Eddy-Current Coupling With Slotted Conductor Disk

Eddy-Current Coupling With Slotted Conductor Disk

Hamideh K.Razavi and Michael https://www.sodocs.net/doc/c64199483.html,mpérth

Hybrid Power Research Group,Department of Mechanical Engineering,Imperial College London,London SW72AZ,U.K. Eddy-current couplings are becoming popular devices for speed and torque control.Ef?ciency of these couplings depends on the ex-citation level;therefore,the routes and density of induced currents affect it signi?cantly.This paper focuses on the design of a squirrel cage-type coupling disk,which forces eddy currents to?ow perpendicular to both magnetic?eld lines and the axis of rotation.Lorentz force and transmitted torque are consequently optimized.The investigation is performed both numerically and experimentally,with results being presented for variable air gaps and speeds.A comparison between plain and slotted disk conductors,tested under identical set-ups,demonstrates the effect of the proposed design on torque throughput and ef?ciency.In addition to this,the in?uence of number and size of slots and the effect of?lling slots with iron are studied by parametric?nite-element modeling veri?ed by experiments. Index Terms—Conductor design,eddy-current coupling,?nite-element analysis.

I.I NTRODUCTION

P ERMANENT-magnet eddy-current couplings(PMECs) have become commercially available since1999[1]. Initially employed to replace conventional variable frequency drives(VFDs)in fans and pumps,eddy-current adjustable speed coupling systems(ASCSs)were promptly recognized by diverse industries[2].

An ASCS consists of a double face magnetic stator,which can spin inside a rotor housing with conductor disks positioned on both sides.A screw mechanism enables speed control by axial movement of the magnet disks and adjustment of the air gaps.As the motor shaft starts rotation,a time-variant magnetic excitation occurs on the conductor disks.Induced eddy currents within the skin depth of the conductors generate a tangential force and hence a reactive torque on the stator of the coupling. In spite of the lower ef?ciency of an ASCS(93%)compared to that of a VFD(95%)[3],it has remarkable advantages such as simplicity and compact design as well as economic tradeoffs. In order to enhance the ef?ciency of an ASCS,stray currents, generated in the conductor disk,should be eliminated.These currents end in ohmic losses by generating heat in the conductor disk[4].Generated heat not only wastes energy but also disturbs the magnetic properties of the permanent magnets,which in turn reduces the torque-transmitting capability of the system.

This paper presents a new design of the conductor disk with slot cuts that facilitates the?ow of currents in appropriate routes in order to avoid stray currents.Precise performance analysis of PMECs attributed to three-dimensional(3-D)electromagnetic ?eld effects is only possible if a3-D numerical technique is used [5]–[7].However,using linear theory,analytical approximation for simpli?ed two-dimensional(2-D)models,representing3-D models,are viable.By this method,models are solved in less time and are less costly,and results are highly credible.

In this research,initially a2-D numerical model for a plain conductor disk with the equivalent geometry is https://www.sodocs.net/doc/c64199483.html,-paring the results to those of experiments validates the model to

Digital Object Identi?er

10.1109/TMAG.2005.862762

Fig.1.Schematic of the coupling.

be re?ned for slotted design.To avoid complicated electromag-

netic?eld analysis,an elementary approach is implemented.It

concludes that a slotted copper disk improves pull-out torque

by15%.Additionally an iron-backing disk with bulges,which

can plug into the slot gaps in the conductor disk,boosts the?ux

density in the region and ampli?es the results.

II.G ENERAL D ESIGN

A magnet rotor with an even number of alternative pole em-

bedded magnets is used.The spider plate is made of aluminum

and the magnets are sintered Nd–Fe–B with residual

induction

G(Fig.1).

A plain copper disk is?xed on an iron backing plate of4mm

thickness and forms the stator part of the coupling.Table I in-

cludes other speci?cations of the coupling.

To make a2–D representation of a slice,containing two adja-

cent magnets,a radial view of the magnet pitch circle is unrolled

as shown in Fig.2.

In Fig.2,the length of the arcs BD and DF

are

and(1)

where

(2)

(3) 0018-9464/$20.00?2006IEEE

TABLE I

C OUPLING S

PECIFICATIONS

Fig.2.Geometry of the 2–D

imaging.

Fig.3.Field map on a 2–D linear model.

Other parameters

are

(4)

(5)

is the number of magnets

and is magnet pitch circle

radius.

