research article study on impedance characteristics of

Research ArticleStudy on Impedance Characteristics of Aircraft Cables

Weilin Li12 Wenjie Liu1 Xiaobin Zhang1 Zhaohui Gao1 Meng Xie1 and Hongxia Wang3

1Department of Electrical Engineering Northwestern Polytechnical University Xirsquoan 710072 China2State Key Laboratory of Electrical Insulation and Power Equipment Xirsquoan Jiaotong University Xirsquoan 710049 China3China Aero-Polytechnology Establishment Beijing 100028 China

Correspondence should be addressed to Weilin Li liweilin907126com

Received 28 July 2015 Accepted 10 March 2016

Academic Editor Christopher J Damaren

Copyright copy 2016 Weilin Li et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Voltage decrease and power loss in distribution lines of aircraft electric power system are harmful to the normal operation ofelectrical equipment andmay even threaten the safety of aircraftThis study investigates how the gap distance (the distance betweenaircraft cables and aircraft skin) and voltage frequency (variable frequency power supplywill be adopted for next generation aircraft)will affect the impedance of aircraft cables To be more precise the forming mechanism of cable resistance and inductance isillustrated in detail and their changing trends with frequency and gap distance are analyzed with the help of electromagnetictheoretical analysis An aircraft cable simulation model is built with Maxwell 2D and the simulation results are consistent withthe conclusions drawn from the theoretical analysis The changing trends of the four core parameters of interest are analyzedresistance inductance reactance and impedance The research results can be used as reference for the applications in VariableSpeed Variable Frequency (VSVF) aircraft electric power system

1 Introduction

VSVF (Variable Speed Variable Frequency) system is nowunder consideration for modern aircraft electric power sys-tem in order to replace CSCF (Constant Speed ConstantFrequency) system due to the fact that it is simpler and moreenergy-efficient and has higher power density [1] Howeverthe use of VSVF system also proposes new challenges such asthe voltage decrease and power loss caused by aircraft cableimpedance

An aircraft cable can be representedwith series connectedresistor and inductor when alternating current flows throughitThe cablersquos resistance and inductancewill not keep constantbut vary due to various factors amongwhich the gap distanceand the voltage frequency matter the most

Nowadays in China data of aircraft cable impedanceand current-carrying capacity used is still determined byHB5795-82 released in 1982 [2] However the data obtainedat 400Hz at that time is not so accurate due to the poorequipment and backward measurement method Moreoverthis industrial standard needs to be expanded as the voltagefrequency in VSVF system is variable

Literatures can be found which analyze or calculate theresistance and inductance of a straight conductor References[3 4] present calculation of total inductance of a straightconductor with direct current (DC) using the Biot-Savartlaw Reference [5] proposes a method to calculate the ACresistance of a straight cable but the inductance is neglectedExperimental study of skin effect which is closely related tovoltage frequency is displayed in [6] The experimental resultcorrectly reflects the change trend of cable resistance andinductance with frequency variation but it lacks theoreticalanalysis In a nutshell problems still exist in the followingaspects

(1) Most papers calculate cable resistance and induc-tance only concerning the condition when DC flowsthrough the conductor [3 4] Other articles study thisissue under AC condition but the conclusion is notsatisfactory

(2) Reference [7] analyzes this problem using a finiteelement magnetic field analysis program but does notsolve the issues completely In addition it is necessaryto popularize themethodwithwhich problems can be

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2016 Article ID 7430293 11 pageshttpdxdoiorg10115520167430293

2 International Journal of Aerospace Engineering

studied by building simulation models because it ismore convenient to change parameters and view thecurrent density and flux density which are not easy toachieve in practical experiments

(3) None of the references above studies how the exter-nal electromagnetic environment will influence theresistance and inductance of transmission lines Forexample the aircraft skin has great impact on aircraftcable impedance More attention should be paid inthis area

Thus it becomes necessary to further study the impe-dance characteristic of aircraft cables

Great efforts have been done in this paperThe impedancecharacteristic of an aircraft cable when AC flows throughit consists of four relations resistance versus frequencyinductance versus frequency resistance versus gap distance(the distance between aircraft cables and aircraft skin) andinductance versus gap distance Change trends of cable resis-tance and inductance with frequency and gap distance areanalyzed based on electromagnetic theory Some derivationsbased on fundamental theory are used An aircraft cablesimulation model is built using Maxwell 2D a product ofANSYS Corporation Simulation results are provided in bothelectromagnetic field graphs and data reports Consistentconclusions are drawn from the two analytical approachesabove In this study the voltage frequency varies within therange of 360Hz to 800Hz According to HB5795-82 the gapdistance ranges from 119903

0(the cablersquos radius) to 110mm The

gap distance is measured from the center of the cable to thesurface of the aircraft skin whichmeans the cable clings to theaircraft skinwhen the gap distance equals the cablersquos radius 119903

0

2 Analysis Based on Electromagnetic Theory

21 Resistance Analysis It is well known that a cablersquos ACresistance is larger than its DC resistanceThis is due to threereasons skin effect proximity effect and external electro-magnetic environment [8] Proximity effect is a phenomenonthat a conductor carrying a high-frequency current inducescopper loss in an adjacent conductor [9] This means at leasttwo wires are required when referring to proximity effect Asto single cable studied in this paper proximity effect does notexist

Skin effect is the phenomenon that AC tends to flowmainly at the surface of a conductor which is different fromdistributing uniformly throughout the cross section of theconductor in the case of DC as shown in Figure 1 Higherfrequency will lead to smaller skin depth The skin effectwill reduce the effective cross-sectional area of the cables andincrease the resistance [10] It should be noted that the ACcurrent density at the center of the cable may not necessarilybe zero In fact the current density at the surface of the cableis only a little larger than that at the center since voltagefrequency used inVSVF system is only several hundred hertz

The AC flowing through a cable induces magnetic fieldwhich generates eddy current in aircraft skin and the eddycurrent causes power losses According to the law of con-servation of energy these losses must come from the power

DC AC

Skin depth

Current density

R

Current density

RCurrent is uniformly distributed

throughout the conductorCurrent is concentrated near thesurface and decays exponentially

towards the center

Figure 1 Comparison between DC and AC distribution in aconductor

systemThis is equivalent to adding an extra resistor based onthe cablersquos original resistance Shorter gap distancewill lead tolarger eddy current And larger eddy current leads to largeradditional resistor This phenomenon can also be explainedfrom amicroscopic point of viewThemagnetic field inducedby eddy current exerts Lorentz force upon electrons in thecable and thus ldquopushesrdquo the current to the top of or ldquopullsrdquo thecurrent to the bottom of the cable This also causes reductionof effective cross-sectional area of the cables and incrementof resistance This point will be discussed in more detail withthe simulation results in the following section

