Utafiti huu unasanifu upya mpangilio wa sumaku za kudumu na nguzo za chuma kwenye rotor ili kupunguza torque ripple katika consequent-pole permanent magnet synchronous motors (CP-PMSM) zinazoweza kutumika kwenye electric power steering (EPS) systems. Katika conventional CP-PMSM structure, kuunda polarity moja ya rotor poles kwa iron pole badala ya permanent magnet hufanya magnetic-flux distribution katika air gap kuwa asymmetric na kuongeza hasa even-order harmonics pamoja na torque ripple. Researchers wamependekeza two new 2D rotor architectures, symmetric na asymmetric, zinazoweka N pole, S pole na iron poles kwa arrangements tofauti kuzunguka rotor circumference ili kutatua problem hii bila kuongeza axial length ya rotor.

Katika finite-element analyses zilizofanywa kwa ANSYS Maxwell 2024R1, stator, 8-pole/12-slot combination, magnet geometry, air gap, rotor na stator dimensions pamoja na operating conditions zilihifadhiwa constant; mainly rotor-pole arrangement na iron-pole arc ratio zilichunguzwa. Katika final 2D analysis, torque ripple ya conventional CP-PMSM ya %36,91 ilishuka hadi %2,76 katika symmetric design na %3,59 katika asymmetric design. Kwa upande mwingine, average torque ilishuka kutoka 4,43 Nm hadi 3,71 na 3,94 Nm mtawalia. Kwa hiyo result haionyeshi tu “torque zaidi”, bali design trade-off kati ya torque capacity na torque quality.

Katika additional 3D finite-element analysis, absolute torque-ripple values ziliongezeka axial leakage flux na end effects zilipojumuishwa. Conventional structure ilitoa %40,8, symmetric design %6,0 na asymmetric design %7,5 torque ripple. Hata hivyo, ranking ya advantage ya proposed rotor arrangements mbili dhidi ya conventional structure iliendelea kubaki. Cogging torque pia ilishuka kutoka 192,38 mNm hadi 54,66 mNm katika symmetric structure na 34,63 mNm katika asymmetric structure.

Proposed pole arrangements hazikubadilisha torque ripple pekee. BEMF total harmonic distortion (THD) ilikuwa %8 katika conventional structure, huku ikiwa %3,2 katika symmetric model na %3,6 katika asymmetric model. Iron loss ilishuka kutoka 18,3 W hadi karibu 16,2 W, na magnet eddy-current loss kutoka 1,02 W hadi karibu 0,79 W. Kwa hiyo simulation results zinaonyesha kwamba smoother magnetic-flux distribution inaweza kutoa advantage kwa pamoja katika torque quality na baadhi ya electromagnetic-loss indicators.

Kwa mtazamo wa Uturuki, umuhimu wa study ni kuonyesha kwamba rotor design inayolenga kupunguza vibration na torque pulsation katika automotive electric power steering motors inaweza kuboreshwa si kwa kutumia magnets zaidi pekee, bali pia kwa kupanga existing magnets na iron poles kwa electromagnetic balance bora zaidi. Hata hivyo, study haijavalidated experimentally kwenye physical EPS motor prototype. Kwa sababu manufacturing tolerances, rotor mechanical strength, inverter nonlinearities, assembly errors, temperature na vibrations za real steering system zinaweza kubadilisha results, reported simulation values hazipaswi kuchukuliwa directly kama serial-production performance.

Kwa nini torque ripple ni muhimu kwenye EPS motor?

Electric power steering system inasaidia steering movement ya driver kwa electric motor. Kwa hiyo si average magnitude ya torque inayozalishwa na motor pekee iliyo muhimu, bali pia jinsi torque hiyo ilivyo smooth katika rotation. Periodic torque variations katika motor zinaweza kuhamia kwenye steering feel, mechanical vibration na acoustic noise.

Main motor family iliyotumika katika study ni permanent magnet synchronous motor. Katika conventional PMSMs, rotor poles zinaweza kutengenezwa kwa permanent magnets, huku katika CP-PMSM approach rotor iron ikitumika badala ya magnet ya polarity moja. Hivyo lengo ni kupunguza kiasi cha permanent magnet.

