Research ArticleApplication of Magnetic Coupling Resonant Wireless PowerSupply in a Torque Online Telemetering System of a Rolling Mill

Jinliang Jia and Xiaoqiang Yan

School of Mechanical Engineering University of Science and Technology Beijing Beijing 100083 China

Correspondence should be addressed to Xiaoqiang Yan yanxqustbeducn

Received 25 February 2020 Accepted 29 April 2020 Published 14 May 2020

Academic Editor Franccedilois Vallee

Copyright copy 2020 Jinliang Jia and Xiaoqiang Yan is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

e torque of the main drive system is one of the most important force and energy parameters of the rolling mill and the straintype torque online telemetry system is a practical method for measuring torque parameters e strain gauges and transmitterson the rotating shaft are driven by a high-frequency induction power system eir installation debugging and maintenanceare cumbersome and their very low power transmission efficiency (PTE) has become a challenging problem for onlinetelemetry systems In this paper a magnetic coupling resonant wireless power supply method is utilized to replace the high-frequency induction power supply rough theoretical and experimental research it is concluded that the magneticallycoupled resonant wireless power supply method can realize long-distance power supply overcoming many shortcomings of thehigh-frequency induction power supply system In the laboratory a maximum PTE of 837 is obtained for a transmissiondistance of 50mm Under the influence of environmental factors common for the transmission shaft of a rolling mill the PTEdecreases by 34 but normal operation of the system can be achieved by adjusting the compensation capacitance eproposed system provides a guarantee for a long-term stable power supply on the measured axis of a rolling mill torque onlinetelemetry system

1 Introduction

e main drive torque of a rolling mill is one of the mostimportant force and energy parameters in the rolling pro-cess It not only reflects the load of the main drive systembut also reflects the dynamic property of the torqueerefore online real-time monitoring of the torque signalcan aid in optimizing the rolling schedule maximizing theefficiency of the rolling mill accurately determining faultsand avoiding production accidents making the rolling millsafe efficient and reliable

Presently the domestic online rolling mill torque te-lemetry system mainly depends on imports from the UnitedStates e system consists of the wireless transmission oftorque signals and a high-frequency induction power supplye high import price cumbersome installation and poorafter-sales service have a great impact on the application ofthe system e domestic wireless signal transmission

technology is mature but the field application stability ofhigh-frequency induction power supply technology is poor

After many years of research University of Science andTechnology Beijing has made great progress on a domesticonline remote measuring system for rolling mill torque [1]e proposed magnetically coupled resonant wireless powersupply system replaces the high-frequency induction powersupply system [2] (Figure 1) It eliminates the need for strictadjustment of the installation gap between the static powersupply ring and the rotating ring (3ndash7mm is generally re-quired) enables long-distance misalignment installationeases disassembly of the inner ring on-site (without firstdisassembling the outer ring) and solves many problemsrelated to field installation debugging installation main-tenance and other shortcomings

In recent years magnetically coupled resonant radiopower transmission technology has become a challengingglobal research hotspot e system design topology

HindawiJournal of Electrical and Computer EngineeringVolume 2020 Article ID 8582131 9 pageshttpsdoiorg10115520208582131

structure model establishment and simulation of magneticcoupling resonance wireless power transfer (MCRWPT)technology have been deeply studied and great progress hasbeen made In 2007 the US MITresearch team took the leadin proposingMCRWPTtechnology and successfully lit 60Wlight bulbs with 40 PTE at a 2m distance [3] In 2008 theIntel Seattle Laboratory Research Group achieved 60Wpower transmission within 1m with 70 PTE [4] In 2009Tokyo University of Japan established a functional rela-tionship between the resonant frequency and the relativeposition of the resonant coil and conducted an experimentalstudy [5] In 2011 a Stanford University scientific researchteam theoretically analyzed 10 kW power transmissionwithin 198m [6] In 2013 Florida International Universityfound that the PTE of magnetic resonance coupling indifferent media can be optimized [7] In 2018 YonseiUniversity proposed that an asymmetric coil can improvethe efficiency and the degree of freedom in terms of positionAt transmission distances of 50mm and 300mm they re-alized transmission efficiencies of 96 and 39 respectively[8] South Korea Advanced Institute of Science and Tech-nology designed a T-type ferrite wireless power transmissionsystem and operated the system in an experiment with thetransmission of 205W power and a total efficiency of 71[9]

e difference between the principle of induction cou-pling and magnetic coupling system was examined andanalyzed at South China University of Technology whosework provided a theoretical basis for further optimizing thetwo system models [10] Research at Hebei University ofTechnology showed that impedance matching has a largeinfluence on PTE and output power and their work pro-posed an optimization method for PTE and output power[11] By establishing a T-type equivalent circuit modelTianjin University of Technology obtained the dynamictransmission curve and constraint function of a

transmission system and found the functional relationshipof maximizing PTE [12] From the analysis of a series-parallel equivalent circuit model Southeast Universityconcluded that output power and PTE are closely related tofrequency and the optimal operating frequency was ob-tained through simulation and experimental analysis [13]rough the study of a dual relay wireless power trans-mission system at Southeast University it was concludedthat output power and PTE are the highest when the optimalturn value exists in the receiving coil [14] rough severalparameter circuit models of a transmission system theconditions of maximum load power under different cou-pling conditions were obtained [15] Chongqing Universityused equivalent circuit theory to model and analyze a sys-tem provided the method to calculate the optimal frequencyof PTE and optimal frequency of transmission powerproposed concepts of optimal resonant frequency and anefficiency synchronization factor and obtained the condi-tions of synchronization between PTE and maximum power[16] A parameter dynamic adjustment method based on achaos optimization algorithm proposed by Hunan Uni-versity improved the efficiency of a noncoaxial system coilwhich has significance for the analysis of radio powertransmission systems [17] Research at Hebei Universityfound that the single resonance structure of multisourcecoils can reduce the load voltage change caused by themagnetic field distribution by utilizing the coupling betweenloads [18]

Research institutions for MCRWPT technology transferefficiency and studies of power transfer theory are ampleHowever there is a lack of experience in the developmentand application of engineering practice and equipmentResearch and problem-solving in this area is a challenge Inthe work presented here MCRWPT technology is studied inthe torque telemetry system of a rolling mill to evaluate anengineering application and gain practical experience