22 Inductance Analysis Inductance is related to self-inductance and mutual inductance Self-inductance consistsof external inductance and internal inductance Externalinductance derives from magnetic flux outside the cable dueto the total current Here we call the current in the cable theldquototal currentrdquo with the purpose of distinguishing it from theldquoportion currentrdquo which is bound up with internal induc-tance External inductance does not change as frequencyvaries because it only depends on cablersquos geometry Internalinductance is related to flux developed by just a portionnot total of the current inside the cable [11] Contrary toexternal inductance frequency variation has an impact oninternal inductance Owing to skin effect higher frequencyresults in less current near the center of the cable and theinternal inductance decreases In extreme cases the internalinductance of a cable would vanish if the frequency were highenough In this case there is no current in the cable and thetotal current flows at the surface of the conductor

Next we will analyze how the gap distance influencescable inductance A simplemodel as shown in Figure 2 is builtfor explanation In this model DC flows through the cableinstead of AC since frequency is no longer considered Thecable has a radius of 119903

0and carries a current 119868 The rectangle

with dotted line at the bottom of the model represents theaircraft skin and the gap distance is 119889

International Journal of Aerospace Engineering 3

I

l

dr

r

d

r0

dS = ldr

Figure 2 A simplified model showing how the gap distanceinfluences the inductance

The following expression can be derived according toAmperersquos circuital law that themagnetomotive force around aclosed path is equal to the total current enclosed by the path

∮

119871=2120587119903

119861 sdot 119889119903 = 1205830sdot sum

119871

119868119894= 1205830sdot 119868 (1)

where 119861 is the flux density 1205830is the permeability of vacuum

and 119903 is the distance between the cable and elementary areawhose width is 119889119903

The DC induces steady magnetic field and so there is

119861 sdot 2120587119903 = 1205830sdot 119868 997904rArr 119861 =

1205830119868

2120587119903

(2)

The elementary flux denoted by 119889Φ is given by

119889Φ = 119861 sdot 119889119878 =

1205830119868

2120587119903

sdot 119897 sdot 119889119903 (3)

where 119897 is the length of the cableTherefore the total flux Φ is

Φ = int119889Φ = int

119889minus1199030

1199030

1205830119868

2120587119903

sdot 119897 119889119903 =

1205830119868119897

2120587

ln(119889 minus 1199030

1199030

) (4)

Then the self-inductance of the cable 119871 is calculated by

119871 =

Φ

119868

=

1205830119897

2120587

ln(119889 minus 1199030

1199030

) asymp

1205830119897

2120587

ln 1198891199030

(5)

It is noted that the self-inductance of a cable is determinedby the gap distance 119889 cablersquos length 119897 and radius 119903

0[12]

The self-inductance is natural logarithmically increased withincreasing gap distance

Eddy current in aircraft skin also induces magnetic fielda portion of which surrounds the cable and that is the reasonwhy mutual inductance exists Firstly higher frequency leadsto more remarkable skin effect and larger eddy current whichin turn induces strongermagnetic field So it is almost impos-sible to verify the impact of frequency on mutual inductanceSecondly flux generated by eddy current surrounding thecable decreases as gap distance increases Larger gap distanceleads to smaller eddy current and weaker magnetic fieldSo it is easy to conclude that mutual inductance decreasesas the gap distance gets larger The cable current density is

Figure 3 An aircraft cable simulation model built in Maxwell 2D

X

Y

Z

Figure 4 Finite element mesh dissection of the simulation model

ten times larger than the eddy current density in aircraftskin so the self-inductance dominates the total inductanceAbove all a cablersquos inductance gets larger as the gap distanceincreases Due to the complex electromagnetic environmentit is difficult or even impossible to calculate quantitatively Itis better to study it by means of simulation if more preciseresults are expected

3 Simulation Model of Aircraft Cable

In this paper the cable model (as seen in Figure 3) is builtusing the electromagnetic field simulation software-Maxwell2D which uses the accurate finite element analysis (FEA)to solve electromagnetic problems [13] The yellow circularring represents insulated layer The red circles denote coresThe green part depicts air gap among the cores The orangerectangle represents aircraft skin (the aircraft skin is notcompletely shown because it is too large compared with thecable) Figure 3 shows the condition when the cable clings tothe aircraft skin Since it is impossible to make the aircraftcable cling to the aircraft skin completely in the laboratorya gap with a length of 2mm on average is inserted betweenthe cable and the aircraft skin for the purpose of comparingthe simulation results and experimental results both ofwhichwill be illustrated below Voltage frequency and gap distancecan be changed in software settings Figure 4 shows the meshdissection of the simulation model partly because the gridsare too dense


J(A

m2)

12551e + 007

12546e + 007

12542e + 007

12537e + 007

12533e + 007

12528e + 007

12523e + 007

12519e + 007

12514e + 007

12509e + 007

12500e + 007

12505e + 007

12495e + 007

12491e + 007

12486e + 007

12482e + 007

12477e + 007

Figure 5 Current density distribution of the cable at 400Hz andgap distance of 110mm

18265e minus 002

17124e minus 002

15982e minus 002

14841e minus 002

13699e minus 002

12558e minus 002

11416e minus 002

10275e minus 002

91330e minus 003

79915e minus 003

68499e minus 003

57084e minus 003

45668e minus 003

34253e minus 003

22837e minus 003

11422e minus 003

60813e minus 007

B(T

)

Figure 6 Flux density distribution of the cable at 400Hz and gapdistance of 110mm

4 Analysis of Simulation Results

41 Analysis of Electromagnetic Field Graphs Since the volt-age frequency in aircraft power system is rather low and thefrequency range is relatively narrow (from 360Hz to 800Hz)the differences are so subtle that the graphs are almostthe same at each frequency point intuitively when the gapdistance is fixed So this part concentrates on current densitydistribution and magnetic flux density distribution graphs atdifferent gap distances and the voltage frequency is fixed at400Hz Figures 5 and 6 show the current density distributionandmagnetic flux density distribution when the gap distanceis 110mm

It can be seen from Figure 5 that the current distributionis very similar to the situation when skin effect occurs Thecurrent density increases from the center to the surface ofthe cable radially The reason why the difference in current

J(A

m2)

