuit equivalent model for establishing permanent-magnet coupler
According to the topological structure of permanent-magnet coupler, the main flux path of permanent-magnet coupler be permanent magnet (5) → Permanent magnetism body disc (4) → air gap (3) → conductor disc (2) → conductor disc back iron (1) → permanent magnetism body disc back iron (6) → permanent magnet (5), lets out Leakage magnetic flux is present at air gap (3).It is unfolded to obtain the two-dimentional magnetic circuit of permanent-magnet coupler at permanent magnet mean radius section Model, conductor disc back iron (1) correspond to main flux magnetic resistance Ri1, conductor disc (2) is corresponding to eddy region induction magnetomotive force FiAnd it is main Magnetic flux magnetic resistance Rc, air gap (3) is corresponding to main flux magnetic resistance RaAnd leakage magnetic flux magnetic resistance Rla、Rlp, permanent magnetism body disc (4), which corresponds to, to be led Magnetic flux magnetic resistance Ri2, permanent magnet (5) is corresponding to permanent magnet magnetic kinetic potential FpAnd main flux magnetic resistance Rp, permanent magnetism body disc back iron (6) corresponds to Main flux magnetic resistance Ri3, according to the above magnetic flux path corresponding relationship, establish the magnetic circuit equivalent model of permanent-magnet coupler.
Third step, the effective magnetic induction intensity for being calculated through conductor disc
If permanent magnet magnetic kinetic potential Fp, eddy region incude magnetomotive force Fi, conductor disc back iron main flux magnetic resistance Ri1, conductor disc master Magnetic flux magnetic resistance Rc, air gap main flux magnetic resistance Ra, leakage magnetic flux magnetic resistance Rl between air gapa, leakage magnetic flux magnetic resistance Rl between magnetp, permanent magnet Disk main flux magnetic resistance Ri2, permanent magnet main flux magnetic resistance Rp, permanent magnetism body disc back iron main flux magnetic resistance Ri3, the sum of leakage magnetic flux magnetic resistance Rl；Expression are as follows:
In formula (7), τpFor the pole span between adjacent permanent magnet center, τmFor the pole span between adjacent permanent magnet body side surface, μri For the relative permeability of permanent magnetism body disc and conductor disc back iron, μrpFor the relative permeability of permanent magnet, lgFor gas length, li1To lead The thickness of body disc back iron, lpFor the axial charging thickness of permanent magnet, li2L is removed for permanent magnetism body discpThickness later, li3For permanent magnetism The thickness of body disc back iron, HpFor permanent magnet coercive force, kiTo incude magnetomotive force conversion factor.
According to Kirchhoff's first law, the corresponding equation group of magnetic circuit equivalent model is obtained are as follows:
In formula (8), φ0For main magnetic flux, φ1For magnetic leakage flux, φ2For across the effective flux of conductor disc, and Have:
Fe=Fp-Fi (9)
The effective flux φ across conductor disc can be derived by (8)2Calculation expression are as follows:
In formula (10),
R=2Ra+2Rc (11)
By the relationship of magnetic flux and magnetic induction intensity, the magnetic induction density B across conductor disc can be calculatedeAre as follows:
4th step, the transmitting torque for calculating permanent-magnet coupler, and compared with result of finite element
By eddy-current loss generate fuel factor ignore, it is believed that eddy-current loss power is completely converted into transmitting torque, according to turn The relationship of square and power can calculate transmitting torque T are as follows:
In formula (13),
ωT=2 π Δ n/60 (14)
In view of brow leakage effect, Russell-Norsworthy correction factor k is introducedc, revised torque T' are as follows:
T'=kcT (15)
In formula (15),
It is found out using formula (15) in view of the revised torque T' of brow leakage effect.
The present invention has fully considered that induction magnetomotive force on the magnetomotive influence of permanent magnet, and has effectively been included in adjacent permanent magnet Leakage magnetic flux between body between permanent magnet itself.Within the scope of the slip of normal work, a kind of permanent-magnet magnetic couple of force is proposed Clutch transmits torque calculation method, and calculates transmitting torque with practical permanent-magnet coupler structure, with finite element method The calculated result contrast verification validity and correctness of this method.The permanent-magnet coupler that this method proposes transmits torque meter Calculation method can realize rapidly and accurately to the work of the torque prediction of permanent-magnet coupler, to engineering permanent-magnet magnetic couple of force in practice The design optimization of clutch has preferable application value.This method is a kind of calculation method with practical implementation value. Calculation method is simple, and computational efficiency is high, and time cost is low.