The ?eld map in Fig.3shows how the ?ux density is con-centrated in and around the magnet projection zone on the con-ductor face.This can be modeled by an exponential waveform (cumulative sinusoidal term)[8],[9].However,in this study,a distribution with a mutual sinusoidal general term is

employed

Fig.4.Magnetic ?ux density on the surface of the copper as a function of '.

[10].It allows a region with zero ?ux density along each period (depicted in Fig.4)which helps analysis in the next step.Fourier expression of the magnetic ?

ield

for

and will hence

become

(6)

with coef ?

cients

(7)

(8)

where is the de ?ection angle

and is the number of har-monics.The new equation (6)also resolves the displacement of the peak ?ux density from the magnet core positions.There-fore,eddy-current density and dispersion over conductive sur-faces will be determined more accurately.

An identical 2-D model to that in Fig.2was constructed in the ?nite-element (FE)environment and solved using transient motion analysis with heat loss consideration.Data input for the magnetic ?eld were collected by solving (6)along

the axis of the 2-D imaging model in Fig.2.

Fig.5illustrates the experimental results as well as the torque features obtained by FE analysis.The reasonable match between results justi ?es the model for the next step.

A plot of the eddy currents on the surface of the conductor is depicted in Fig.6.It suggests that whereas only radial segments of each vortex contribute to the drag force,de ?ection is mainly tangential.A remedy to this disarray is to eliminate presence of conducting material physically and force currents to ?ow in radial routes.

III.S LOTTED C ONDUCTOR

Using parametric modeling of the FE analysis,a range of sizes and numbers of the slot cuts for the conductor disk was tested.Fig.7shows a 3-D image and Table II contains geome-tries of the samples.

Radial length of eddy-current formation on the conductor face has been regarded for cutting dimensions [11],[12].

RAZA VI AND LAMP éRTH:EDDY-CURRENT COUPLING WITH SLOTTED CONDUCTOR DISK

407

Fig. https://www.sodocs.net/doc/c64199483.html,parison between numerical and experimental results (2mm air

gap).

Fig.6.

Eddy-current plot on the

conductor.

Fig.7.3-D image of slotted copper disk.

TABLE II

S LOTTED C

ONDUCTORS

To calculate the effective length of the slot in the vertical magnetic ?eld,a simple geometrical method is employed.In

any time

instant

,position of the slot cut against

magnet Fig.8.Slot cuts projection on the rotor

disk.

can be described either as an offset angle or linear distance

denoted

by

(see Fig.8),

where

for

Otherwise

Number of slots

(9)Number of

magnets

(10)

and is the ?rst offset (can be assumed

zero).

and are the same as in Fig.2.

Chord BE in Fig.8represents the effective

length .It can be seen

that

(11)

and

(12)

Since

(13)

by ?

nding from (13)and substituting in

(12),

is

obtained:

(14)

Also from Fig.8,for the

angle

equal

to

we

have

(15)

408IEEE TRANSACTIONS ON MAGNETICS,VOL.42,NO.3,MARCH

2006

Fig.9.Arbitrary bars in magnet projection

zone.

Fig.10.Field graph for slotted conductor.

Consequently,which is the distance between

point and

the center of the disk in Fig.8,can be calculated

by

(16)

According to Faraday ’s law [13],the induced voltage in a moving conductor,surrounded by a magnetic ?eld

(in Fig.9),will

be

(17)(18)

and is the slip speed.Fig.10shows how ?ux lines pass through a slotted conductor.

The zero magnetic ?eld region in Fig.4is excluded from anal-ysis.This not only simpli ?es the modeling and avoids lengthy calculation but also improves the accuracy of the magnetic ?eld density in each zone.For bar of the conductor,a direct

current is

generated:

(19)

in

which

(20)

Fig.11.

Torque characteristics,comparison for 2mm air

gap.

Fig.12.

Torque characteristics comparison for a 48slotted disk.

Resistivity and bar cross section

area are considered con-stant.Each moving bar in the magnetic ?eld now can be treated as a moving wire carrying a dc current.Considering primary ?eld exclusively,Lorentz

force will

be

(21)

and

torque

(22)

A solution to a 60slotted disk model is in Fig.11and com-pared to experiments.In contrast to Fig.5,maximum torque shows 13%improvement which is an undoubted bene ?t of the new design for torque transfer applications [14].