12749e + 007

12722e + 007

12694e + 007

12667e + 007

12640e + 007

12612e + 007

12585e + 007

12558e + 007

12530e + 007

12503e + 007

12448e + 007

12476e + 007

12421e + 007

12394e + 007

12366e + 007

12339e + 007

12312e + 007

Figure 7 Current density distribution at 400Hz and gap distanceof 1199030

J (Am2)

minus14728e+003

minus55555e+004

minus10964e+005

minus16372e+005

minus21780e+005

minus27188e+005

minus38005e+005

minus32596e+005

minus43413e+005

minus48821e+005

minus54229e+005

minus59637e+005

minus65046e+005

minus70454e+005

minus75862e+005

minus81270e+005

minus86678e+005

Figure 8 Eddy current density distribution in the aircraft skin at400Hz and gap distance of 119903

0

density is not significant is that 400Hz is rather low comparedwith radio frequency which is always higher than 1MHz

Amperersquos circuital law can be used to analyze Figure 6The magnetic field is weakest at the center of the cable whereit contains least current and is strongest at the surface whereit surrounds the total current Beyond the surface the fluxdensity decreases as the integration path gets longer whilethe current that the path encloses remains the same (the totalcurrent)

Figure 7 shows the current distribution when the cableclings to the aircraft skin The eddy current distribution inthe aircraft skin as seen in Figure 8 is also displayed

Owing to the eddy current in the aircraft skin Figure 7differs from Figure 5 obviously The current density is largestat the top of the cable and decreases vertically to the bottomof the cable This phenomenon is not obvious when the gapdistance is 110mm as depicted in Figure 5 The reason is that110mm is much larger than the cablersquos radius 119903

0 which is less

than 3mm and the eddy current in the aircraft skin is so lowthat the eddy effect is negligible In fact the current distribu-tion is always influenced by the aircraft skin more or less

Minus current density in aircraft skin as shown in Fig-ure 8 means the eddy current flows in the opposite directioncompared with the cable current It is easy to understand that


(moves vertically inward)

Eddy current in the aircraft skin(flows vertically inward)

FLorentz

Beddy current

eminus

Figure 9The effect of aircraft skin on the cable current distribution

19351e minus 002

18142e minus 002

16932e minus 002

15723e minus 002

14513e minus 002

13304e minus 002

12094e minus 002

10885e minus 002

96756e minus 003

84661e minus 003

72567e minus 003

60473e minus 003

48378e minus 003

36284e minus 003

24189e minus 003

12095e minus 003

47834e minus 008

B(T

)

Figure 10 Flux density distribution at 400Hz and gap distance of1199030

the closer the cable to the aircraft skin the larger the eddycurrent density

Figure 9 explains how the aircraft skin influences thedistribution of the cable current According to the softwaresettings the cable current is positive namely vertical to thepaper outward and that means the current carriers-electronsmove vertical to the paper inward Figure 8 implies thatthe eddy current is negative inducing magnetic field whichexerts straight up force on the electrons according to Lorentzforce law As a result the current flows as if it is ldquopushedrdquoto the top of the cable Larger gap distance leads to weakermagnetic field and less Lorentz force And the cable currentdistributionwill bemore likely the same as Figure 5 Differentcurrent density means different effective cross-sectional areaof the cable Shorter gap distance results in less effective cross-sectional area and larger resistance

The flux density distribution under this condition isshown in Figure 10 Eddy current also makes the flux densitydistributed unsymmetrically compared with Figure 6 Theblue part no longer locates at the exact center of the cable as ifit is also ldquopushedrdquo by the aircraft skin Special attention shouldbe paid that the maximum flux density locates at the bottomof the cable where the current density is the lowest As shownin Figure 10 the color is darker at the bottom of the cablethan that at the top of it From Figures 7 and 8 we can see thatthe difference between the maximum and minimum currentdensity in the cable is 00437 times 107 Am2 which is only half ofthe largest eddy current density as high as 86678 times 105 Am2

350 400 450 500 550 600 650 700 750 800Frequency (Hz)

270

275

280

285

290

295

300

305Ansoft LLC Simulation resistance

Resis

tanc

e(m

Ohm

)

Figure 11 Resistance versus frequency curve at gap distance of 1199030

(mOhmm)

and the eddy effect should not be neglected Both the cablecurrent and the eddy current generate rightward magneticfield at the bottom of the cable and that is why minimumcurrent density corresponds to maximum flux density

There are two points that need to be further explainedFirstly the current excitationrsquos initial phase is 0 and allthe simulation graphs are derived at this moment whichmeans different current and flux density distribution willbe obtained if other phases are chosen when viewing thesimulation results Secondly as illustrated before the graphsare almost the same at each frequency point intuitively whenthe gap distance is fixed For example when the cable clingsto the aircraft skin and the frequency is 800Hz anothercurrent density distribution graph can be obtained Thisgraph is very similar to Figure 7 which is obtained whenthe cable clings to the aircraft skin and the frequency is400HzTheonly difference between the two graphs is that thesame color in the legends represents different current densityHowever these two points above will not affect the resultsof the research For example no matter what direction theeddy current is namely whether the aircraft skin ldquopushesrdquo orldquopullsrdquo the cable current effective cross-sectional area of thecable decreases and resistance increases Current distributionaffects resistance and flux density influences inductanceCable impedance is a result of comprehensive effect of allthese factors mentioned above

42 Analysis of Simulation Data The simulation results canbe viewed in a simpler way When the cable clings to the air-craft skin resistance increases and inductance decreases withhigher frequency as shown in Figures 11 and 12The resistanceand inductance data at different gap distances can be obtainedby changing the simulation model In fact the change trendsof resistance and inductance as frequency increases at othergap distances are the same as the condition when the cableclings to the aircraft skin All the simulation data underdifferent conditions (different frequencies and different gapdistances) is shown in Figures 13 and 14 The resistance andinductance of 1000 meters of the cable are derived by simplymultiplying 1000 to the data obtained from simulation whichcalculates one meter of the model using FEA by default


350 400 450 500 550 600 650 700 750 800450460470480490500510520530540

Ansoft LLC Simulation inductance

Frequency (Hz)

Indu

ctan

ce (n

H)

Figure 12 Inductance versus frequency curve at gap distance of 1199030

(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)

Resistance simulation results

(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0

Figure 13 Resistance simulation data (Ωkm)

Same conclusions can be drawn from Figures 13 and14 The resistance of aircraft cables increases as a result ofvoltage frequency increases and gap distance decreases Theinductance of aircraft cables increases as a result of voltagefrequency decreases and gap distance increases

5 Impedance Characteristics ofBunched Wires

In order to make full use of the limited space inside the cabinand to install the electric wires easily wires on the aircraft aregenerally laid bunched together There is no doubt that theimpedance of wires transmitting electric power will changewhen thewires laid pattern changes from single and separatedinto multiple and bunched To ensure the safe operation ofthe wire and to guarantee that the electrical equipment willnot work improperly as the voltage drop on the wire is too