2 Theoretical Research

21 SystemComposition MCRWPT technology uses a spaceelectromagnetic field as a medium uses two or more elec-tromagnetic systems with the same resonant frequency andhigh quality factor and realizes wireless power transmissionthrough a magnetic coupling resonant method A high-frequency induction power supply is based on the principleof electromagnetic induction using a high-frequency powersupply to generate a magnetic field with air as a magneticmedium to make an inner and outer loop coil inductionpower supply e installation distance between the innerand outer loop coils must be within several millimeters tosupply normal induction power MCRWPT technologywhich utilizes the magnetic coupling resonant technologycan achieve high-efficiency power transmission with a largerdislocation range of the inner and outer rings and it canfacilitate installation of the rolling mill torque online te-lemetry system

e MCRWPT system consists of four parts a powersupply module an electromagnetic transmitting module anelectromagnetic receiving module and a load module as

1

2

3

45

6 7

Figure 1 Component assembly diagram of the original torquetelemetry system 1-static power ring 2-rotating ring 3-straingauge conductor 4-welded strain gauge 5-system state indicatorlamp 6-flange 7-main control unit

2 Journal of Electrical and Computer Engineering

shown in Figure 2e power supply module is composed ofa rectifier and a high-frequency inverter which providessuitable resonant frequency voltage input for the electro-magnetic transmitting module e electromagnetic trans-mitting module converts a high-frequency input voltage intoa high-frequency magnetic field and strong magneticcoupling occurs between the space electromagnetic field andthe electromagnetic receiving module e electromagneticreceiving module converts magnetic energy into electricenergy and outputs it to the load module through constantvoltage rectification e electromagnetic transmitting andreceiving modules are key parts of the power supply systemFunctionality of the transmitting and receiving modules inthe resonant state ensures the power transmission ere-fore the transmitting and receiving modules are composedof high quality factor resonant coils with identical structuresand parameters and a resonant compensation capacitor Inthe torque telemetry system the transmitter and strain gaugeon the measured axis are used as load modules to consumeenergy To ensure optimal PTE of the system the impedanceat the load end and the internal resistance at the powersupply end are always matched

Cylindrical spiral coils and plane spiral coils as shown inFigure 3 are primarily used [19] e magnetic field in-tensity at the edge of the helical coil is greater than that atthe center e magnetic induction intensity of the planardisc coil decreases from inside to outside and the magneticinduction intensity is the largest at the center of the coile two coil structures have their own characteristics andcan be selected according to application requirements

22 $eoretical Analysis To optimize the power transmis-sion efficiency it is usually necessary to compensate for thecapacitance of the resonant coil to reach the resonant statee compensation circuit is divided into four forms Series-Series (SS) Series-Parallel (SP) Parallel-Parallel (PP) andParallel-Series (PS) as shown in Figure 4 To achieve theresonant state of the system the imaginary part of the totalresistance of the system after capacitance compensation iszero e compensation capacitance of the SP PP and PSstructures is related to the load resistance and only thecompensation capacitance of the receiving and transmitting

terminals of SS structures is independent of the load Be-cause the load resistance of the online torque telemetrysystem varies during its operation an SS structure is chosenfor the capacitance compensation circuit in this paper

Presently there are two main MCRWPT researchmethods coupled mode theory and equivalent circuit the-ory Each research method has its own benefits Coupledmode theory is a mathematical method that describes acomplex coupled system as an energy transmission processof an independent single system from the perspective ofenergy simplifying and clarifying the analysis and calcu-lation Equivalent circuit theory establishes an equivalentcircuit model based on the basic principle of a circuit and theequivalent calculation method which is intuitive and easy tounderstand Depending on the specific parameters of thecircuit the voltage and current changes in the circuit areanalyzed to calculate the PTE and power of the systemelectric energy In this paper equivalent circuit theory isused to study the process of power transmission Itsequivalent circuit model is shown in Figure 5

In Figure 5 US represents high-frequency power supplyexcitation RS represents internal resistance of power supplyR1 represents equivalent resistance of transmitter C1 rep-resents compensation capacitance of transmitter L1 repre-sents transmitting coil L2 represents receiving coil R2represents equivalent resistance of receiver C2 representscompensation capacitance of receiver RL represents loadresistance M represents mutual inductance betweentransmitting coil and receiving coil i1 represents loopcurrent of transmitter and i2 represents loop current ofreceiver

According to Kirchhoffrsquos law the equations of the circuitin Figure 5 are listed in (1) and (2)

RSi1 + R1i1 + jωL1i1 +i1

jωC1minus jωMi2 US (1)

minus jωMi1 + jωL2i2 + R2i2 + RLi2 +i2

jωC2 0 (2)

e simultaneous solutions to (1) and (2) give thecurrent of the transmitting and receiving coils respectively

i1 US

RS + R1 + jωL1 + 1jωC1( 1113857 minus jωMR2 + RL + jωL2 + 1jωC2( 1113857( 1113857 (3)

i2 jωMUS

R2 + RL + jωL2 + 1jωC2( 1113857( 1113857 RS + R1 + jωL1 + 1jωC1( 1113857( 1113857 minus (jωM)2 (4)

When the system is in the resonant state the structureand parameters of the transmitting and receiving coils areidentical and the impedance of the transmitting and re-ceiving ends matches erefore if C1 C2 C L1 L2 Lω 2πf (1

LC

radic) and R1 +RS R2 +RL R the system

PTE of the system is maximized us formulas (3) and (4)can be simplified as follows

i1 USR

R2 minus (jωM)2

i2 jωMUS

R2 minus (jωM)2

(5)

From this it can be concluded that the output and inputpower of the system are respectively

Journal of Electrical and Computer Engineering 3

Pin USi1 + i21Rs

U2SR R2 + ω2M2( 1113857 + U2

SR2Rs

R2 + ω2M2( )2 (6)

Pout i22RL

ω2M2U2SRL

R2 + ω2M2( )2 (7)

From formulas (6) and (7) the PTE of the system can becalculated as follows

η Pout

Pin

ω2M2RL

R3 + R2Rs + ω2M2( 1113857 (8)

Electromagneticreceiving module

Loadmodule

Powermodule

Electromagneticemission module

Figure 2 Structure diagram of MCRWPT system

(a) (b)

Figure 3 Structure diagram of a MCRWPT system (a) Cylindrical spiral coil (b) Planar spiral coil

C1

L1

R1

Us

C2

L2

RL

(a)

C1

L1

R1

Us

C2

L2

RL

(b)

C1

L1

R1

Us

C2

L2

RL

(c)

C1

L1

R1

UsC2

L2

RL

(d)

Figure 4 Capacitance compensation circuit (a) SS structure (b) SP structure (c) PP structure (d) PS structure