Hata hivyo, material advantage hii ina electromagnetic cost: kwa sababu magnet pole na iron pole hazina magnetic behavior ileile, air-gap flux density kuzunguka rotor hupoteza ideal symmetry yake.

Main problem katika conventional CP-PMSM ni nini?

Katika conventional structure, main magnetic flux inayotoka kwenye permanent magnet hupita kupitia stator na kurudi kwenye rotor core kupitia iron pole inayounda opposite polarity. Lakini kwa sababu pole moja ni actual permanent magnet na opposite pole ni ferromagnetic rotor material, air-gap field inayozalishwa na poles hizi mbili si exact symmetry ya kila nyingine.

Air-gap flux-density comparison ya study inaonyesha kwamba conventional CP-PMSM inazalisha higher content hasa katika even-order harmonics kuliko ordinary surface-magnet PMSM. Harmonics hizi zinaharibu BEMF waveform na kusababisha periodic variations katika electromagnetic torque.

Kwa hiyo main design approach ya study si kuongeza magnet quantity, bali kuboresha magnetic-flux symmetry kwa kubadilisha N, S na iron-pole sequence kuzunguka rotor circumference.

Axial solution iliyotumika awali ilikuwa ipi?

Katika previous approach, N-CP-PMSM na S-CP-PMSM rotors ziliunganishwa stacked kando ya motor axis. Kwa sababu even-order BEMF harmonics za structures hizi mbili zina approximately opposite character, kutumia structures hizi pamoja kunaweza kusababisha baadhi ya harmonics kujifuta partially.

Hata hivyo, hii inahitaji rotor sections mbili kuunganishwa axially. Researchers wanaeleza kwamba solution hii inaweza kutengeneza axial leakage flux, kuhitaji additional air gap kati ya rotors, kuongeza axial length ya motor na kufanya three-dimensional finite-element analysis kuwa necessary kwa electromagnetic-behavior evaluation.

Lengo la new study ni kupata similar harmonic-balancing effect si katika axial direction ya rotor, bali ndani ya circumferential pole arrangement ya single rotor.

Nini kinabadilika katika proposed rotor architecture?

Motors tatu zimelinganishwa:

• conventional CP-PMSM,
• CP-PMSM yenye symmetric pole arrangement,
• CP-PMSM yenye asymmetric pole arrangement.

Stator, slot na pole count, permanent-magnet shape, air gap, stack length na electromagnetic operating conditions za motors zimehifadhiwa sawa. Hivyo main difference katika results imelenga kutokea kwenye rotor-pole arrangement.

Symmetric rotor arrangement inafanyaje kazi?

Katika symmetric CP-PMSM, poles zimepangwa kwa N pole – iron pole – iron pole – S pole katika half mechanical period. Hivyo, tofauti na conventional CP-PMSM, permanent magnets za both N na S polarities zipo ndani ya same mechanical period.

Purpose ni kusambaza field effects za two different polarities kwa balance zaidi kuzunguka rotor na kupunguza magnetic asymmetry ya single-polarity conventional CP-PMSM.

Main flux ya permanent magnet hupita kupitia air gap hadi stator na kurudi kupitia adjacent iron pole. Hata hivyo, flux-path diagram ya study inaonyesha kwamba sehemu ya flux inaweza kuelekezwa kwenye permanent magnet nyingine badala ya intended iron pole, na kutengeneza leakage-flux path.

Kwa nini segmented rotor inatumika?

Katika proposed new structures zote mbili, rotor core imesegmented kati ya pole pairs. Purpose ni kufanya unwanted magnetic-leakage path kati ya permanent magnet na neighboring poles iwe difficult na kuelekeza larger share ya main flux kwenye air gap.

Researchers wanaeleza kwamba katika practical EPS motor, mechanical strength ya segmented rotor kama hii inaweza kuungwa mkono kwa non-magnetic bridges au retaining sleeves. Hata hivyo, mechanical solution hii haikutengenezwa kama physical prototype wala kufanyiwa strength test katika study.

Tofauti ya asymmetric rotor arrangement ni nini?

Asymmetric model pia inaunganisha N na S permanent-magnet poles na iron poles kwenye same rotor circumference; lakini sequence si symmetric katika mechanical period.