350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)

Inductance simulation results

Frequency (Hz)

110mm75mm

50mm30mmr0

Figure 14 Inductance simulation data (mHkm)

T1

T2

T3

T4T5

T6

T7

Figure 15 The basic model of bunched wires

large it is necessary to study the impedance characteristics ofthe bunched laid wires

The basic model of bunched laid wires is shown inFigure 15 and the seven wires are named T1 to T7 separatelyThe factor influencing the wirersquos impedance under test is thecurrent amplitude and phase Different wire diameter meansthe amplitude of the current flowing through the wire isdifferent Besides when multiple wires are bunched togetherthe core wire T1 of the bunch is affected most severely bythe neighborhood wires mutual inductance and proximityeffect and its impedance change is larger compared to beinglaid alone Therefore this paper studies how the core wirersquosimpedance of bunched laid wires changes when the externalwires diameter and phase of current are different

There are five main laid patterns of the bunched wires forone main-generator (setting the frequency at 400Hz)

The first type the seven wires diameters are equal to eachother and the current amplitude and phase are also the samewhose amplitudes are all 10 V which is shown in Figure 15


T1

T2

T3

T4T5

T6

T7

Figure 16 The second laid pattern

T1

T2

T3

T4T5

T6

T7

Figure 17 The third laid pattern

T1

T2

T3

T4T5

T6

T7

Figure 18 The fourth laid pattern

The second type the diameter from T2 to T7 is smallerthanT1 and the current flowing through them is 5A whereasthe current of T1 is 10 A and every wirersquos initial phase is 0degree which is shown in Figure 16

The third type the diameter from T2 to T7 is greater thanT1 and the current flowing through them is 20A whereas thecurrent of T1 is 10 A and every wirersquos initial phase is 0 degreewhich is shown in Figure 17

The fourth type T3 and T6 have the same diameter asT1 and the three wiresrsquo current is 10 A whereas T2 and T5have greater diameter than T1 whose current is 20A and thediameter of T4 and T7 is smaller than T1 with 5A currentflowing through them shown in Figure 18 And every wirersquosinitial phase is 0 degree

A

A

A

BB

C

C

Figure 19 The fifth laid pattern

Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750

Time (ms)Name X Ym1m2

52000 0036956250 141421

Name Delta(X) Delta(Y) Slope(Y) InvSlope(Y)d(m1 m2) 04250 141053 331888 00301

VM1V times 250

AM1Iimported

imported

Figure 20 Voltage and current waveforms obtained by cosimula-tion

The fifth type the seven wires diameters are equal toeach other and the current flowing through them is 10VTo maximize the symmetry A phase electric is connected toT1 T2 and T5 B phase electric is connected to T3 and T6and C phase electric is connected to T4 and T7 as shown inFigure 19

Figure 20 shows the voltage and current waveforms of thestudied wire obtained by cosimulation

Comparing the impedance data of the first three types itcan be found that the core wirersquos impedance value increaseswith the external wires current amplitude increasing Thisis because the proximity effect and the mutual inductionbetween the core wire and the external wires increase whenthe external wires current amplitude increasesThe proximityeffect makes the core wire resistance increase and themutualinduction makes the cores wire reactance increase so thetotal impedance value of the core wire increases

As for the fourth type even though the average currenton each wire is equal to the first one the wire diameter andthe current flowing through the wires is asymmetric makingthe voltage drop on wire T1 largest so the impedance value ofT1 is largest


J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)

Figure 21 The current density and the magnetic field intensity distribution on wire T1 under the first laid pattern

J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)

Figure 22 The current density and the magnetic field intensity distribution on wire T1 under the fourth laid pattern

Next the current density and the magnetic field intensitydistribution on wire T1 under the first and the fourth laidpatterns are studied

As can be seen from Figure 21 the current densitydistribution on wire T1 is uniform when the current withinthe external wires is the same as the current of the core wireand this is because the proximity effects from external wirescancel each other whereas external wires present that thecurrent density is small near the side of the core wire andlarge away from the side of the core wire In Figure 22 thecurrent density distribution onwire T1 appears not uniformlycompared with that in Figure 21 and this is because thecurrent in T2 and T5 is larger than the current in T1 whereasthe current in T4 and T7 is smaller than that in T1 hencethe proximity effect is significant where T1 is close to T2and T5 making the current density become smaller and theproximity effect is weak where T1 is close to T4 and T7 whichmakes the current density relatively large and the equivalentcross-sectional area which the current in T1 flows throughdecreases so the resistance of wire T1 increases

Themagnetic field intensity distribution on wire T1 is thesame as the corresponding current density distribution in thefirst and fourth types separately but the flux on the crosssection of wire T1 in the fourth type is much larger than thatin the first type so the reactance value of wire T1 in the fourthtype is larger compared with that in the first type

Comparing the data in the first type with the data in thefifth type in Table 1 it can be seen that the impedance of wireT1 being laid three-phase symmetrically is much smaller thanthat laid bunched together when wires are flowing throughthe same phase current and the impedance of T1 in the fifthtype is even smaller than the impedance of T1 in the secondtype From the above analysis of the two wiresrsquo impedancematrix in the modeling section it can be learned that ifthree-phase symmetric current flows through the externalwires the synthetic voltage drop on wire T1 will be weakenedgreatly making the impedance value of the core wire T1 least

This finding can be viewed as useful reference for aero-nautical engineering To ensure the safe operation of thewire in bunched laid wires and to reduce voltage drop and


V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor

Current and voltageacquisition

Dataprocessing

Aerial

Isolatingtransformer

A

(aluminium alloy)

Adjustableload

cable (30m)2mm aircraft skin

Figure 23 Laboratory experiment setup

Table 1 Impedance of the core wire T1

Laid patterns 119885 (Ωkm) 119877 (Ωkm) 119883 (Ωkm)I 16051 14101 15989II 9341 12870 9251III 29225 18350 29167IV 52015 45695 51813V 3090 11735 2858

power loss in distribution lines we should follow these rulesif the external wires can be laid three-phase symmetricallythey cannot be laid bunched together if the external wiresflow through the same phase current When it has to belaid bunched together the diameter of the external wiresshould be smaller than that of the core wire to weaken theinfluence of proximity effect on the core wire in bunchedwires And external wires with different diameter are avoidedbeing bunched laid together

6 Comparison between SimulationResults and Experimental Results

Impedance measurement experiment on aircraft cables wasconducted in laboratory by using spectral analysis method[14 15] for 30m of the aircraft cable based on which thesimulation model is built The experimental setup is shownin Figure 23