Detailed description of the invention
Fig. 1 is permanent-magnet coupler transmitting torque calculation method flow diagram proposed by the present invention
Fig. 2 is the topological structure schematic diagram of permanent-magnet coupler, wherein 1- conductor disc back iron, 2- conductor disc, 3- gas Gap, 4- permanent magnetism body disc, 5- permanent magnet, 6- permanent magnetism body disc back iron.
Fig. 3 is the round equivalent eddy region schematic diagram of permanent-magnet coupler, wherein 7- permanent magnet inward flange, 8- permanent magnetism Body radial edges, 9- permanent magnetism outer rim, the round equivalent eddy region of 10-.
Fig. 4 is permanent-magnet coupler two dimensional flux paths schematic diagram, wherein 1- disk back iron, 2- conductor disc, and 3- air gap, 4- permanent magnetism body disc, 5- permanent magnet, 6- permanent magnetism body disc back iron, heavy line-main flux, dotted line-leakage magnetic flux intersect circle and solid Point circle-induction magnetomotive force.
Fig. 5 is the magnetic circuit equivalent model schematic diagram of permanent magnetism axial direction coupler, wherein φ0For main magnetic flux, φ1For magnetic leakage Flux, φ2For across the effective flux of conductor disc, FpFor permanent magnet magnetic kinetic potential, FiMagnetomotive force, R are incuded for eddy regioni1For Conductor disc back iron main flux magnetic resistance, RcFor conductor disc main flux magnetic resistance, RaFor air gap main flux magnetic resistance, RlaThe magnetic leakage between air gap Logical magnetic resistance, RlpThe leakage magnetic flux magnetic resistance between magnet, Ri2For permanent magnetism body disc main flux magnetic resistance, RpFor permanent magnet main flux magnetic resistance, Ri3 For permanent magnetism body disc back iron main flux magnetic resistance, Rl is the sum of leakage magnetic flux magnetic resistance.
Fig. 6 is permanent-magnet coupler transmitting torque calculation method proposed by the present invention and finite element method comparison knot Fruit figure.
Specific embodiment
The present invention is further elaborated with reference to the accompanying drawings and examples.
The present embodiment selects an input speed 1500r/min and 5 number of magnetic pole pairs two-conductor disk symmetrical structure permanent-magnets The transmitting torque of coupler is calculated.
Wherein, input speed 1500r/min and the 5 basic rulers of number of magnetic pole pairs two-conductor disk symmetrical structure permanent-magnet coupler It is very little are as follows: the size a=40mm of permanent magnet inward flange, is the outer peripheral size b=60mm of permanent magnet, and permanent magnet radial edges are hung down Ruler cun L=57mm, electricalresistivityρ=1.75 × 10 of conductor disc-2Ω·mm2/ m, conductor disc thickness lc=6mm, vacuum magnetic conductance Rate μ0=4 π × 10-7H/m, conductor disc relative permeability μrc=0.999999, the pole span τ between adjacent permanent magnet centerp= 79.5mm, the pole span τ between adjacent permanent magnet body side surfacemThe relative permeability μ of=29.5mm, permanent magnetism body disc and conductor disc back ironri =2000, the relative permeability μ of permanent magnetrp=1.05, gas length lg=4mm, the thickness l of conductor disc back ironi1=10mm, forever The axial charging thickness l of magnetp=25mm, permanent magnetism body disc remove lpThickness l lateri2=1mm, the thickness of permanent magnetism body disc back iron li3=10mm, permanent magnet coercive force Hp=-1000KA/m incudes magnetomotive force conversion factor ki=1.8~2.5.