Kulingana na magnetic-flux-path analysis ya study, symmetric structure ina two distinct leakage-flux paths, wakati asymmetric structure ina one main leakage path kutoka N pole kuelekea S pole. Asymmetric pole arrangement hivyo inazalisha different air-gap field distribution na different torque/harmonic balance relative kwa symmetric structure.

Kwa nini iron-pole arc ratio ni critical?

Ili kutobadilisha permanent-magnet quantity katika rotor design, researchers wamehifadhi permanent-magnet arc ratio constant na kuchagua iron-pole arc ratio \(\alpha_{iron}\) ya lower-cost rotor iron kama main design variable.

Iron-pole arc ratio iliscanwa katika all models kati ya 0,4 na 0,9. Permanent-magnet arc ratio ilihifadhiwa fixed katika 0,8.

\(\alpha_{iron}\) inapobadilika:

• kiasi ambacho magnetic flux inaconcentrate katika iron pole,
• magnitude ya leakage flux,
• magnetic saturation ya iron pole,
• torque harmonics,
• average torque,
• torque ripple

hubadilika pamoja.

Kwa nini karibu 0,55 ilionekana advantageous?

Symmetric model ilichunguzwa kama detailed example. Flux paths na torque harmonics za \(\alpha_{iron}=0,4\), 0,55 na 0,9 conditions zililinganishwa.

Wakati \(\alpha_{iron}=0,4\), flux inaconcentrate zaidi kwenye iron pole kutokana na high magnetic reluctance. Wakati \(\alpha_{iron}=0,9\), magnetic reluctance ya leakage path kati ya neighboring iron poles hupungua na flux zaidi inaelekezwa kwenye undesired route.

Katika \(\alpha_{iron}=0,55\), study ilionyesha smoother flux distribution. Katika torque spectrum, dominant third na sixth harmonics zilionekana kupungua katika point hii, na torque ripple ikakaribia minimum huku average torque ikihifadhiwa.

Iron-pole arc ratios zilizochaguliwa kwa final comparison:

Air-gap magnetic field ilibadilikaje?

Katika conventional CP-PMSM, magnetic flux inadistribute kwa concentration zaidi na asymmetrically karibu na iron pole. Katika symmetric na asymmetric models, redistribution ya N na S magnets imeboresha balance kati ya positive na negative half-periods za air-gap flux density.

FFT analysis pia ilionyesha kwamba new structures zimesuppress baadhi ya low-order harmonics. Katika study, hili linaelezwa na dominant harmonics zinazotengenezwa na N-CP-PMSM na S-CP-PMSM kuwa na approximately opposite phase relationship.

Kwa sababu new rotors zinasambaza pole types hizi mbili kwenye single rotor circumference, si harmonics zote bali sehemu yake inaweza kujifuta.

BEMF waveform iliboreshwa kiasi gani?

Lower THD inaonyesha kwamba BEMF waveform iko closer na ideal sinusoidal shape. New rotor-pole arrangements zote mbili zilitoa lower harmonic distortion kuliko conventional CP-PMSM; symmetric structure ilitoa lowest value katika metric hii.

Main result katika torque ripple ni nini?

Katika final 2D finite-element analysis, average torque ya conventional motor ilikuwa 4,43 Nm na torque ripple %36,91.

Katika symmetric rotor arrangement, average torque ilishuka hadi 3,71 Nm huku torque ripple ikishuka hadi %2,76. Katika asymmetric rotor arrangement, average torque ilikuwa 3,94 Nm na torque ripple %3,59.

Important aspect ya results hizi ni kwamba absolute torque ripple katika 3D analysis ilikuwa higher kuliko 2D prediction. Axial leakage flux na end effects zilipojumuishwa, absolute performance numbers za 2D model hazikubaki exactly sawa. Hata hivyo, proposed rotor designs zote mbili ziliendelea kuonyesha significantly lower torque ripple kuliko conventional CP-PMSM.

Kwa nini average torque ilishuka?

Conventional CP-PMSM ilizalisha highest average torque kwa sababu ina lower leakage magnetic flux kuliko new structures. New pole arrangements ziliboresha magnetic-field symmetry na harmonic behavior, lakini pia zilitengeneza baadhi ya additional leakage-flux paths.

Kwa hiyo study haisemi kwamba new rotor arrangement ni superior katika every electromagnetic metric. Main result ni kupata much smoother torque output kwa kutoa sehemu fulani ya average torque.