The current flows through contactor current transduceraircraft cables adjustable load and aircraft skin and groundsuccessively A filter capacitor is connected in parallel withthe aircraft cable with the purpose of smoothing harmonicwaves Overcurrent can be avoided owing to the adjustableload Aircraft cables are laid above the aircraft skin with thegap distance ranging from the cablersquos radius 119903

0to 110mm

The ammeter and voltmeter imply that the current data andvoltage data are both needed including each amplitude andphase The data is not acquired using actual ammeter andvoltmeter which are too inaccurate The current is measured

350 400 450 500 550 600 650 700 750 800

Resistance data from experiment

Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23

Figure 24 Resistance data from experiment (Ωkm)

using a current transducer produced by LEM Company andconverted into a voltage signal with a precise resistance Boththe converted voltage signal and the voltage across the mea-sured aircraft cable are collected at a sampling rate as high as200 ks using GEN7t high-speed data acquisition equipmentHBM Corporation [16] Then the data is processed by com-puter program to calculate the resistance and inductance ofthe aircraft cableThe results have been converted from roomtemperature to 20∘C and are shown in Figures 24 and 25

Same conclusion as illustrated in Section 4 can be drawnfrom the laboratory test data This finding can be viewed asuseful reference for aeronautical engineering For exampleit is better to lay the aircraft cables clinging to the aircraftskin to reduce the cross talk [17] but the resistance is largestunder this condition and this means more power loss Even


350 400 450 500 550 600 650 700 750 800

1

11Inductance data from experiment

06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0

Figure 25 Inductance data from experiment (mHkm)

if the gap distance is no longer considered the resistance at800Hz is nearly eighteen percent larger than that at 360Hzand it implies more power loss as well However shorter gapdistance and higher frequency become advantages when itcomes to the inductance because the inductance is less underthese conditions As is known to all inductance of a cablecauses phase lag of the current and that is the reason whyreactive power exists Less inductance leads to lower reactivepower and the generator could be designed smaller andlighter Compromise has to be reached when laying aircraftcables on aircraft

It should be noticed that although the trend of thesimulation data shows good consistency with the laboratorytest data the absolute value of the inductance differs a lot Forinstance the error is as large as 20 when the cable clings tothe aircraft skin All these are due to reasons as follows

(1) Due to business secret protection and other reasonsit is impossible to get accurate values of the sizes andmaterials of the cables and aircraft skin which areextremely important in modeling process Relativepermittivity relative permeability bulk conductivitydielectric loss tangent and magnetic loss tangent areall essential parametersThemodel used in this paperis constructed based on authorrsquos experience and datasearched from the Internet

(2) The simulation model is not accurate enough Forexample parallel nickel-clad copper cores are usedinstead of stranded conductors for convenience ofmodeling And also actual aircraft cables consistof armors sheaths gaskets and other componentsexcept for conductors and insulations which make upthe simulation model roughly [17 18]

(3) The model simulates the resistance and inductanceof cables that are arranged straightly but it is hardto realize in an area-limited laboratory Thus thesimulation data cannot take the proximity effect andother electromagnetic interferences into account

7 Data Analysis

In fact impedance measurement experiments are carriedout on six types of cables which are denoted by A B C D Eand F respectively and 119903A gt 119903B gt 119903C gt 119903D gt 119903E gt 119903F (119903 is theradius of the cable) The simulation model built in Section 3is based on B In this section four parameters of interestare analyzed resistance 119877 inductance 119871 reactance 119883 andimpedance 119885

For each type of cables as illustrated before 119877 increasesas a result of voltage frequency increases and gap distancedecreases And the larger 119903 the smaller the absolute value of119877 when voltage frequency and gap distance are the same 119877increases more rapidly when the cable clings to the aircraftskin compared with other gap distances

For each type of cables as illustrated before 119871 increasesas a result of voltage frequency decreases and gap distanceincreases And the larger 119903 the smaller the absolute value of119871 when voltage frequency and gap distance are the same 119871decreases more rapidly when the cable clings to the aircraftskin compared with other gap distances

From the equation 119883 = 120596119871 = 2120587119891119871 we knowthat 119883 is determined by both voltage frequency 119891 and 119871Although inductance decreases with frequency increasing119883 still increases with frequency increasing according tothe calculation results This means increasing frequency hasgreater effect on 119883 than decreasing 119871 And the larger 119903 thesmaller the absolute value of 119883 when voltage frequency andgap distance are the same

From the equation 119885 = radic1198772 + 1198832 we know that 119885 isdetermined by both 119877 and 119883 When the voltage frequencyand gap distance are the same both of 119877 and 119883 becomesmaller as 119903 increases so 119885 becomes smaller as 119903 increasesAnd for a certain type of cable both 119877 and 119883 get largeras frequency increases so 119885 becomes larger as frequencyincreases However the influence of gap distance on 119885 is notas simple because 119877 and 119883 follow different change trends asgap distance increases For cables with smaller 119903 like D E andF 119877 is much larger than 119883 (119877 ≫ 119883) and 119877 dominates 119883so how the gap distance affects 119885 depends on how the gapdistance affects 119877 while for cables with larger 119903 like A Band C 119883 is not much less than 119877 or even larger than thatso how the gap distance affects 119885 depends on how the gapdistance affects both 119877 and 119883 For A and B 119885 increases asthe gap distance increases For D E and F119885 decreases as thegap distance increases For C119885 decreases as the gap distanceincreases in low-frequency range and 119885 increases as the gapdistance increases in high-frequency range

8 Conclusions

This finding of this paper can be viewed as useful referencefor aeronautical engineering To reduce voltage decrease and


power loss in distribution lines in the process of impedancecalculation for aircraft electrical power grid cables with largeradius should be placed near the aircraft skinwhile thosewithsmaller radius should be placed as far away from the aircraftskin as possible

The above analysis only takes grid impedance intoaccount and a compromise formula may have to be adoptedunder comprehensive considerations For example it is betterto lay aircraft cables clinging to aircraft skin to reduce thecross talk but the resistance is largest under this conditionand this means more power loss Even if the gap distanceis no longer considered the resistance at 800Hz is largerthan that at 360Hz and it implies more power loss as wellHowever shorter gap distance and higher frequency becomeadvantages when it comes to the inductance because theinductance is less under these conditions Less inductanceleads to lower reactive power and the generator could bedesigned smaller and lighter Compromise has to be reachedwhen laying cables on aircrafts

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is supported by State Key Laboratory of ElectricalInsulation and Power Equipment (Grant no EIPE14203)the Shaanxi Key Laboratory of Small and Special ElectricalMachines and Drive Technology (Grant no 2013SSJ1001)State Key Laboratory of Alternate Electrical Power Systemwith Renewable Energy Sources (Grant no LAPS15018) theFundamental Research Funds for the Central Universities(Grant no 3102015ZY052) and the National Nature ScienceFoundation of China (Grant no 51407144)

