Fully Analytical Calculation Method for Suspension Force Between Permanent Magnet and Coil in Magnetic Levitation Positioning Systems

Fully Analytical Calculation Method for Suspension Force Between Permanent Magnet and Coil in Magnetic Levitation Positioning Systems | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Fully Analytical Calculation Method for Suspension Force Between Permanent Magnet and Coil in Magnetic Levitation Positioning Systems 陈墨仙 This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8533815/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In six-degree-of-freedom (6-DoF) magnetic levitation positioning systems, accurate calculation of the suspension force between permanent magnets and coils is critical for system design and control. A fully analytical calculation method is proposed for the repulsive suspension force between square coils and cubic permanent magnets. This method derives a closed-form analytical expression for the x-component magnetic flux density B x generated by the permanent magnet in space using the magnetic charge model and Maxwell’s equations, and further obtains an analytical integral formula for the z-component suspension force F z through the Lorentz force equation. Compared with traditional three-dimensional finite element method (3D-FEM), the fully analytical method can compute the force field distribution quickly and accurately without numerical integration. By introducing an integration range correction coefficient and dynamically adjusting the integration boundaries of the four coil sides, the accuracy of force calculation under displacement variations is effectively improved. Experimental verification results show that the error between analytical calculation results and measured values is less than 5%, meeting the design requirements of high-precision magnetic levitation positioning systems. Magnetic levitation Fully analytical method Magnetic charge model Lorentz force Coefficient correction Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Positioning Systems\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Magnetic levitation, Fully analytical method, Magnetic charge model, Lorentz force, Coefficient correction","lastPublishedDoi":"10.21203/rs.3.rs-8533815/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8533815/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn six-degree-of-freedom (6-DoF) magnetic levitation positioning systems, accurate calculation of the suspension force between permanent magnets and coils is critical for system design and control. A fully analytical calculation method is proposed for the repulsive suspension force between square coils and cubic permanent magnets. This method derives a closed-form analytical expression for the x-component magnetic flux density \u003cem\u003eB\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e generated by the permanent magnet in space using the magnetic charge model and Maxwell’s equations, and further obtains an analytical integral formula for the z-component suspension force \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e through the Lorentz force equation. Compared with traditional three-dimensional finite element method (3D-FEM), the fully analytical method can compute the force field distribution quickly and accurately without numerical integration. By introducing an integration range correction coefficient and dynamically adjusting the integration boundaries of the four coil sides, the accuracy of force calculation under displacement variations is effectively improved. Experimental verification results show that the error between analytical calculation results and measured values is less than 5%, meeting the design requirements of high-precision magnetic levitation positioning systems.\u003c/p\u003e","manuscriptTitle":"Fully Analytical Calculation Method for Suspension Force Between Permanent Magnet and Coil in Magnetic Levitation Positioning Systems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-08 03:20:36","doi":"10.21203/rs.3.rs-8533815/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0ed653a5-80d5-4a64-957d-bcfcf642d0c0","owner":[],"postedDate":"January 8th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-01-08T03:20:36+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-08 03:20:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8533815","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8533815","identity":"rs-8533815","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}