Katika applications kama EPS ambapo driver anaweza kuhisi mechanical feedback directly kupitia steering wheel, researchers wanasema reductions katika torque ripple, vibration na cogging torque zinaweza kufanya trade-off hii kuwa meaningful.

Cogging torque ilibadilikaje?

Cogging torque ni no-load periodic torque component inayotokana na interaction ya rotor magnets na stator slots. Katika study, kubadilisha rotor-pole arrangement pia kulibadilisha cogging-torque harmonics kwa kiasi kikubwa.

Asymmetric design, ingawa ilionyesha harmonic distortion kidogo higher kuliko symmetric model kwa %3,6 BEMF THD, ilifikia lowest cogging torque ya 34,63 mNm. Result hii pia inaonyesha kwamba symmetric na asymmetric architectures zina different advantages katika different performance metrics.

Je, losses ziliongezeka?

Researchers pia walikagua kama low torque ripple ilipatikana kwa gharama ya higher electromagnetic loss.

Katika proposed models zote mbili, iron na magnet eddy-current losses zilizoripotiwa na study zilikuwa lower kuliko conventional model. Kwa hiyo katika electromagnetic conditions zilizochunguzwa, torque-ripple reduction haikupatikana kwa gharama ya kuongeza two main loss components hizi.

Kwa nini 2D design ni muhimu?

Main geometric advantage ya proposed structure ni kuunganisha N na S consequent-pole effects kwenye single rotor circumference badala ya kuweka sections mbili tofauti za motor stacked kwenye rotor axis.

Hivyo lengo ni kuepuka additional axial rotor length na axial air-gap requirement kati ya rotors mbili katika previous axial-combination approach.

Hata hivyo, study yenyewe pia ilifanya 3D FEA kwenye selected models. Kwa hiyo statement ya “haihitaji 3D analysis” haipaswi kumaanisha kwamba results ni completely independent of three-dimensional physical effects. Kwa kweli, 3D results zinaonyesha torque na torque-ripple values tofauti na 2D model.

Matokeo yanayoungwa mkono na utafiti

• Rearrangement ya N, S na iron poles kuzunguka rotor inaweza kuboresha air-gap magnetic-flux symmetry ya CP-PMSM.
• Proposed symmetric na asymmetric structures zilipunguza BEMF harmonic distortion katika model iliyochunguzwa.
• Katika 2D FEA, torque ripple ilishuka kutoka %36,91 hadi %2,76 na %3,59.
• 3D FEA ilibadilisha absolute values lakini ikahifadhi low-torque-ripple trend ya proposed structures.
• Cogging torque ilihesabiwa kuwa lower katika new rotor arrangements zote mbili kuliko conventional CP-PMSM.
• Iron loss na magnet eddy-current loss hazikuongezeka katika proposed models; badala yake lower values ziliripotiwa katika source.
• Iron-pole arc ratio iliathiri significantly balance kati ya torque na torque ripple.
• Kwa symmetric model, around \(\alpha_{iron}=0,55\) ilihusishwa na lower third na sixth torque harmonics.

Matokeo ambayo utafiti hauungi mkono au bado haujavalidate

• Proposed rotors hazijatestwa experimentally kwenye physical EPS motor prototype.
• Real vehicle steering feel au driver comfort haijapimwa.
• Hakuna physical sound measurement iliyofanywa kwa acoustic noise.
• Mechanical strength ya segmented rotor haijavalidated kwa experimental rotor-speed tests.
• Effect ya manufacturing tolerances kwenye torque ripple haijapimwa quantitatively.
• Inverter nonlinearities na real control-system errors hazijajumuishwa experimentally.
• Results za study haziwezi kuchukuliwa automatically kuwa valid kwa different pole/slot combinations au different motor sizes.
• Serial-production cost au manufacturability ya new structures haijatathminiwa kwa quantitative cost study.

Mbinu na Matokeo ya Utafiti

Main design parameters za finite-element model

Ili comparison ilenge rotor-pole arrangement, stator structure, pole/slot count, permanent-magnet shape, air-gap length, stack length na analysis conditions zilihifadhiwa sawa. Magnet na iron-pole thicknesses pia ziliwekwa fixed katika 3 mm kwa all models.