4 Journal of Electrical and Computer Engineering

It can be seen from formula (8) that the PTE of the powersupply system is related to the resonant frequency of thesystem the mutual inductance value M between coils andthe resistance value of the systeme resistance value of thesystem includes the equivalent resistance value of thetransmitting and receiving coils the internal resistance ofthe power supply and the load resistance value e PTE ofthe system can be obtained by substituting the angularfrequency ω 2πf into formula (8)

η 4π2f2M2RL

R3 + R2Rs + 4π2f2M2( 1113857 (9)

From the above analysis it can be seen that changing theresonant frequency f mutual inductanceM and resistance R ofthe system can improve the PTE of the power supply system

e equivalent resistance of the system depends on thequality factor of the coil used in the system which is definedas

Q ωL

R (10)

In the formula ω is the working angle frequency L isthe inductance of the coil and R is the total loss resistance ofthe coil It is composed of DC resistance and dielectric loss ofhigh-frequency resistance e resonant frequency of thesystem is related to the parameters of the system hardwareand the power supply frequency e mutual inductance ofcoils depends on the material radius turns and the distancebetween the two coils

e calculation method for coil mutual inductance M isgiven in [20] and formula (11)

M πμ0

n1n2

radicr1r2( 1113857

2

2D3 (11)

In the formula μ0 4π times 10minus 7 Hmiddotmminus 1 is the vacuumpermeability n1 n2 and r1 r2 are the turns and radius of thetransmitting coil and the receiving coil respectively and D isthe distance between the transmitting coil and the receivingcoilWhen the diameter of themeasured axis is determined theradius of the resonant coil is fixed and the mutual inductancevalue is mainly determined by the number of turns of the coiland the distance between the coils Parameters for the exampleof the measured shaft of a rolling mill are shown in Table 1

e self-resistance of the coil is [21]

R

ωμ02σ

1113970l

2πa (12)

In the formula σ 57times107 smiddotmminus 1 is the conductivity ofthe coil copper wire l is the length of the coil and a is thediameter of the coil

Evaluation with the Origin data analysis software showsthat the PTE of the system varies as the resonant frequencyof the system varies from 1 to 10MHz the coil spacing variesfrom 50 to 600mm and the coil diameter is set to 200 400700 and 900mm e analyzed cases are shown in Figure 6

Figure 6(a) shows that when the coil diameter is 200mmand the distance between transmitting and receiving coils ismore than 100mm the PTE of the system is close to zeroWhen the distance between transmitting and receiving coilsis less than 100mm the PTE of the system observablychanges with a smaller distance between coils corre-sponding to a higher system PTE Increasing the resonantfrequency of the system improves the PTE providing sig-nificant benefits Figure 6(d) shows that when the coil di-ameter is 900mm the PTE of the system observably changeswith a change in resonant frequency and coil spacing Whenthe frequency increases and the coil spacing decreases thePTE of the system increases continuously and when the coilspacing is less than 200mm the PTE of the system exceeds50 rough comparison it can be seen that when the coildiameter is larger a change in coil spacing and frequency hasa greater impact on the PTE and a higher PTE can bemaintained When the coil diameter is smaller the overallPTE of the system is low and only by reducing the coilspacing can the PTE of the system be significantly improved

e results of the theoretical study show that the PTE of apower supply system varies with the resonant frequency thecoil spacing and the coil diameter When applied to a rollingmill depending on the diameter of the axis installed in atelemetry system and the field environment the powersupply system can achieve higher PTE by choosing ap-propriate power frequency matching capacitance and coilspacing for a given coil diameter

3 Experimental Results and Analysis

31 Experimental Design and Analysis Based on the theo-retical research results coils with diameters of 700mm and400mm are experimentally studied as shown in Figure 7

e power supply frequency is 5MHz and the coildiameter is 700mm and 400mm respectivelyWhen the coildiameter is 700mm and the coil spacing is 50mm the

Table 1 Modeling parameter

Parameter name Numerical valueDrive shaft diameter (mm) 200sim900Coil diameter (mm) 200sim900Coil turns 5Power supply amplitude (V) 5Power frequency (MHz) 1sim10Resistance value of telemetering device (Ω) 325

L1 L2

R1

Us

C2

RL

Rs

R2

M

C1

i1 i2

Figure 5 Equivalent circuit of MCRWPT

Journal of Electrical and Computer Engineering 5

waveforms of the primary coil supply voltage and the sec-ondary coil induction voltage are obtained as shown inFigure 8

e relationship between PTE and coil spacing is ob-tained by changing coil spacing A comparison of PTE in

terms of the experimentally and theoretically calculatedefficiency of the system is shown in Figure 9

From Figure 9 it can be seen that the PTE varies with coilspacing when the resonant frequency is fixed For the400mm coil diameter the PTE of the system changes

05

04

03

02

01

010

86

42

0

η

D (m

m)

f (MHz) 600500

400300

200100

0

0538004842043040376603228026900215201614010760053800000

η

(a)

10

08

04

06

02

00

η

108

64

20

f (MHz) D (mm)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(b)

10

08

04

06

02

0

η

108

64

20

f (MHz)

D (mm)600 500 400 300 200 1000

1000

09000

08000

07000

06000

05000

04000

03000

02000

01000

0000

η

(c)

10

08

04

06

02

0

η

108

64

20

f (MHz)D (m

m)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(d)

Figure 6 Variation of η with f and D (a) Coil diameter of 200mm (b) Coil diameter of 400mm (c) Coil diameter of 700mm (d) Coildiameter of 900mm

(a) (b)

Figure 7 Experimental device setup photos (a) Coil diameter 700mm (b) Coil diameter 400mm

6 Journal of Electrical and Computer Engineering

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

shown in Figure 2e power supply module is composed ofa rectifier and a high-frequency inverter which providessuitable resonant frequency voltage input for the electro-magnetic transmitting module e electromagnetic trans-mitting module converts a high-frequency input voltage intoa high-frequency magnetic field and strong magneticcoupling occurs between the space electromagnetic field andthe electromagnetic receiving module e electromagneticreceiving module converts magnetic energy into electricenergy and outputs it to the load module through constantvoltage rectification e electromagnetic transmitting andreceiving modules are key parts of the power supply systemFunctionality of the transmitting and receiving modules inthe resonant state ensures the power transmission ere-fore the transmitting and receiving modules are composedof high quality factor resonant coils with identical structuresand parameters and a resonant compensation capacitor Inthe torque telemetry system the transmitter and strain gaugeon the measured axis are used as load modules to consumeenergy To ensure optimal PTE of the system the impedanceat the load end and the internal resistance at the powersupply end are always matched