The 3-D graph in Fig.12depicts torque properties against two other dimensions,air gaps and speeds.Trends in this graph,though for a 48slotted disk,have been similarly observed for all other prototypes.

The methodology has been implemented for the range of slotted disks in Table II.Results are shown in Fig.13.It is ap-parent from 24(2)and 48slotted disks comparisons,that despite the progress made by the slotted disks on torque characteristics,

RAZA VI AND LAMP éRTH:EDDY-CURRENT COUPLING WITH SLOTTED CONDUCTOR DISK

409

Fig.13.Torque characteristics comparison for 2mm air gap (Dashed lines interpolate groups of

data).

Fig.14.Back iron plate with protrusions.a compromise exists between the number and width of the slots.Taking into account the complexity of the manufacturing,the optimization of the slot size and numbers need to be rigorous for each particular application [15].

IV .S LOTTED C ONDUCTOR F ILLED W ITH I RON

Filling slots with iron reduces the air gap and increases the ?ux density in the region.For this purpose,iron-backing plates,as shown in Fig.14,with slot shape protrusions were made.By this revision,the magnetic ?eld is stronger between conductor bars,similar to Fig.15.Moreover,higher gradients over time generate a considerable boost on torque measures.

Table III summarizes the effect of iron in slots obtained from experiments.An average increase of 50%is achievable by using a protruded iron disk.Detailed results for torque ?gures of a 48slotted disk are shown in Fig.16.In this case,at 1200rpm a 47%increase to plain conductor results is obtained.

Hysteresis and end leakage have more in ?uence when iron is used in slots.This was clearly sensed by a torque transducer mounted on the shaft while testing at different speeds.Slow ac-celeration and high frequency of speed alterations intensi ?es the effects and causes immediate drop down in torque responses.

V .C ONCLUSION

A new design for the conductor disk of an axial ?ux eddy-current coupling is presented in this paper.In order to

analyze

Fig.15.

Field map for coupling with iron ?lled slotted

conductor.

Fig.16.Torque characteristics comparison for 2mm air gap.

TABLE III

A VERAGE I NCREASE IN T ORQUE M EASURES

FOR I RON F ILLED

S LOTTED C

ONDUCTORS

the performance of the coupling and compare it to its general design,a 2-D FE model was https://www.sodocs.net/doc/c64199483.html,paring analytical results to those of experiments reveals that the 2-D model is reliable.The methodology is based on linear theory with minor modi ?cations in the magnetic ?eld distribution.

Computing the new magnetic ?eld quantities requires a sepa-rate analytical solution.Although this calculation is straightfor-ward,it interrupts the FE analysis and hence increases the total solution time.This is predominantly due to the need to insert the results manually into the model.These modi ?cations enable the analysis of the new coupling design in 2-D whereas normally a full 3-D solution will be required.

The results of experiments and analysis proved that a cou-pling with a slotted conductor transfers higher torque than it does with a conventional plain conductor.Therefore,a variety of the slotted designs including slot cuts packed with iron was studied.It is inferred that the maximum number of slots is not necessarily the optimum since adequate material must exist to carry generated currents.As a result,a compromise between the width and number of bars is inevitable.Axial loads and

410IEEE TRANSACTIONS ON MAGNETICS,VOL.42,NO.3,MARCH2006

heat exchange characteristics of the new design are still to be investigated.

A CKNOWLEDGMENT

This work was supported by Imperial College London.

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Hamideh K.Razavi is a Researcher in transmission technology in hybrid power-trains.Her former studies were on manufacturing with a broad experi-ence in automotive industries.

Michael https://www.sodocs.net/doc/c64199483.html,mpérth is Lecturer of design,CAD,electronics and instrumen-tation in the Mechanical Engineering Department of Imperial College London, London,U.K.He is head of the hybrid power research group,which focuses on sustainable energy technologies,hybrid electric vehicles,including simulation and permanent-magnet machines.