Analysis software na design approach

Electromagnetic analyses zilifanywa kwa ANSYS Maxwell 2024R1. Main design na parametric analysis zilifanywa kwa 2D FEA. Final selected rotors pia zilitathminiwa kwa three-dimensional FEA ili kukagua kama axial leakage flux na end effects zinabadilisha result trend.

Iron-pole arc-ratio sweep

Permanent-magnet arc ratio ilihifadhiwa fixed katika 0,8 huku iron-pole arc ratio ikibadilishwa katika range:

\[ 0,4 \leq \alpha_{iron} \leq 0,9 \]

.

Baada ya parametric analysis, kwa kuzingatia balance kati ya torque ripple na average torque:

• kwa conventional model \(\alpha_{iron}=0,50\),
• kwa symmetric model \(\alpha_{iron}=0,55\),
• kwa asymmetric model \(\alpha_{iron}=0,55\)

zilichaguliwa.

Definition ya torque ripple

Katika study, torque ripple ilihesabiwa kama:

\[ T_{ripple}= \frac{T_{max}-T_{min}}{T_{avg}}\times100\% \]

. Hapa \(T_{max}\) na \(T_{min}\) zinawakilisha maximum na minimum values za torque waveform, na \(T_{avg}\) ni average electromagnetic torque.

Definition ya cogging torque

Peak-to-peak cogging torque imefafanuliwa kwa:

\[ T_{cogging}=T_{cog,max}-T_{cog,min} \]

.

BEMF total harmonic distortion

Harmonic distortion ya back electromotive force waveform ilitathminiwa kwa:

\[ THD= \frac{\sqrt{\sum_{n=2}^{\infty}E_n^2}}{E_1} \]

. \(E_1\) inawakilisha fundamental harmonic amplitude na \(E_n\) n-th harmonic component. Lower THD ina maana BEMF waveform iko closer kwa sinusoidal form.

Final electromagnetic performance comparison

Je, kuna single winner kati ya symmetric na asymmetric structure?

Results zinaonyesha kwamba hakuna single model iliyo best katika all performance metrics.

Symmetric design:

• imetoa lowest 2D torque ripple: %2,76,
• imetoa lowest 3D torque ripple: %6,0,
• imetoa lowest BEMF THD value: %3,2,
• lakini ina lower average torque kati ya proposed models mbili.

Asymmetric design:

• 2D torque yake ni higher kuliko symmetric structure kwa 3,94 Nm,
• 3D torque yake ni higher kuliko symmetric structure kwa 3,83 Nm,
• imetoa lowest cogging torque ya 34,63 mNm,
• lakini torque ripple ni kidogo higher kuliko symmetric structure.

Kwa hiyo rotor selection inategemea ni metric gani inapewa priority zaidi kati ya torque capacity, torque ripple, cogging torque na BEMF harmonics.

Difference kati ya 2D na 3D results ina maana gani?

Katika 3D model, torque ya conventional motor imebadilika kutoka 4,43 Nm hadi 4,36 Nm, torque ya symmetric model kutoka 3,71 Nm hadi 3,60 Nm, na torque ya asymmetric model kutoka 3,94 Nm hadi 3,83 Nm.

More pronounced difference iko kwenye torque ripple: wakati symmetric na asymmetric models zilitoa %2,76 na %3,59 katika 2D analysis, values zilikuwa %6,0 na %7,5 katika 3D analysis. Hii inaonyesha kwamba axial leakage flux na end effects zinaweza kuwa important kwa absolute result.

Hata hivyo, main ranking kati ya models tatu haikubadilika. Kwa hiyo researchers wanatathmini kwamba 2D design approach imecapture correctly main trend kati ya rotor-pole arrangements.

Numerical inconsistencies ndani ya source

Torque-ripple reduction: Abstract ya article inataja approximately 33,3 na 34,1 percentage-point reductions kwa proposed models. Katika final Table 2, conventional, symmetric na asymmetric values ni %36,91, %2,76 na %3,59 mtawalia. Raw values hizi zinatoa approximately 34,15 percentage-point difference kwa symmetric na approximately 33,32 kwa asymmetric. Kwa hiyo relation ya reductions mbili katika abstract na model ordering haiko wazi.