Cylindrical spiral coils and plane spiral coils as shown inFigure 3 are primarily used [19] e magnetic field in-tensity at the edge of the helical coil is greater than that atthe center e magnetic induction intensity of the planardisc coil decreases from inside to outside and the magneticinduction intensity is the largest at the center of the coile two coil structures have their own characteristics andcan be selected according to application requirements

22 $eoretical Analysis To optimize the power transmis-sion efficiency it is usually necessary to compensate for thecapacitance of the resonant coil to reach the resonant statee compensation circuit is divided into four forms Series-Series (SS) Series-Parallel (SP) Parallel-Parallel (PP) andParallel-Series (PS) as shown in Figure 4 To achieve theresonant state of the system the imaginary part of the totalresistance of the system after capacitance compensation iszero e compensation capacitance of the SP PP and PSstructures is related to the load resistance and only thecompensation capacitance of the receiving and transmitting

terminals of SS structures is independent of the load Be-cause the load resistance of the online torque telemetrysystem varies during its operation an SS structure is chosenfor the capacitance compensation circuit in this paper

Presently there are two main MCRWPT researchmethods coupled mode theory and equivalent circuit the-ory Each research method has its own benefits Coupledmode theory is a mathematical method that describes acomplex coupled system as an energy transmission processof an independent single system from the perspective ofenergy simplifying and clarifying the analysis and calcu-lation Equivalent circuit theory establishes an equivalentcircuit model based on the basic principle of a circuit and theequivalent calculation method which is intuitive and easy tounderstand Depending on the specific parameters of thecircuit the voltage and current changes in the circuit areanalyzed to calculate the PTE and power of the systemelectric energy In this paper equivalent circuit theory isused to study the process of power transmission Itsequivalent circuit model is shown in Figure 5

In Figure 5 US represents high-frequency power supplyexcitation RS represents internal resistance of power supplyR1 represents equivalent resistance of transmitter C1 rep-resents compensation capacitance of transmitter L1 repre-sents transmitting coil L2 represents receiving coil R2represents equivalent resistance of receiver C2 representscompensation capacitance of receiver RL represents loadresistance M represents mutual inductance betweentransmitting coil and receiving coil i1 represents loopcurrent of transmitter and i2 represents loop current ofreceiver

According to Kirchhoffrsquos law the equations of the circuitin Figure 5 are listed in (1) and (2)

RSi1 + R1i1 + jωL1i1 +i1

jωC1minus jωMi2 US (1)

minus jωMi1 + jωL2i2 + R2i2 + RLi2 +i2

jωC2 0 (2)

e simultaneous solutions to (1) and (2) give thecurrent of the transmitting and receiving coils respectively

i1 US

RS + R1 + jωL1 + 1jωC1( 1113857 minus jωMR2 + RL + jωL2 + 1jωC2( 1113857( 1113857 (3)

i2 jωMUS

R2 + RL + jωL2 + 1jωC2( 1113857( 1113857 RS + R1 + jωL1 + 1jωC1( 1113857( 1113857 minus (jωM)2 (4)

When the system is in the resonant state the structureand parameters of the transmitting and receiving coils areidentical and the impedance of the transmitting and re-ceiving ends matches erefore if C1 C2 C L1 L2 Lω 2πf (1

LC

radic) and R1 +RS R2 +RL R the system

PTE of the system is maximized us formulas (3) and (4)can be simplified as follows

i1 USR

R2 minus (jωM)2

i2 jωMUS

R2 minus (jωM)2

(5)

From this it can be concluded that the output and inputpower of the system are respectively

Journal of Electrical and Computer Engineering 3

Pin USi1 + i21Rs

U2SR R2 + ω2M2( 1113857 + U2

SR2Rs

R2 + ω2M2( )2 (6)

Pout i22RL

ω2M2U2SRL

R2 + ω2M2( )2 (7)

From formulas (6) and (7) the PTE of the system can becalculated as follows

η Pout

Pin

ω2M2RL

R3 + R2Rs + ω2M2( 1113857 (8)

Electromagneticreceiving module

Loadmodule

Powermodule

Electromagneticemission module

Figure 2 Structure diagram of MCRWPT system

(a) (b)

Figure 3 Structure diagram of a MCRWPT system (a) Cylindrical spiral coil (b) Planar spiral coil

C1

L1

R1

Us

C2

L2

RL

(a)

C1

L1

R1

Us

C2

L2

RL

(b)

C1

L1

R1

Us

C2

L2

RL

(c)

C1

L1

R1

UsC2

L2

RL

(d)

Figure 4 Capacitance compensation circuit (a) SS structure (b) SP structure (c) PP structure (d) PS structure

4 Journal of Electrical and Computer Engineering

It can be seen from formula (8) that the PTE of the powersupply system is related to the resonant frequency of thesystem the mutual inductance value M between coils andthe resistance value of the systeme resistance value of thesystem includes the equivalent resistance value of thetransmitting and receiving coils the internal resistance ofthe power supply and the load resistance value e PTE ofthe system can be obtained by substituting the angularfrequency ω 2πf into formula (8)

η 4π2f2M2RL

R3 + R2Rs + 4π2f2M2( 1113857 (9)

From the above analysis it can be seen that changing theresonant frequency f mutual inductanceM and resistance R ofthe system can improve the PTE of the power supply system

e equivalent resistance of the system depends on thequality factor of the coil used in the system which is definedas

Q ωL

R (10)

In the formula ω is the working angle frequency L isthe inductance of the coil and R is the total loss resistance ofthe coil It is composed of DC resistance and dielectric loss ofhigh-frequency resistance e resonant frequency of thesystem is related to the parameters of the system hardwareand the power supply frequency e mutual inductance ofcoils depends on the material radius turns and the distancebetween the two coils

e calculation method for coil mutual inductance M isgiven in [20] and formula (11)

M πμ0

n1n2

radicr1r2( 1113857

2

2D3 (11)

In the formula μ0 4π times 10minus 7 Hmiddotmminus 1 is the vacuumpermeability n1 n2 and r1 r2 are the turns and radius of thetransmitting coil and the receiving coil respectively and D isthe distance between the transmitting coil and the receivingcoilWhen the diameter of themeasured axis is determined theradius of the resonant coil is fixed and the mutual inductancevalue is mainly determined by the number of turns of the coiland the distance between the coils Parameters for the exampleof the measured shaft of a rolling mill are shown in Table 1

e self-resistance of the coil is [21]

R

ωμ02σ

1113970l

2πa (12)

In the formula σ 57times107 smiddotmminus 1 is the conductivity ofthe coil copper wire l is the length of the coil and a is thediameter of the coil