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偶联 coupling

偶联coupling 一个化学反应发生时其它反应以化学计量学的关系相伴进行的现象。主要用于如下三种情形：[1]氧化与还原的偶联。电子供体AH2在氧化成A时，电子受体B必须还原成BH2，此时称这二个反应为偶联。例如在醇发酵中3-磷酸甘油醛的脱氢与乙醛的还原以NAD+为媒介由二个脱氢酶的作用相偶联。[2]氧化还原反应或分解反应与磷酸化反应相偶联。在生物体内酶反应中可看到放能反应的进行与由ADP和正磷酸生成ATP（吸能反应）相偶联。这是由一个酶直接作用，或由二种以上的酶作用经由中间物的生成而进行的，这样的偶联因为直接把反应的自由能以高能磷酸键的形式贮存，所以是重要的。还有与逆反应的偶联，即与ATP的分解相偶联，发生吸能的合成和氧化还原反应，或肌肉收缩、主动运输等。 偶联反应 偶联反应（英文：Coupling reaction），也作偶连反应、耦联反应、氧化偶联，是由两个有机化学单位(moiety)进行某种化学反应而得到一个有机分子的过程.这里的化学反应包括格氏试剂与亲电体的反应(Grinard),锂试剂与亲电体的反应,芳环上的亲电和亲核反应(Diazo, Addition-Elimination),还有钠存在下的Wutz反应,由于偶联反应 (Coupling Reaction)含义太宽,一般前面应该加定语.而且这是一个比较非专业化的名词. 狭义的偶联反应是涉及有机金属催化剂的碳-碳键生成反应，根据类型的不同，又可分为交叉偶联和自身偶联反应。进行偶联反应时，介质的酸碱性是很重要的。一般重氮盐与酚类的偶联反应，是在弱碱性介质中进行的。在此条件下，酚形成苯氧负离子，使芳环电子云密度增加，有利于偶联反应的进行。重氮盐与芳胺的偶联反应，是在中性或弱酸性介质中进行的。在此条件下，芳胺以游离胺形式存在，使芳环电子云密度增加，有利于偶联反应进行。如果溶液酸性过强，胺变成了铵盐，使芳环电子云密度降低，不利于偶联反应，如果从重氮盐的性质来看，强碱性介质会使重氮盐转变成不能进行偶联反应的其它化合物。偶氮化合物是一类有颜色的化合物，有些可直接作染料或指示剂。在有机分析中，常利用偶联反应产生的颜色来鉴定具有苯酚或芳胺结构的药物。 常见的偶联反应包括： 反应名称－－年代－－反应物A－－反应物B －－类型－－催化剂－－注Wurtz反应 1855 R-X sp³ 自身偶联 Na Glaser偶联反应 1869 R-X sp 自身偶联 Cu Ullmann反应 1901 R-X sp² 自身偶联 Cu Gomberg-Bachmann反应 1924 R-N2X sp² 自身偶联以碱作介质 Cadiot-Chodkiewicz偶联反应 1957 炔烃 sp R-X sp 交叉偶联 Cu 以碱作介质 Castro-Stephens偶联反应 1963 R-Cu sp R-X sp² 交叉偶联 Kumada偶联反应 1972 R-MgBr sp²、sp³ R-X sp² 交叉偶联 Pd或Ni Heck反应 1972 烯烃 sp² R-X sp² 交叉偶联 Pd 以碱作介质

管件中英文对照

管件中英文对照等径直通equal coupling 异径直通reducing coupling 内牙直通 female coupling 外牙直通 straight tube with outside 90等径弯头 90 equal elbow 45等径弯头 45 equal elbow 外牙弯头 male elbow 内牙弯头 female elbow 等径三通 equal tee 异径三通 reducing tee 内牙三通female tee 外牙三通 male tee 管帽cap sch代表压力 lr长半径或1倍半 大小 SIZE 数量 QTY 碳钢弯头 Carbon Steel Elbow 不锈钢弯头 Stainless Steel Elbow 高压弯头 High-Pressure Elbow 同心异径管 Concentric Reducers 偏心异径管 Eccentric Reducers 高压异径管 High-pressure Reducers 不锈钢等径三通 Stainless Straight Tee 碳钢等径三通 Carbon Straight Tee 不锈钢等径四通 Stainless Straight Cross 高压三通 High-pressure Tee 锻制三通 Forged Tee 异径接头 Template 管帽 Caps 法兰flange 长径和短径弯头 long and short radius elbows 同心和偏心异径接头 concentric and eccentric reducers 等径和异径三通 straight and reducing outlet tees 大小头 CONCENTRIC REDUCER Tee Equal 相等的三通 等径三通Straight Tee 异径三通Reducing Tee 等径四通Straight Cross 90°短半径弯头90°SS Elbow (SR) 90°长半径弯头90°SS Elbow (LR) 高压厚壁弯头Thickness Elbow U型管Return Bend 盲法兰Blank Flange 弯管Bends 翻边stub ends