References

[1] G H Cheng ldquoCurrent situation and development of electricalpower system on large civil aircraftsrdquo Civil Aircraft Design andResearch vol 4 pp 2ndash4 2008

[2] HB5795-82 Current-Carrying Capacity of Aircraft Cables ThirdMinistry of Machinery Industry of Peoplersquos Republic of ChinaBeijing China 1982

[3] P Priyanka ldquoCalculation of total inductance of a straightconductor of finite lengthrdquo Physics Education pp 193ndash199 2009

[4] M Vitelli ldquoCalculation of per-unit-length resistance and inter-nal inductance in 2-D skin-effect current driven problemsrdquoIEEE Transactions on Electromagnetic Compatibility vol 44 no4 pp 529ndash538 2002

[5] X Z Wu ldquoResistance calculation of AC transmission linesrdquoElectric Wire and Cable vol 5 pp 2ndash6 1998

[6] B Z Lu and Z C Liu ldquoExperimental study of skin effectrdquoPhysics Examination and Testing vol 4 pp 16ndash17 2004

[7] E J Woods ldquoHigh-frequency characterization of power wiringfor modelingrdquo in Proceedings of the IEEE International ElectricMachines and Drives Conference (IEMDC rsquo99) pp 722ndash724IEEE Seattle Wash USA May 1999

[8] W Li W Liu S Liu R Ji and X Zhang ldquoImpedance character-istics study of three-phase aircraft power wiresrdquo Measurementvol 78 pp 235ndash244 2016

[9] R W Erickson and D Maksimovic Fundamentals of PowerElectronics Kluwer Academic Publishers New York NY USA2nd edition 2001

[10] W Li A Monti and F Ponci ldquoFault detection and classificationin medium voltage dc shipboard power systems with waveletsand artificial neural networksrdquo IEEE Transactions on Instru-mentation andMeasurement vol 63 no 11 pp 2651ndash2665 2014

[11] X D Liang A C Qiu and C X Sun China Electrical Engineer-ing Cannon China Electric Power Press Beijing China 2009

[12] Inductance of a Straight Conductor httpnpteliitmacincoursesWebcourse-contentsIIT-KANPURpower-systemchap-ter 11 4html

[13] B Zhao and H L Zhang Engineering Application of Ansoft12 inElectromagnetic Field ChinaWater Power Press Beijing China2011

[14] F Correa Alegria and A Cruz Serra ldquoComparison between twodigital methods for active power measurementrdquo in Proceedingsof the IEEE International Conference on Industrial Technology(ICIT rsquo10) pp 211ndash216 IEEE Vi a del Mar Chile March 2010

[15] T Y Liu Study on impedance measurement methods of aircraftcables [PhD dissertation] Northwestern Polytechnical Univer-sity (NWPU) Xirsquoan China 2011

[16] W Li M Ferdowsi M Stevic A Monti and F Ponci ldquoCosim-ulation for smart grid communicationsrdquo IEEE Transactions onIndustrial Informatics vol 10 no 4 pp 2374ndash2384 2014

[17] L G Ruan L Cai Q Xiao and L Wang ldquoAnalysis of crosstalkamong aircraft wiresrdquo Civil Aircraft Design and Research vol 4pp 16ndash19 2008

[18] J B Li C Lin and J H LiManual on Electrical Cables SelectionChemical Industry Press Beijing China 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



studied by building simulation models because it ismore convenient to change parameters and view thecurrent density and flux density which are not easy toachieve in practical experiments

(3) None of the references above studies how the exter-nal electromagnetic environment will influence theresistance and inductance of transmission lines Forexample the aircraft skin has great impact on aircraftcable impedance More attention should be paid inthis area

Thus it becomes necessary to further study the impe-dance characteristic of aircraft cables

Great efforts have been done in this paperThe impedancecharacteristic of an aircraft cable when AC flows throughit consists of four relations resistance versus frequencyinductance versus frequency resistance versus gap distance(the distance between aircraft cables and aircraft skin) andinductance versus gap distance Change trends of cable resis-tance and inductance with frequency and gap distance areanalyzed based on electromagnetic theory Some derivationsbased on fundamental theory are used An aircraft cablesimulation model is built using Maxwell 2D a product ofANSYS Corporation Simulation results are provided in bothelectromagnetic field graphs and data reports Consistentconclusions are drawn from the two analytical approachesabove In this study the voltage frequency varies within therange of 360Hz to 800Hz According to HB5795-82 the gapdistance ranges from 119903

0(the cablersquos radius) to 110mm The

gap distance is measured from the center of the cable to thesurface of the aircraft skin whichmeans the cable clings to theaircraft skinwhen the gap distance equals the cablersquos radius 119903

0

2 Analysis Based on Electromagnetic Theory

21 Resistance Analysis It is well known that a cablersquos ACresistance is larger than its DC resistanceThis is due to threereasons skin effect proximity effect and external electro-magnetic environment [8] Proximity effect is a phenomenonthat a conductor carrying a high-frequency current inducescopper loss in an adjacent conductor [9] This means at leasttwo wires are required when referring to proximity effect Asto single cable studied in this paper proximity effect does notexist

Skin effect is the phenomenon that AC tends to flowmainly at the surface of a conductor which is different fromdistributing uniformly throughout the cross section of theconductor in the case of DC as shown in Figure 1 Higherfrequency will lead to smaller skin depth The skin effectwill reduce the effective cross-sectional area of the cables andincrease the resistance [10] It should be noted that the ACcurrent density at the center of the cable may not necessarilybe zero In fact the current density at the surface of the cableis only a little larger than that at the center since voltagefrequency used inVSVF system is only several hundred hertz

The AC flowing through a cable induces magnetic fieldwhich generates eddy current in aircraft skin and the eddycurrent causes power losses According to the law of con-servation of energy these losses must come from the power

DC AC

Skin depth

Current density

R

Current density

RCurrent is uniformly distributed

throughout the conductorCurrent is concentrated near thesurface and decays exponentially

towards the center

Figure 1 Comparison between DC and AC distribution in aconductor

systemThis is equivalent to adding an extra resistor based onthe cablersquos original resistance Shorter gap distancewill lead tolarger eddy current And larger eddy current leads to largeradditional resistor This phenomenon can also be explainedfrom amicroscopic point of viewThemagnetic field inducedby eddy current exerts Lorentz force upon electrons in thecable and thus ldquopushesrdquo the current to the top of or ldquopullsrdquo thecurrent to the bottom of the cable This also causes reductionof effective cross-sectional area of the cables and incrementof resistance This point will be discussed in more detail withthe simulation results in the following section