Evaluation with the Origin data analysis software showsthat the PTE of the system varies as the resonant frequencyof the system varies from 1 to 10MHz the coil spacing variesfrom 50 to 600mm and the coil diameter is set to 200 400700 and 900mm e analyzed cases are shown in Figure 6

Figure 6(a) shows that when the coil diameter is 200mmand the distance between transmitting and receiving coils ismore than 100mm the PTE of the system is close to zeroWhen the distance between transmitting and receiving coilsis less than 100mm the PTE of the system observablychanges with a smaller distance between coils corre-sponding to a higher system PTE Increasing the resonantfrequency of the system improves the PTE providing sig-nificant benefits Figure 6(d) shows that when the coil di-ameter is 900mm the PTE of the system observably changeswith a change in resonant frequency and coil spacing Whenthe frequency increases and the coil spacing decreases thePTE of the system increases continuously and when the coilspacing is less than 200mm the PTE of the system exceeds50 rough comparison it can be seen that when the coildiameter is larger a change in coil spacing and frequency hasa greater impact on the PTE and a higher PTE can bemaintained When the coil diameter is smaller the overallPTE of the system is low and only by reducing the coilspacing can the PTE of the system be significantly improved

e results of the theoretical study show that the PTE of apower supply system varies with the resonant frequency thecoil spacing and the coil diameter When applied to a rollingmill depending on the diameter of the axis installed in atelemetry system and the field environment the powersupply system can achieve higher PTE by choosing ap-propriate power frequency matching capacitance and coilspacing for a given coil diameter

3 Experimental Results and Analysis

31 Experimental Design and Analysis Based on the theo-retical research results coils with diameters of 700mm and400mm are experimentally studied as shown in Figure 7

e power supply frequency is 5MHz and the coildiameter is 700mm and 400mm respectivelyWhen the coildiameter is 700mm and the coil spacing is 50mm the

Table 1 Modeling parameter

Parameter name Numerical valueDrive shaft diameter (mm) 200sim900Coil diameter (mm) 200sim900Coil turns 5Power supply amplitude (V) 5Power frequency (MHz) 1sim10Resistance value of telemetering device (Ω) 325

L1 L2

R1

Us

C2

RL

Rs

R2

M

C1

i1 i2

Figure 5 Equivalent circuit of MCRWPT

Journal of Electrical and Computer Engineering 5

waveforms of the primary coil supply voltage and the sec-ondary coil induction voltage are obtained as shown inFigure 8

e relationship between PTE and coil spacing is ob-tained by changing coil spacing A comparison of PTE in

terms of the experimentally and theoretically calculatedefficiency of the system is shown in Figure 9

From Figure 9 it can be seen that the PTE varies with coilspacing when the resonant frequency is fixed For the400mm coil diameter the PTE of the system changes

05

04

03

02

01

010

86

42

0

η

D (m

m)

f (MHz) 600500

400300

200100

0

0538004842043040376603228026900215201614010760053800000

η

(a)

10

08

04

06

02

00

η

108

64

20

f (MHz) D (mm)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(b)

10

08

04

06

02

0

η

108

64

20

f (MHz)

D (mm)600 500 400 300 200 1000

1000

09000

08000

07000

06000

05000

04000

03000

02000

01000

0000

η

(c)

10

08

04

06

02

0

η

108

64

20

f (MHz)D (m

m)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(d)

Figure 6 Variation of η with f and D (a) Coil diameter of 200mm (b) Coil diameter of 400mm (c) Coil diameter of 700mm (d) Coildiameter of 900mm

(a) (b)

Figure 7 Experimental device setup photos (a) Coil diameter 700mm (b) Coil diameter 400mm

6 Journal of Electrical and Computer Engineering

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

Pin USi1 + i21Rs

U2SR R2 + ω2M2( 1113857 + U2

SR2Rs

R2 + ω2M2( )2 (6)

Pout i22RL

ω2M2U2SRL

R2 + ω2M2( )2 (7)

From formulas (6) and (7) the PTE of the system can becalculated as follows

η Pout

Pin

ω2M2RL

R3 + R2Rs + ω2M2( 1113857 (8)

Electromagneticreceiving module

Loadmodule

Powermodule

Electromagneticemission module

Figure 2 Structure diagram of MCRWPT system

(a) (b)

Figure 3 Structure diagram of a MCRWPT system (a) Cylindrical spiral coil (b) Planar spiral coil

C1

L1

R1

Us

C2

L2

RL

(a)

C1

L1

R1

Us

C2

L2

RL

(b)

C1

L1

R1

Us

C2

L2

RL

(c)

C1

L1

R1

UsC2

L2

RL

(d)

Figure 4 Capacitance compensation circuit (a) SS structure (b) SP structure (c) PP structure (d) PS structure

4 Journal of Electrical and Computer Engineering

It can be seen from formula (8) that the PTE of the powersupply system is related to the resonant frequency of thesystem the mutual inductance value M between coils andthe resistance value of the systeme resistance value of thesystem includes the equivalent resistance value of thetransmitting and receiving coils the internal resistance ofthe power supply and the load resistance value e PTE ofthe system can be obtained by substituting the angularfrequency ω 2πf into formula (8)

η 4π2f2M2RL

R3 + R2Rs + 4π2f2M2( 1113857 (9)

From the above analysis it can be seen that changing theresonant frequency f mutual inductanceM and resistance R ofthe system can improve the PTE of the power supply system

e equivalent resistance of the system depends on thequality factor of the coil used in the system which is definedas

Q ωL

R (10)

In the formula ω is the working angle frequency L isthe inductance of the coil and R is the total loss resistance ofthe coil It is composed of DC resistance and dielectric loss ofhigh-frequency resistance e resonant frequency of thesystem is related to the parameters of the system hardwareand the power supply frequency e mutual inductance ofcoils depends on the material radius turns and the distancebetween the two coils

e calculation method for coil mutual inductance M isgiven in [20] and formula (11)

M πμ0

n1n2

radicr1r2( 1113857

2

2D3 (11)

In the formula μ0 4π times 10minus 7 Hmiddotmminus 1 is the vacuumpermeability n1 n2 and r1 r2 are the turns and radius of thetransmitting coil and the receiving coil respectively and D isthe distance between the transmitting coil and the receivingcoilWhen the diameter of themeasured axis is determined theradius of the resonant coil is fixed and the mutual inductancevalue is mainly determined by the number of turns of the coiland the distance between the coils Parameters for the exampleof the measured shaft of a rolling mill are shown in Table 1

e self-resistance of the coil is [21]

R

ωμ02σ

1113970l

2πa (12)