As shown in Figure 1, permanent-magnet coupler proposed by the present invention transmits torque calculation method flow diagram, calculation method Specific step is as follows；
The first step calculates conductor disk area totality eddy-current loss power
The equivalent eddy region of circle is taken in conductor disc first, Δ n takes 5r/min, by fixed a, b, L value in front Substitution formula (2), obtains Se=0.0034m2；P, Δ n are substituted into formula (3), obtain ω=2.618rad/s.Permanent magnet axial charging, Round equivalent eddy region moves in magnetic field and cutting magnetic line, and the variation across round equivalent eddy region magnetic flux is abided by Expression formula (1) is followed, by SeFormula (1) is substituted into ω, obtains φ=0.0034Becos2.618t。
According to Faraday's electromagnetic induction law and formula (4), the induced electricity that the round equivalent eddy region of conductor disc generates is obtained Kinetic potential obtains E=0.009Besin2.618t；By ρ, lc、μ0、μrc, ω substitute into formula (6), obtain Δ D'=0.1017；According to formula (5) conductor disc totality eddy-current loss power Pe=9.16 × 10-5Be 2。
Second step, the magnetic circuit equivalent model for establishing permanent-magnet coupler
According to the topological structure of permanent-magnet coupler, the main flux path of permanent-magnet coupler be permanent magnet (5) → Permanent magnetism body disc (4) → air gap (3) → conductor disc (2) → conductor disc back iron (1) → permanent magnetism body disc back iron (6) → permanent magnet (5), lets out Leakage magnetic flux is present at air gap (3), as shown in Figure 2,3.It is unfolded to obtain permanent-magnet coupling at permanent magnet mean radius section The two-dimentional magnetic circuit model of device, conductor disc back iron (1) correspond to conductor disc back iron main flux magnetic resistance Ri1, conductor disc (2) is corresponding to whirlpool It flows region and incudes magnetomotive force FiAnd conductor disc main flux magnetic resistance Rc, air gap (3) is corresponding to air gap main flux magnetic resistance RaAnd it is let out between air gap Leakage magnetic flux magnetic resistance Rla, leakage magnetic flux magnetic resistance Rl between magnetp, permanent magnetism body disc (4) is corresponding to permanent magnetism body disc main flux magnetic resistance Ri2, forever Magnet (5) corresponds to permanent magnet magnetic kinetic potential FpAnd permanent magnet main flux magnetic resistance Rp, permanent magnetism body disc back iron (6) is corresponding to permanent magnetism body disc Back iron main flux magnetic resistance Ri3, according to the above magnetic flux path corresponding relationship, the magnetic circuit equivalent model of permanent-magnet coupler is established, such as Fig. 4, shown in 5.
Third step, the effective magnetic induction intensity for being calculated through conductor disc
By ki2.5 are taken, permanent magnet magnetic kinetic potential F available according to formula (7)p=32960A, eddy region incude magnetomotive force Fi=0.073Be, conductor disc back iron main flux magnetic resistance Ri1=55482H-1, conductor disc main flux magnetic resistance Rc=3.35 × 106H-1、 Air gap main flux magnetic resistance Ra=2.234 × 106H-1, leakage magnetic flux magnetic resistance Rl between air gapa=1.027 × 109H-1, leak between magnet Magnetic flux magnetic resistance Rlp=1.51 × 108H-1, permanent magnetism body disc main flux magnetic resistance Ri2=5.584 × 105H-1, permanent magnet main flux magnetic resistance Rp=1.7 × 107H-1, permanent magnetism body disc back iron main flux magnetic resistance Ri3=55482H-1。
According to Kirchhoff's first law, obtaining the corresponding equation group of magnetic circuit equivalent model is (8).In formula (8), φ0For Main magnetic flux, φ1For magnetic leakage flux, φ2For across the effective flux of conductor disc.By formula (8), formula (9), formula (10) and formula (11) magnetic induction density B across conductor disc can be calculatede=0.8021T.
4th step, the transmitting torque for calculating permanent-magnet coupler, and compared with result of finite element
By eddy-current loss generate fuel factor ignore, it is believed that eddy-current loss power is completely converted into transmitting torque, according to turn The relationship of square and power, formula (13), formula (14) can calculate transmitting torque T=227.5785Nm；In view of brow leakage Effect introduces Russell-Norsworthy correction factor kc, can calculate revised torque by formula (15) and formula (16) is T'=117.7376Nm.
Δ n is taken into 10r/min, the first step is repeated to four-step calculation process, obtains T'=143.496Nm；Δ n is taken 15r/min repeats the first step to four-step calculation process, obtains T'=158.068Nm；Δ n is taken into 20r/min, repeats the One step obtains T'=167.7216Nm to four-step calculation process；Δ n is taken into 30r/min, repeats the first step to the 4th step meter Calculation process, obtains T'=179.8273Nm；Δ n is taken into 40r/min, the first step is repeated to four-step calculation process, obtains T' =187.0365Nm；Δ n is taken into 50r/min, the first step is repeated to four-step calculation process, obtains T'=191.6959N m；Δ n is taken into 100r/min, the first step is repeated to four-step calculation process, obtains T'=200.3062Nm；Δ n is taken 150r/min repeats the first step to four-step calculation process, obtains T'=201.0865Nm；Δ n is taken into 200r/min, is repeated The first step obtains T'=199.8484Nm to four-step calculation process.
