Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws
In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple...
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| Veröffentlicht in: | IEEE transactions on magnetics 2016-08, Vol.52 (8), p.1-13 |
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| creator | Carlstedt, Matthias Weise nee Porzig, Konstantin Ziolkowski, Marek Schmidt, Reinhard Brauer, Hartmut |
| description | In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples. |
| doi_str_mv | 10.1109/TMAG.2016.2539927 |
| format | Article |
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Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples.</description><identifier>ISSN: 0018-9464</identifier><identifier>EISSN: 1941-0069</identifier><identifier>DOI: 10.1109/TMAG.2016.2539927</identifier><identifier>CODEN: IEMGAQ</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Constants ; Dimensional analysis ; eddy currents ; Force ; Lorentz covariance ; Lorentz force ; Magnetic levitation ; Magnetism ; Mathematical analysis ; Mathematical model ; Mathematical models ; Maxwell's equations ; permanent magnet (PM) ; Permeability ; Representations ; Scaling laws ; similarity ; Superconducting magnets</subject><ispartof>IEEE transactions on magnetics, 2016-08, Vol.52 (8), p.1-13</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2016</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c326t-82090d2d3d29c786969caf2496399388b3d8941e4661efc7c42f6a3c292dc0903</citedby><cites>FETCH-LOGICAL-c326t-82090d2d3d29c786969caf2496399388b3d8941e4661efc7c42f6a3c292dc0903</cites><orcidid>0000-0002-1598-6429</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/7429773$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/7429773$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>Carlstedt, Matthias</creatorcontrib><creatorcontrib>Weise nee Porzig, Konstantin</creatorcontrib><creatorcontrib>Ziolkowski, Marek</creatorcontrib><creatorcontrib>Schmidt, Reinhard</creatorcontrib><creatorcontrib>Brauer, Hartmut</creatorcontrib><title>Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws</title><title>IEEE transactions on magnetics</title><addtitle>TMAG</addtitle><description>In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples.</description><subject>Constants</subject><subject>Dimensional analysis</subject><subject>eddy currents</subject><subject>Force</subject><subject>Lorentz covariance</subject><subject>Lorentz force</subject><subject>Magnetic levitation</subject><subject>Magnetism</subject><subject>Mathematical analysis</subject><subject>Mathematical model</subject><subject>Mathematical models</subject><subject>Maxwell's equations</subject><subject>permanent magnet (PM)</subject><subject>Permeability</subject><subject>Representations</subject><subject>Scaling laws</subject><subject>similarity</subject><subject>Superconducting magnets</subject><issn>0018-9464</issn><issn>1941-0069</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkE9LwzAYh4MoOKcfQLwEvHjpzL8ljbcxtylUPGzehBDTVDLaZiYtMj-9KRsevOQlvM_vhd8DwDVGE4yRvN-8zFYTgjCfkCmVkogTMMKS4QwhLk_BCCGcZ5Jxdg4uYtymL5tiNALvi9i5RnfOt9BXsPDBtt0PXPpgLFwG38BH19g2pr2u4Sw9--jiA1y7xtU6uG4P177uh3yEui3h2ujatZ-w0N_xEpxVuo726jjH4G252MyfsuJ19TyfFZmhhHdZTpBEJSlpSaQROZdcGl0RJnlqQvP8g5Z5qmIZ59hWRhhGKq6pIZKUJkXpGNwd7u6C_-pt7FTjorF1rVvr-6hwTqecMSlwQm__oVvfh1RroBBPVpAUicIHygQfY7CV2oVkKewVRmrwrQbfavCtjr5T5uaQcdbaP14wIoWg9Bd2rHrC</recordid><startdate>201608</startdate><enddate>201608</enddate><creator>Carlstedt, Matthias</creator><creator>Weise nee Porzig, Konstantin</creator><creator>Ziolkowski, Marek</creator><creator>Schmidt, Reinhard</creator><creator>Brauer, Hartmut</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SP</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>JG9</scope><scope>L7M</scope><scope>F28</scope><scope>FR3</scope><orcidid>https://orcid.org/0000-0002-1598-6429</orcidid></search><sort><creationdate>201608</creationdate><title>Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws</title><author>Carlstedt, Matthias ; Weise nee Porzig, Konstantin ; Ziolkowski, Marek ; Schmidt, Reinhard ; Brauer, Hartmut</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c326t-82090d2d3d29c786969caf2496399388b3d8941e4661efc7c42f6a3c292dc0903</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Constants</topic><topic>Dimensional analysis</topic><topic>eddy currents</topic><topic>Force</topic><topic>Lorentz covariance</topic><topic>Lorentz force</topic><topic>Magnetic levitation</topic><topic>Magnetism</topic><topic>Mathematical analysis</topic><topic>Mathematical model</topic><topic>Mathematical models</topic><topic>Maxwell's equations</topic><topic>permanent magnet (PM)</topic><topic>Permeability</topic><topic>Representations</topic><topic>Scaling laws</topic><topic>similarity</topic><topic>Superconducting magnets</topic><toplevel>online_resources</toplevel><creatorcontrib>Carlstedt, Matthias</creatorcontrib><creatorcontrib>Weise nee Porzig, Konstantin</creatorcontrib><creatorcontrib>Ziolkowski, Marek</creatorcontrib><creatorcontrib>Schmidt, Reinhard</creatorcontrib><creatorcontrib>Brauer, Hartmut</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on magnetics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Carlstedt, Matthias</au><au>Weise nee Porzig, Konstantin</au><au>Ziolkowski, Marek</au><au>Schmidt, Reinhard</au><au>Brauer, Hartmut</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws</atitle><jtitle>IEEE transactions on magnetics</jtitle><stitle>TMAG</stitle><date>2016-08</date><risdate>2016</risdate><volume>52</volume><issue>8</issue><spage>1</spage><epage>13</epage><pages>1-13</pages><issn>0018-9464</issn><eissn>1941-0069</eissn><coden>IEMGAQ</coden><abstract>In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. 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| subjects | Constants Dimensional analysis eddy currents Force Lorentz covariance Lorentz force Magnetic levitation Magnetism Mathematical analysis Mathematical model Mathematical models Maxwell's equations permanent magnet (PM) Permeability Representations Scaling laws similarity Superconducting magnets |
| title | Estimation of Lorentz Force From Dimensional Analysis: Similarity Solutions and Scaling Laws |
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