In the formula σ 57times107 smiddotmminus 1 is the conductivity ofthe coil copper wire l is the length of the coil and a is thediameter of the coil

Evaluation with the Origin data analysis software showsthat the PTE of the system varies as the resonant frequencyof the system varies from 1 to 10MHz the coil spacing variesfrom 50 to 600mm and the coil diameter is set to 200 400700 and 900mm e analyzed cases are shown in Figure 6

Figure 6(a) shows that when the coil diameter is 200mmand the distance between transmitting and receiving coils ismore than 100mm the PTE of the system is close to zeroWhen the distance between transmitting and receiving coilsis less than 100mm the PTE of the system observablychanges with a smaller distance between coils corre-sponding to a higher system PTE Increasing the resonantfrequency of the system improves the PTE providing sig-nificant benefits Figure 6(d) shows that when the coil di-ameter is 900mm the PTE of the system observably changeswith a change in resonant frequency and coil spacing Whenthe frequency increases and the coil spacing decreases thePTE of the system increases continuously and when the coilspacing is less than 200mm the PTE of the system exceeds50 rough comparison it can be seen that when the coildiameter is larger a change in coil spacing and frequency hasa greater impact on the PTE and a higher PTE can bemaintained When the coil diameter is smaller the overallPTE of the system is low and only by reducing the coilspacing can the PTE of the system be significantly improved

e results of the theoretical study show that the PTE of apower supply system varies with the resonant frequency thecoil spacing and the coil diameter When applied to a rollingmill depending on the diameter of the axis installed in atelemetry system and the field environment the powersupply system can achieve higher PTE by choosing ap-propriate power frequency matching capacitance and coilspacing for a given coil diameter

3 Experimental Results and Analysis

31 Experimental Design and Analysis Based on the theo-retical research results coils with diameters of 700mm and400mm are experimentally studied as shown in Figure 7

e power supply frequency is 5MHz and the coildiameter is 700mm and 400mm respectivelyWhen the coildiameter is 700mm and the coil spacing is 50mm the

Table 1 Modeling parameter

Parameter name Numerical valueDrive shaft diameter (mm) 200sim900Coil diameter (mm) 200sim900Coil turns 5Power supply amplitude (V) 5Power frequency (MHz) 1sim10Resistance value of telemetering device (Ω) 325

L1 L2

R1

Us

C2

RL

Rs

R2

M

C1

i1 i2

Figure 5 Equivalent circuit of MCRWPT

Journal of Electrical and Computer Engineering 5

waveforms of the primary coil supply voltage and the sec-ondary coil induction voltage are obtained as shown inFigure 8

e relationship between PTE and coil spacing is ob-tained by changing coil spacing A comparison of PTE in

terms of the experimentally and theoretically calculatedefficiency of the system is shown in Figure 9

From Figure 9 it can be seen that the PTE varies with coilspacing when the resonant frequency is fixed For the400mm coil diameter the PTE of the system changes

05

04

03

02

01

010

86

42

0

η

D (m

m)

f (MHz) 600500

400300

200100

0

0538004842043040376603228026900215201614010760053800000

η

(a)

10

08

04

06

02

00

η

108

64

20

f (MHz) D (mm)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(b)

10

08

04

06

02

0

η

108

64

20

f (MHz)

D (mm)600 500 400 300 200 1000

1000

09000

08000

07000

06000

05000

04000

03000

02000

01000

0000

η

(c)

10

08

04

06

02

0

η

108

64

20

f (MHz)D (m

m)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(d)

Figure 6 Variation of η with f and D (a) Coil diameter of 200mm (b) Coil diameter of 400mm (c) Coil diameter of 700mm (d) Coildiameter of 900mm

(a) (b)

Figure 7 Experimental device setup photos (a) Coil diameter 700mm (b) Coil diameter 400mm

6 Journal of Electrical and Computer Engineering

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

It can be seen from formula (8) that the PTE of the powersupply system is related to the resonant frequency of thesystem the mutual inductance value M between coils andthe resistance value of the systeme resistance value of thesystem includes the equivalent resistance value of thetransmitting and receiving coils the internal resistance ofthe power supply and the load resistance value e PTE ofthe system can be obtained by substituting the angularfrequency ω 2πf into formula (8)

η 4π2f2M2RL

R3 + R2Rs + 4π2f2M2( 1113857 (9)

From the above analysis it can be seen that changing theresonant frequency f mutual inductanceM and resistance R ofthe system can improve the PTE of the power supply system

e equivalent resistance of the system depends on thequality factor of the coil used in the system which is definedas

Q ωL

R (10)

In the formula ω is the working angle frequency L isthe inductance of the coil and R is the total loss resistance ofthe coil It is composed of DC resistance and dielectric loss ofhigh-frequency resistance e resonant frequency of thesystem is related to the parameters of the system hardwareand the power supply frequency e mutual inductance ofcoils depends on the material radius turns and the distancebetween the two coils

e calculation method for coil mutual inductance M isgiven in [20] and formula (11)

M πμ0

n1n2

radicr1r2( 1113857

2

2D3 (11)

In the formula μ0 4π times 10minus 7 Hmiddotmminus 1 is the vacuumpermeability n1 n2 and r1 r2 are the turns and radius of thetransmitting coil and the receiving coil respectively and D isthe distance between the transmitting coil and the receivingcoilWhen the diameter of themeasured axis is determined theradius of the resonant coil is fixed and the mutual inductancevalue is mainly determined by the number of turns of the coiland the distance between the coils Parameters for the exampleof the measured shaft of a rolling mill are shown in Table 1

e self-resistance of the coil is [21]

R

ωμ02σ

1113970l

2πa (12)

In the formula σ 57times107 smiddotmminus 1 is the conductivity ofthe coil copper wire l is the length of the coil and a is thediameter of the coil

Evaluation with the Origin data analysis software showsthat the PTE of the system varies as the resonant frequencyof the system varies from 1 to 10MHz the coil spacing variesfrom 50 to 600mm and the coil diameter is set to 200 400700 and 900mm e analyzed cases are shown in Figure 6