ABAQUS的接触问题中 Tie MPC和Coupling的区别和使用原则

ABAQUS的接触问题中，Tie、MPC和Coupling的区别和使用原则依个人经验和理解，针对ABAQUS的接触问题中，Tie、MPC和Coupling的区别和使用原则在此做个总结。不足之处，希望多多评改。TKS! ========= 梵音静思（QQ 974112936）?Tie：在刚度数据传递上相当于两个面刚性连接，绑定区域不发生相对运动和变形，刚度较大；在约束形式上tie约束为面对面的约束，主要是用于点（一个或多个，但不能是RP）和面以及面与面之间的绑定约束，用悬臂梁算模态的方法，测试RP和面之间用tie绑定完全没效果。 ?Coupling：可以理解为对接触问题的一种简化方式。Coupling可用于建立参考点（只测试过RP点）和关注对象之间（耦合点）的约束，关注对象和参考点之间有相同的刚体运动，可以在参考点上施加约束载荷。在约束形式上coupling为点对面的一中约束。 其中，coupling分为两种：运动耦合和分布耦合 （1）运动耦合：即在此区域的各节点与参考点之间建立一种运动上的约束关系。 （2）分布耦合：在此区域的各节点与参考点之间建立一种约束关系，但是对此区域上各节

点的运动进行了加权处理，使在此区域上受到的合力和合力距与施加在参考点上的力和力矩相等效。换言之，分布耦合允许面上的各部分之间发生相对变形，比运动耦合中的面更柔软。 其中，Coupling的类型又分为三种： 001. Kinematic：约束耦合点与参考点之间的刚体运动，可有选择性的约束6个自由度，6个自由度全选择的时候相当于MPC中的Beam约束。通常是一个点和多个点之间的耦合约束 002. Contimuum distributing（木用过~待补充） 003. D-coupling：着重于强调耦合间的力和力矩的传递，而对于位移的耦合不是刚性的。 一般来讲，分布耦合处的刚度小于运动耦合处的刚度。 MPC：MPC功能最强大，选项也最多。这里的选择总会让人感觉到困惑···MPC下面有很多子类，相对而言选择性强些，对于点对点的约束很直观，如果能结合一些网格划分工具中的功能，是很容易定义多个点和另外多个点之间的对应MPC关系的。对于大位移、大变形问题时，使用MPC其精度更高、约束更为“柔性”，与实际工程问题教接近，也就是说对于几何非线性问题的处理上MPC更为靠谱。

联轴器英语词汇和句子(中英对照)

联轴器英语词汇和句子（中英对照） 一、联轴器术语 coupling 联轴器 rigid coupling 刚性联轴器 solid coupling 刚性联轴器 muff coupling 套筒联轴器 fast coupling 刚性联轴器 nonrigid coupling 非刚性联轴器 fixed rigid coupling 固定式刚性联轴器 butt-muff coupling刚性联轴器，套筒联轴器 spring coupling 弹性联轴器 flexible coupling 挠性联轴器 elastic coupling 弹性联轴器 gear type flexible coupling 齿式挠性联轴器 semi-flexible coupling 半挠性联轴器 flexible link coupling 挠性杆联轴器 fine-tooth flexible coupling 细牙挠性联轴器 pin type flexible coupling 销钉式挠性联轴器 double-claw flexible coupling 双爪式挠性联轴器 flange coupling 凸缘联轴器 flanged coupling 凸缘联轴器 double slider coupling 十字滑块联轴器 Oldham coupling十字滑块联轴器 universal coupling万向联轴器 slipper type universal coupling 滑块式万向联轴器 crosshead coupling 滑块联轴器 chain coupling 链式联轴器 roller chain coupling 滚子链联轴器 membrane coupling 膜片联轴器 laminated membrane coupling 金属膜片联轴器 sleeve coupling 套筒联轴器 clamping coupling 夹壳联轴器 二、联轴器术语 1. The coupling shall be rated using a service factor of 1.75. 联轴器应采用1.75的“运行系数”来定额定值。 2.In other instances, a group of elements is combined to form a subassembly , such as bearings, couplings and clutches. 另外的一些情况下，一类元件被结合形成一个组件，比如轴承，联轴器和离合器。