Within the scope of the slip of normal work, permanent-magnet coupler proposed by the present invention transmits torque calculation method and has The result for limiting first calculation method is compared, as shown in Figure 6.It can be seen from the figure that transmitting torque meter proposed by the present invention Calculation method and FEM calculation prevention result have good consistency, it was demonstrated that method proposed by the invention is correct and effective 's.
The invention proposes a kind of permanent-magnet couplers to transmit torque calculation method, and with practical permanent-magnet coupler Structure Calculation transmitting torque, with the calculated result contrast verification of the finite element method validity and correctness of this method.This Method has fully considered that induction magnetomotive force on the magnetomotive influence of permanent magnet, and has effectively been included between adjacent permanent magnet and forever Leakage magnetic flux between magnet itself.Within the scope of the slip of normal work, permanent-magnet coupler transmitting proposed by the present invention Torque calculation method can realize rapidly and accurately to the work of the torque prediction of permanent-magnet coupler, to engineering permanent magnetism in practice The design optimization of magnetic coupling has preferable application value.

Claims (1)

1. a kind of permanent-magnet coupler transmits torque calculation method, characterized in that this method first will be produced in conductor disc Fan-shaped eddy region is equivalent to calculate conductor disk area totality eddy-current loss function according to Faraday's electromagnetic induction law at circle Rate；Then it according to the topological structure of permanent-magnet coupler, establishes comprising main flux, leakage magnetic flux, useful flux and induction magnetic The magnetic circuit equivalent model of kinetic potential, and make corresponding simplification；According to the design size of permanent-magnet coupler, permanent magnet magnetic is calculated Kinetic potential, eddy region induction magnetomotive force, main flux magnetic resistance, leakage magnetic flux magnetic resistance are calculated and are worn in conjunction with Kirchhoff's first law Cross effective magnetic induction intensity of conductor disc；Finally calculate the transmitting torque of permanent-magnet coupler；The specific step of calculation method It is rapid as follows:
The first step calculates conductor disk area totality eddy-current loss power
The equivalent eddy region of circle is taken in conductor disc first, permanent magnet axial charging, round equivalent eddy region is in magnetic It is moved in, and cutting magnetic line；Variation across round equivalent eddy region magnetic flux follows following formula:
φ=BeSecosωt (1)
In formula (1), BeFor across effective magnetic induction intensity of round equivalent eddy region, t is time, SeFor round equivalent vortex The area in region, and have:
Se=1.2 (a+b) L/2 (2)
And
The π p Δ n/60 of ω=2 (3)
In formula (2), a is the size of permanent magnet inward flange, and b is the outer peripheral size of permanent magnet, and L is hanging down for permanent magnet radial edges Ruler cun；
In formula (3), p is permanent magnet magnetic number of pole-pairs, slip of the Δ n between permanent magnetism body disc and conductor disc；
According to Faraday's electromagnetic induction law, the induced electromotive force E that the round equivalent eddy region of conductor disc generates is obtained are as follows:
Conductor disc totality eddy-current loss power PeAre as follows:
In formula (5), R is conductor disc equivalent resistance, and is had:
In formula (6), ρ is the resistivity of conductor disc, lcFor conductor disc thickness, μ0For space permeability, μrcFor conductor disc relative magnetic permeability Rate；
Second step, the magnetic circuit equivalent model for establishing permanent-magnet coupler
According to the topological structure of permanent-magnet coupler, the main flux path of permanent-magnet coupler is permanent magnet (5) → permanent magnetism Body disc (4) → air gap (3) → conductor disc (2) → conductor disc back iron (1) → permanent magnetism body disc back iron (6) → permanent magnet (5), magnetic leakage It is logical to be present at air gap (3)；It is unfolded to obtain the two-dimentional magnetic circuit model of permanent-magnet coupler at permanent magnet mean radius section, Conductor disc back iron (1) corresponds to main flux magnetic resistance Ri1, conductor disc (2) is corresponding to eddy region induction magnetomotive force FiAnd main flux magnetic Hinder Rc, air gap (3) is corresponding to main flux magnetic resistance RaAnd leakage magnetic flux magnetic resistance Rla、Rlp, permanent magnetism body disc (4) is corresponding to main flux magnetic Hinder Ri2, permanent magnet (5) is corresponding to permanent magnet magnetic kinetic potential FpAnd main flux magnetic resistance Rp, permanent magnetism body disc back iron (6) is corresponding to main flux Magnetic resistance Ri3, according to the above magnetic flux path corresponding relationship, establish the magnetic circuit equivalent model of permanent-magnet coupler；