22 Inductance Analysis Inductance is related to self-inductance and mutual inductance Self-inductance consistsof external inductance and internal inductance Externalinductance derives from magnetic flux outside the cable dueto the total current Here we call the current in the cable theldquototal currentrdquo with the purpose of distinguishing it from theldquoportion currentrdquo which is bound up with internal induc-tance External inductance does not change as frequencyvaries because it only depends on cablersquos geometry Internalinductance is related to flux developed by just a portionnot total of the current inside the cable [11] Contrary toexternal inductance frequency variation has an impact oninternal inductance Owing to skin effect higher frequencyresults in less current near the center of the cable and theinternal inductance decreases In extreme cases the internalinductance of a cable would vanish if the frequency were highenough In this case there is no current in the cable and thetotal current flows at the surface of the conductor

Next we will analyze how the gap distance influencescable inductance A simplemodel as shown in Figure 2 is builtfor explanation In this model DC flows through the cableinstead of AC since frequency is no longer considered Thecable has a radius of 119903

0and carries a current 119868 The rectangle

with dotted line at the bottom of the model represents theaircraft skin and the gap distance is 119889


I

l

dr

r

d

r0

dS = ldr



∮

119871=2120587119903

119861 sdot 119889119903 = 1205830sdot sum

119871

119868119894= 1205830sdot 119868 (1)




119861 sdot 2120587119903 = 1205830sdot 119868 997904rArr 119861 =

1205830119868

2120587119903

(2)


119889Φ = 119861 sdot 119889119878 =

1205830119868

2120587119903

sdot 119897 sdot 119889119903 (3)



119889minus1199030

1199030

1205830119868

2120587119903

sdot 119897 119889119903 =

1205830119868119897

2120587

ln(119889 minus 1199030

1199030

) (4)


119871 =

Φ

119868

=

1205830119897

2120587

ln(119889 minus 1199030

1199030

) asymp

1205830119897

2120587

ln 1198891199030

(5)


0[12]




X

Y

Z






J(A

m2)

12551e + 007

12546e + 007

12542e + 007

12537e + 007

12533e + 007

12528e + 007

12523e + 007

12519e + 007

12514e + 007

12509e + 007

12500e + 007

12505e + 007

12495e + 007

12491e + 007

12486e + 007

12482e + 007

12477e + 007


18265e minus 002

17124e minus 002

15982e minus 002

14841e minus 002

13699e minus 002

12558e minus 002

11416e minus 002

10275e minus 002

91330e minus 003

79915e minus 003

68499e minus 003

57084e minus 003

45668e minus 003

34253e minus 003

22837e minus 003

11422e minus 003

60813e minus 007

B(T

)





J(A

m2)

12749e + 007

12722e + 007

12694e + 007

12667e + 007

12640e + 007

12612e + 007

12585e + 007

12558e + 007

12530e + 007

12503e + 007

12448e + 007

12476e + 007

12421e + 007

12394e + 007

12366e + 007

12339e + 007

12312e + 007


J (Am2)

minus14728e+003

minus55555e+004

minus10964e+005

minus16372e+005

minus21780e+005

minus27188e+005

minus38005e+005

minus32596e+005

minus43413e+005

minus48821e+005

minus54229e+005

minus59637e+005

minus65046e+005

minus70454e+005

minus75862e+005

minus81270e+005

minus86678e+005


0





0 which is less






FLorentz

Beddy current

eminus


19351e minus 002

18142e minus 002

16932e minus 002

15723e minus 002

14513e minus 002

13304e minus 002

12094e minus 002

10885e minus 002

96756e minus 003

84661e minus 003

72567e minus 003

60473e minus 003

48378e minus 003

36284e minus 003

24189e minus 003

12095e minus 003

47834e minus 008

B(T

)





350 400 450 500 550 600 650 700 750 800Frequency (Hz)

270

275

280

285

290

295

300


Resis

tanc

e(m

Ohm

)


(mOhmm)





350 400 450 500 550 600 650 700 750 800450460470480490500510520530540


Frequency (Hz)

Indu

ctan

ce (n

H)


(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)


(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0





350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)


Frequency (Hz)

110mm75mm

50mm30mmr0


T1

T2

T3

T4T5

T6

T7







T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










I

l

dr

r

d

r0

dS = ldr



∮

119871=2120587119903

119861 sdot 119889119903 = 1205830sdot sum

119871

119868119894= 1205830sdot 119868 (1)




119861 sdot 2120587119903 = 1205830sdot 119868 997904rArr 119861 =

1205830119868

2120587119903

(2)


119889Φ = 119861 sdot 119889119878 =

1205830119868

2120587119903

sdot 119897 sdot 119889119903 (3)



119889minus1199030

1199030

1205830119868

2120587119903

sdot 119897 119889119903 =

1205830119868119897

2120587

ln(119889 minus 1199030

1199030

) (4)


119871 =

Φ

119868

=

1205830119897

2120587

ln(119889 minus 1199030

1199030

) asymp

1205830119897

2120587

ln 1198891199030

(5)


0[12]




X

Y

Z






J(A

m2)

12551e + 007

12546e + 007

12542e + 007

12537e + 007

12533e + 007

12528e + 007

12523e + 007

12519e + 007

12514e + 007

12509e + 007

12500e + 007

12505e + 007

12495e + 007

12491e + 007

12486e + 007

12482e + 007

12477e + 007


18265e minus 002

17124e minus 002

15982e minus 002

14841e minus 002

13699e minus 002

12558e minus 002

11416e minus 002

10275e minus 002

91330e minus 003

79915e minus 003

68499e minus 003

57084e minus 003

45668e minus 003

34253e minus 003

22837e minus 003

11422e minus 003

60813e minus 007

B(T

)





J(A

m2)

12749e + 007

12722e + 007

12694e + 007

12667e + 007

12640e + 007

12612e + 007

12585e + 007

12558e + 007

12530e + 007

12503e + 007

12448e + 007

12476e + 007

12421e + 007

12394e + 007

12366e + 007

12339e + 007

12312e + 007


J (Am2)

minus14728e+003

minus55555e+004

minus10964e+005

minus16372e+005

minus21780e+005

minus27188e+005

minus38005e+005

minus32596e+005

minus43413e+005

minus48821e+005

minus54229e+005

minus59637e+005

minus65046e+005

minus70454e+005

minus75862e+005

minus81270e+005

minus86678e+005


0





0 which is less






FLorentz

Beddy current

eminus


19351e minus 002

18142e minus 002

16932e minus 002

15723e minus 002

14513e minus 002

13304e minus 002

12094e minus 002

10885e minus 002

96756e minus 003

84661e minus 003

72567e minus 003

60473e minus 003

48378e minus 003

36284e minus 003

24189e minus 003

12095e minus 003

47834e minus 008

B(T

)