Values katika introduction: Introduction inasema torque ripple kwa symmetric na asymmetric models imepungua approximately 42,61 na 41,78 percentage points relative kwa conventional motor. Numbers hizi hazilingani mathematically na initial torque ripple ya %36,91 katika final Table 2. Raw values za Table 2 zimetumika katika final performance comparison.

Average-torque reduction: Katika same introduction paragraph, average torque inasemekana kupungua approximately %14,12 na %8,98 katika symmetric na asymmetric models. Final Table 2, however, ina 2D torque values za 4,43, 3,71 na 3,94 Nm. Difference hii kati ya percentages katika source na final table haijasahihishwa kimya kimya.

Experimental-validation boundary

Study haikufanya physical motor manufacturing, dynamometer test, real EPS system test au vehicle test. Results zote zinategemea electromagnetic finite-element analysis.

Waandishi wanaeleza wazi kwamba katika practical application, manufacturing tolerances, assembly errors, inverter nonlinearity na mechanical vibration zinaweza kusababisha difference kati ya simulation na measurement. Ingawa proposed rotor arrangement inatarajiwa kuhifadhi torque-ripple-reduction trend katika practice, expectation hii haijathibitishwa experimentally katika current study.

Maelezo ya Chanzo na Mbinu

Jina kamili asilia la utafiti: Design of Rotor Pole Arrangement for Torque Ripple Reduction in Consequent Pole Permanent Magnet Synchronous Motors

Waandishi: Chaewon Jo, Seonghwi Kim, Ju Lee.

Author order: Order katika source imehifadhiwa exactly.

Corresponding author: Ju Lee.

Equal contribution/co-first author: Hakuna statement kama hiyo katika source.

Taasisi: Department of Electrical Engineering, Hanyang University, Seoul, Republic of Korea; The Industry-University Cooperative Foundation, Hanyang University, Seoul, Republic of Korea.

Jarida: Machines.

Mchapishaji: MDPI.

Bibliographic record: Machines 2026, 14(6), 662.

DOI: 10.3390/machines14060662.

Official publication link:https://doi.org/10.3390/machines14060662

Publication date: 8 June 2026.

Source type na peer-review status: Ni peer-reviewed original research article. Scientific validation inategemea finite-element analysis na model comparison.

Leseni: Creative Commons Attribution (CC BY).

Funding: Study iliungwa mkono na Korea Institute of Energy Technology Evaluation and Planning (KETEP) na Republic of Korea Ministry of Trade, Industry & Energy (MOTIE) chini ya No. RS-2024-00420625.

Data availability: Imeelezwa kwamba original contributions za research ziko kwenye article na additional questions zinaweza kuelekezwa kwa corresponding author.

Conflict of interest: Waandishi wametangaza kwamba hakuna conflict of interest.

Author contributions: Chaewon Jo na Ju Lee katika conceptualization; Chaewon Jo katika methodology, software, formal analysis, investigation na data curation; Chaewon Jo na Ju Lee katika validation; Chaewon Jo na Seonghwi Kim katika review/editing na visualization; Ju Lee katika supervision, project administration na funding acquisition. Source inaeleza kwamba authors wote wamesoma na kuapprove published version.

Motor geometries, magnetic-flux explanations, analysis conditions, formulas, harmonic behavior, torque, torque ripple, cogging torque na loss values katika Verianla article hii zinategemea source study iliyochunguzwa. Hakuna new scientific experiment au finding kutoka external sources iliyoongezwa isipokuwa bibliographic identity verification.

Main methodological boundary: Study haina experimental validation kwenye physical motor prototype au real EPS system. Main design ilitengenezwa kwa 2D finite-element analysis na selected structures zikakaguliwa additionally kwa 3D FEA. Manufacturing tolerances, assembly errors, inverter effects, mechanical vibration, rotor mechanical strength na real vehicle conditions hazijatathminiwa experimentally.

Source-internal numerical inconsistency note: Kuna baadhi ya percentage statements zisizolingana kati ya abstract, introduction na final Table 2 kuhusu torque-ripple reduction na average-torque decrease. Kwa hiyo katika Verianla article, raw values zilizotolewa wazi katika Table 2 zimetumika kwa final electromagnetic comparison, na other statements hazijasahihishwa kimya kimya.