Third step, the effective magnetic induction intensity for being calculated through conductor disc
If permanent magnet magnetic kinetic potential Fp, eddy region incude magnetomotive force Fi, permanent magnet magnetic kinetic potential Fp, eddy region incude magnetomotive force Fi、 Conductor disc back iron main flux magnetic resistance Ri1, conductor disc main flux magnetic resistance Rc, air gap main flux magnetic resistance Ra, leakage magnetic flux magnetic resistance between air gap Rla, leakage magnetic flux magnetic resistance Rl between magnetp, permanent magnetism body disc main flux magnetic resistance Ri2, permanent magnet main flux magnetic resistance Rp, permanent magnetism body disc back iron Main flux magnetic resistance Ri3, the sum of Rl leakage magnetic flux magnetic resistance；Expression are as follows:
In formula (7), τpFor the pole span between adjacent permanent magnet center, τmFor the pole span between adjacent permanent magnet body side surface, μriFor permanent magnetism The relative permeability of body disc and conductor disc back iron, μrpFor the relative permeability of permanent magnet, lgFor gas length, li1For conductor disc back The thickness of iron, lpFor the axial charging thickness of permanent magnet, li2L is removed for permanent magnetism body discpThickness later, li3For permanent magnetism body disc back The thickness of iron, HpFor permanent magnet coercive force, kiTo incude magnetomotive force conversion factor；
According to Kirchhoff's first law, the corresponding equation group of magnetic circuit equivalent model is obtained are as follows:
In formula (8), φ0For main magnetic flux, φ1For magnetic leakage flux, φ2For across the effective flux of conductor disc, and have:
Fe=Fp-Fi (9)
The effective flux φ across conductor disc is derived by (8)2Calculation expression are as follows:
In formula (10),
R=2Ra+2Rc (11)
By the relationship of magnetic flux and magnetic induction intensity, the magnetic induction density B across conductor disc can be calculatedeAre as follows:
4th step, the transmitting torque for calculating permanent-magnet coupler
The fuel factor that eddy-current loss generates is ignored, it is believed that eddy-current loss power is completely converted into transmitting torque, according to torque and The relationship of power calculates transmitting torque T are as follows:
In formula (13),
ωT=2 π Δ n/60 (14)
In view of brow leakage effect, Russell-Norsworthy correction factor k is introducedc, revised torque T' are as follows:
T'=kcT (15)
In formula (15),
It is found out using formula (15) in view of brow leakage effect, revised torque T'.
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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111859694A (en) * 2020-07-28 2020-10-30 大连理工大学 Heat source loss calculation method for permanent magnet magnetic coupler
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CN112287558A (en) * 2020-11-09 2021-01-29 大连理工大学 Method for calculating energy-saving power and energy-saving rate of permanent magnet speed regulator
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CN112685875A (en) * 2020-12-07 2021-04-20 大连理工大学 Method for calculating output torque of groove digging type magnetic speed regulator by optimal groove opening ratio

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Publication number Priority date Publication date Assignee Title
CN111859694A (en) * 2020-07-28 2020-10-30 大连理工大学 Heat source loss calculation method for permanent magnet magnetic coupler
CN112182844A (en) * 2020-09-04 2021-01-05 大连理工大学 Effective magnetic potential calculation method for permanent magnet magnetic coupler
CN112421932A (en) * 2020-10-16 2021-02-26 大连理工大学 Eddy current loss power calculation method of mining permanent magnet coupler
CN112287558A (en) * 2020-11-09 2021-01-29 大连理工大学 Method for calculating energy-saving power and energy-saving rate of permanent magnet speed regulator
CN112541154A (en) * 2020-11-26 2021-03-23 东南大学 Method for calculating magnetic circuit power
CN112541154B (en) * 2020-11-26 2021-10-08 东南大学 Method for calculating magnetic circuit power
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CN112685875A (en) * 2020-12-07 2021-04-20 大连理工大学 Method for calculating output torque of groove digging type magnetic speed regulator by optimal groove opening ratio
CN112685875B (en) * 2020-12-07 2022-09-20 大连理工大学 Method for calculating output torque of groove digging type magnetic speed regulator by optimal groove opening ratio

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