350 400 450 500 550 600 650 700 750 800Frequency (Hz)

270

275

280

285

290

295

300


Resis

tanc

e(m

Ohm

)


(mOhmm)





350 400 450 500 550 600 650 700 750 800450460470480490500510520530540


Frequency (Hz)

Indu

ctan

ce (n

H)


(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)


(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0





350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)


Frequency (Hz)

110mm75mm

50mm30mmr0


T1

T2

T3

T4T5

T6

T7







T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










J(A

m2)

12551e + 007

12546e + 007

12542e + 007

12537e + 007

12533e + 007

12528e + 007

12523e + 007

12519e + 007

12514e + 007

12509e + 007

12500e + 007

12505e + 007

12495e + 007

12491e + 007

12486e + 007

12482e + 007

12477e + 007


18265e minus 002

17124e minus 002

15982e minus 002

14841e minus 002

13699e minus 002

12558e minus 002

11416e minus 002

10275e minus 002

91330e minus 003

79915e minus 003

68499e minus 003

57084e minus 003

45668e minus 003

34253e minus 003

22837e minus 003

11422e minus 003

60813e minus 007

B(T

)





J(A

m2)

12749e + 007

12722e + 007

12694e + 007

12667e + 007

12640e + 007

12612e + 007

12585e + 007

12558e + 007

12530e + 007

12503e + 007

12448e + 007

12476e + 007

12421e + 007

12394e + 007

12366e + 007

12339e + 007

12312e + 007


J (Am2)

minus14728e+003

minus55555e+004

minus10964e+005

minus16372e+005

minus21780e+005

minus27188e+005

minus38005e+005

minus32596e+005

minus43413e+005

minus48821e+005

minus54229e+005

minus59637e+005

minus65046e+005

minus70454e+005

minus75862e+005

minus81270e+005

minus86678e+005


0





0 which is less






FLorentz

Beddy current

eminus


19351e minus 002

18142e minus 002

16932e minus 002

15723e minus 002

14513e minus 002

13304e minus 002

12094e minus 002

10885e minus 002

96756e minus 003

84661e minus 003

72567e minus 003

60473e minus 003

48378e minus 003

36284e minus 003

24189e minus 003

12095e minus 003

47834e minus 008

B(T

)





350 400 450 500 550 600 650 700 750 800Frequency (Hz)

270

275

280

285

290

295

300


Resis

tanc

e(m

Ohm

)


(mOhmm)





350 400 450 500 550 600 650 700 750 800450460470480490500510520530540


Frequency (Hz)

Indu

ctan

ce (n

H)


(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)


(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0





350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)


Frequency (Hz)

110mm75mm

50mm30mmr0


T1

T2

T3

T4T5

T6

T7







T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












FLorentz

Beddy current

eminus


19351e minus 002

18142e minus 002

16932e minus 002

15723e minus 002

14513e minus 002

13304e minus 002

12094e minus 002

10885e minus 002

96756e minus 003

84661e minus 003

72567e minus 003

60473e minus 003

48378e minus 003

36284e minus 003

24189e minus 003

12095e minus 003

47834e minus 008

B(T

)





350 400 450 500 550 600 650 700 750 800Frequency (Hz)

270

275

280

285

290

295

300


Resis

tanc

e(m

Ohm

)


(mOhmm)





350 400 450 500 550 600 650 700 750 800450460470480490500510520530540


Frequency (Hz)

Indu

ctan

ce (n

H)


(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)


(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0





350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)


Frequency (Hz)

110mm75mm

50mm30mmr0


T1

T2

T3

T4T5

T6

T7







T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










350 400 450 500 550 600 650 700 750 800450460470480490500510520530540


Frequency (Hz)

Indu

ctan

ce (n

H)


(nHm)

350 400 450 500 550 600 650 700 750 800

3

Frequency (Hz)


(Ωkm

)

29

28

27

26

25

24

110mm75mm

50mm30mmr0





350 400 450 500 550 600 650 700 750 800

05

06

07

08

09

1

(mH

km

)


Frequency (Hz)

110mm75mm

50mm30mmr0


T1

T2

T3

T4T5

T6

T7







T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7


T1

T2

T3

T4T5

T6

T7





A

A

A

BB

C

C


Simplorer1

m1m2

XY plot 1

Y1

1250

750

250

minus250

minus750

minus1250

750500250 1000 1250 1500 1750


52000 0036956250 141421


VM1V times 250

AM1Iimported

imported







J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










J(A

m2)

10967e + 006

10872e + 006

10777e + 006

10681e + 006

10586e + 006

10490e + 006

10395e + 006

10299e + 006

10204e + 006

10108e + 006

99176e + 005

10013e + 006

98222e + 005

97267e + 005

96313e + 005

95359e + 005

94404e + 005

13665e minus 003

12890e minus 003

12115e minus 003

11340e minus 003

10564e minus 003

97892e minus 004

90141e minus 004

82389e minus 004

74637e minus 004

66885e minus 004

59134e minus 004

51382e minus 004

43630e minus 004

35878e minus 004

28127e minus 004

20375e minus 004

12623e minus 004

B(T

)


J(A

m2)

16657e + 006

16201e + 006

15746e + 006

15290e + 006

14835e + 006

14379e + 006

13924e + 006

13468e + 006

13013e + 006

12557e + 006

11646e + 006

12102e + 006

11191e + 006

10735e + 006

10279e + 006

98239e + 005

93684e + 005

17288e minus 003

16258e minus 003

15228e minus 003

14198e minus 003

13168e minus 003

12138e minus 003

11108e minus 003

10078e minus 003

90478e minus 004

80177e minus 004

69876e minus 004

59576e minus 004

49275e minus 004

38974e minus 004

28673e minus 004

18373e minus 004

80721e minus 005

B(T

)








V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










V

Powersupplyvoltage

Currenttransducer

Capacitor

Contactor


Dataprocessing

Aerial


A

(aluminium alloy)

Adjustableload









0to 110mm


350 400 450 500 550 600 650 700 750 800


Frequency (Hz)

(Ωkm

)

110mm75mm

50mm30mmr0

32

31

3

29

28

27

26

25

24

23





350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










350 400 450 500 550 600 650 700 750 800

1


06

07

08

09

(mH

km

)

Frequency (Hz)

110mm75mm

50mm30mmr0







7 Data Analysis






8 Conclusions





Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Competing Interests


Acknowledgments


References





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article study on impedance characteristics of

Documents