Figure 6(a) shows that when the coil diameter is 200mmand the distance between transmitting and receiving coils ismore than 100mm the PTE of the system is close to zeroWhen the distance between transmitting and receiving coilsis less than 100mm the PTE of the system observablychanges with a smaller distance between coils corre-sponding to a higher system PTE Increasing the resonantfrequency of the system improves the PTE providing sig-nificant benefits Figure 6(d) shows that when the coil di-ameter is 900mm the PTE of the system observably changeswith a change in resonant frequency and coil spacing Whenthe frequency increases and the coil spacing decreases thePTE of the system increases continuously and when the coilspacing is less than 200mm the PTE of the system exceeds50 rough comparison it can be seen that when the coildiameter is larger a change in coil spacing and frequency hasa greater impact on the PTE and a higher PTE can bemaintained When the coil diameter is smaller the overallPTE of the system is low and only by reducing the coilspacing can the PTE of the system be significantly improved

e results of the theoretical study show that the PTE of apower supply system varies with the resonant frequency thecoil spacing and the coil diameter When applied to a rollingmill depending on the diameter of the axis installed in atelemetry system and the field environment the powersupply system can achieve higher PTE by choosing ap-propriate power frequency matching capacitance and coilspacing for a given coil diameter

3 Experimental Results and Analysis

31 Experimental Design and Analysis Based on the theo-retical research results coils with diameters of 700mm and400mm are experimentally studied as shown in Figure 7

e power supply frequency is 5MHz and the coildiameter is 700mm and 400mm respectivelyWhen the coildiameter is 700mm and the coil spacing is 50mm the

Table 1 Modeling parameter

Parameter name Numerical valueDrive shaft diameter (mm) 200sim900Coil diameter (mm) 200sim900Coil turns 5Power supply amplitude (V) 5Power frequency (MHz) 1sim10Resistance value of telemetering device (Ω) 325

L1 L2

R1

Us

C2

RL

Rs

R2

M

C1

i1 i2

Figure 5 Equivalent circuit of MCRWPT

Journal of Electrical and Computer Engineering 5

waveforms of the primary coil supply voltage and the sec-ondary coil induction voltage are obtained as shown inFigure 8

e relationship between PTE and coil spacing is ob-tained by changing coil spacing A comparison of PTE in

terms of the experimentally and theoretically calculatedefficiency of the system is shown in Figure 9

From Figure 9 it can be seen that the PTE varies with coilspacing when the resonant frequency is fixed For the400mm coil diameter the PTE of the system changes

05

04

03

02

01

010

86

42

0

η

D (m

m)

f (MHz) 600500

400300

200100

0

0538004842043040376603228026900215201614010760053800000

η

(a)

10

08

04

06

02

00

η

108

64

20

f (MHz) D (mm)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(b)

10

08

04

06

02

0

η

108

64

20

f (MHz)

D (mm)600 500 400 300 200 1000

1000

09000

08000

07000

06000

05000

04000

03000

02000

01000

0000

η

(c)

10

08

04

06

02

0

η

108

64

20

f (MHz)D (m

m)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(d)

Figure 6 Variation of η with f and D (a) Coil diameter of 200mm (b) Coil diameter of 400mm (c) Coil diameter of 700mm (d) Coildiameter of 900mm

(a) (b)

Figure 7 Experimental device setup photos (a) Coil diameter 700mm (b) Coil diameter 400mm

6 Journal of Electrical and Computer Engineering

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

waveforms of the primary coil supply voltage and the sec-ondary coil induction voltage are obtained as shown inFigure 8

e relationship between PTE and coil spacing is ob-tained by changing coil spacing A comparison of PTE in

terms of the experimentally and theoretically calculatedefficiency of the system is shown in Figure 9

From Figure 9 it can be seen that the PTE varies with coilspacing when the resonant frequency is fixed For the400mm coil diameter the PTE of the system changes

05

04

03

02

01

010

86

42

0

η

D (m

m)

f (MHz) 600500

400300

200100

0

0538004842043040376603228026900215201614010760053800000

η

(a)

10

08

04

06

02

00

η

108

64

20

f (MHz) D (mm)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(b)

10

08

04

06

02

0

η

108

64

20

f (MHz)

D (mm)600 500 400 300 200 1000

1000

09000

08000

07000

06000

05000

04000

03000

02000

01000

0000

η

(c)

10

08

04

06

02

0

η

108

64

20

f (MHz)D (m

m)

600500

400300

200100

0

10000900008000070000600005000040000300002000010000000

η

(d)

Figure 6 Variation of η with f and D (a) Coil diameter of 200mm (b) Coil diameter of 400mm (c) Coil diameter of 700mm (d) Coildiameter of 900mm

(a) (b)

Figure 7 Experimental device setup photos (a) Coil diameter 700mm (b) Coil diameter 400mm

6 Journal of Electrical and Computer Engineering

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

rapidly and a high efficiency of power transmission can bemaintained only when the coil spacing is less than 100mmWhen the coil diameter is 700mm the overall PTE of thesystem is greatly improved e PTE of the system can stillexceed 50 with coil spacing up to 250mm e experi-mental PTE trend is largely consistent with the results oftheoretical research

e developed rollingmill torque telemetry system basedon magnetic coupling resonant wireless power supply hasbeen installed and applied on the output axles of main drivemotors of several continuous rolling mills as shown inFigure 10(a) A limitation of the original inductive powersupply mode is that the transmission distance cannot exceedapproximately 7mm to achieve stable power transmission Amagnetically coupled wireless power supply removes thatlimitation and can supply power efficiently and steadily overa large distance (generally approximately 200mm) whichsignificantly eases system installation and maintenance

During the manufacturing and debugging of theequipment the induction coil centers of the primary andsecondary sides of the telemetry system pass through theaxis while the drive shaft of the rolling mill passes throughthe coil centers after being installed on-site e presence ofthe drive shaft of a rolling mill changes the inductance of thecoil and the mutual inductance between the coils whichmakes the system unable to work in the resonant state andresults in a decrease in PTE and power

e field test results for the 400mm diameter drive shaftare shown in Figure 10 and the test data results for the400mm shaft are shown in Table 2

Table 2 shows that the primary side inductance changerate is 129 the secondary side inductance change rate is128 and the PTE is reduced by 34 e change of in-ductance under the influence of a transmission shaft canchange the resonant state of the system By adjusting thecapacitance of the primary side resonant circuit the system

(a) (b)

Figure 8 Experimental waveform diagrams (a) Voltage waveform of primary coil supply (b) Induced voltage waveform of secondary coil

50 100 150D (mm)

200 250 300

10

08

06

04

02

00

η

η1η2

η3η4

Figure 9 Simulation and experimental efficiency comparison chart

Journal of Electrical and Computer Engineering 7

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

can maintain a high PTE thus ensuring that the telemetryequipment can maintain its normal working state

e system has been running steadily for more than oneyear in several continuous rolling mills as shown inFigure 11(a) e real-time waveform of the collected torquesignal is shown in Figure 11(b)

4 Conclusions

In this paper the power supply of a rotating ring in an onlinetorque telemetry system is studied e developed magneticcoupling resonant wireless power supply system replaces thehigh-frequency induction power supply system e rela-tionship between mutual inductance coil spacing and PTEwas obtained through mathematical derivation Origin dataanalysis software was used to simulate the variation trend ofsystem PTE for different coil diameters and transmissionspacing By designing an experimental platform to test thepower transfer efficiency when the coil diameter is 700mm

and 400mm when the pitch is 50mm the results show thatthe simulation results are basically consistent with the ex-perimental results In the field application the PTE of theradio power transmission system was reduced by 34 due tothe influence of the transmission shaft of the rolling mill Anadjustment of the primary compensation capacitance canallow the system to meet the normal power demand andensure normal operation e influence of the transmissionshaft on the efficiency of power transmission in a telemetrysystem is the next key research direction

Data Availability

e datasets supporting the conclusions of this article areincluded within the article

Conflicts of Interest

e authors declare no conflicts of interest

(a) (b)

Figure 11 Installed system and torque signal time domain analysis diagrams (a) Photo of an on-site torque telemetry device (b) Torquesignal waveform and spectrum plots

(a) (b)

Figure 10 Field test setup photos

Table 2 Field test data results

Change of primary inductance Secondary inductance changeΔU2 η ()

L1 L1prime L1 L2 L2prime L2978 852 126 967 843 124 21 minus 34

8 Journal of Electrical and Computer Engineering

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9

Acknowledgments

is work was financially supported by 12th Five-YearNational Science and Technology Support Plan PrecisionStrip Steel Product Quality Optimization and Key Equip-ment Research and Development (Grant no2015BAF30B00) and Fundamental Research Funds for theCentral Universities (Grant no FRF-AT-19-001)

References

[1] X Q Yan and X B Cui ldquoTorque telemetering system of maindrive system for rolling mill based on nRF9E5rdquo Journal ofMicrocomputer Information vol 29 no 1ndash9 pp 107-1082007

[2] X Q Yan H Zhang and S L Yang ldquoTorque monitor systemof main drive system for rolling millrdquo Journal of MetallurgicalEquipment vol 12 no 6 pp 63ndash66 2001

[3] X M Fan X Y Mo and X Zhang ldquoResearch status andapplication of wireless power transfer via coupled magneticresonancesrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 12 pp 75ndash82 2013

[4] Z M Zhao Y M Zhang and K N Chen ldquoNew progress ofmagnetically-coupled resonant wireless power transfer tech-nologyrdquo Journal of Proceedings of the CSEE vol 33 no 3pp 1ndash13 2013

[5] C Chen ldquoResearch on electromagnetic problems and op-timization design of magnetic resonant wireless powertransfer systemrdquo Doctoral Dissertation Southeast UniversityNanjing China 2016

[6] F X Yang ldquoResearch on key technologies of wireless powertransfer networks based on inductively coupled powertransferrdquo Doctoral Dissertation Southeast UniversityNanjing China 2012

[7] O Jonah ldquoOptomization of wireless power transfer viamagnetic resonance in different mediardquoDoctoral DissertationFlorida International University Miami FL USA 2013

[8] T-H Kim G-H Yun W Y Lee and J-G Yook ldquoAsym-metric coil structures for highly efficient wireless powertransfer systemsrdquo IEEE Transactions on Microwave $eoryand Techniques vol 66 no 7 pp 3443ndash3451 2018

[9] Y Shin J Park and J KimWireless Power Transfer System forUnmanned Vehicle Using T-Shape Ferrite Structure WileyHoboken NJ USA 2018

[10] X J Shu and B Zhang ldquoEnergy model and characteristicanalysis for inductively coupled power transfer systemrdquoJournal of Automation of Electric Power System vol 41 no 2pp 28ndash32 2017

[11] Y Li Q X Yang and H Y Chen ldquoAnalysis of factorsinfluencing power and efficiency in wireless power transfersystemrdquo Journal of Advanced Technology of Electrical Engi-neering and Energy vol 31 no 3 pp 31ndash34 2012

[12] X Zhang Q X Yang and H Y Chen ldquoModeling and designand experimental verification of contactless power trans-mission systems via electromagnetic resonant couplingrdquoJournal of Proceedings of the CSEE vol 32 no 21 pp 153ndash1582012

[13] X L Huang J J Ji and L L Tan ldquoStudy on series-parallelmodel of wireless power transfer via magnetic resonancecouplingrdquo Journal of Transactions of China ElectrotechnicalSociety vol 28 no 3 pp 171ndash176 2013

[14] W Wang X L Huang and Y L Zhou ldquoModeling and PTEanalysis of wireless power transmission system with dual

relaysrdquo Journal of Transactions of China ElectrotechnicalSociety vol 29 no 9 pp 1ndash6 2014

[15] RW Porto V J Brusamarello I Muller F L Cabrera Riantildeoand F Rangel De Sousa ldquoWireless power transfer for con-tactless instrumentation and measurementrdquo IEEE Instru-mentation ampMeasurementMagazine vol 20 no 4 pp 49ndash542017

[16] Z D Tang F Yang and Y Y Xu ldquoResearch on power ef-ficiency synchronization of wireless power transfer magneticresonant couplingrdquo Journal of Transactions of China Elec-trotechnical Society vol 32 pp 190ndash197 2017

[17] Z Q Li S D Huang and X F Yuan ldquoA method of pre-venting frequency splitting in magnetic resonant wirelesspower transfer systemrdquo Journal of Transactions of ChinaElectrotechnical Society vol 32 no 8 pp 152ndash159 2017

[18] Z Yan T F Wang and X C Zhang ldquoOptimization of thesource coil of magnetic coupling resonant wireless powertransmission system with class E power amplifierrdquo Journal ofTransactions of China Electrotechnical Society vol 32 no 10pp 162ndash167 2017

[19] L L Tan X L Huang and J F Zhao ldquoOptimization designfor disc resonators of a wireless power transmission systemrdquoJournal of Transactions of China Electrotechnical Societyvol 28 no 8 pp 1ndash6 2013

[20] Y Sun L Zhang and Z H Wang ldquoConstant voltage outputof wireless power transfer system based on AC envelopemodulationrdquo Journal of Automation of Electric Power Systemvol 41 no 2 pp 33ndash37 2017

[21] S Assawaworrarit X Yu and S Fan ldquoRobust wireless powertransfer using a nonlinear parity-time-symmetric circuitrdquoNature vol 546 no 7658 pp 387ndash390 2017

Journal of Electrical and Computer Engineering 9