Omnidirectional magnetic field generators, or Omnimagnets, are electromagnetic devices used for non-contact manipulation tasks. Supplying current to an Omnimagnet generates a magnetic field and generates Joule heating, which can cause overheating. Omnimagnets are thermally limited. Omnimagnet design currently relies on advanced thermal-electromagnetic simulations, which can vary widely between applications. Currently, there is no generalized understanding for coupled thermal-electromagnetic effects. This work addresses this knowledge gap by developing a universal framework for estimating Omnimagnet performance directly from the design and operating conditions. Scaling analysis is used to determine the coupling between thermal and electromagnetic effects in terms of design variables and base principles. The scaling relationships are used to define a figure of merit <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta\)</EquationSource> </InlineEquation> where a higher <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta\)</EquationSource> </InlineEquation> indicates a superior design. Equations are fitted to simulated Omnimagnet performance for multiple cooling mechanisms (convection, radiation) and different electromagnetic priorities (dipole moment m, m/mass). Quantitative relationships are developed that can predict Omnimagnet performance across a spectrum of designs without requiring advanced thermal and electromagnetic simulations (i.e. <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(m =\)</EquationSource> </InlineEquation> 530<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq4.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="36" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta _{conv}\)</EquationSource> </InlineEquation> for convectively-cooled Omnimagnets, where <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq5.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="223" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta _{conv} = h^{0.5}(T_{max}-T_{\infty })^{0.5}L_{max}^{3.5}\)</EquationSource> </InlineEquation> is the figure of merit). The figure of merit <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41598_2025_16141_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\eta\)</EquationSource> </InlineEquation> can also be used to gauge Omnimagnet performance for new applications, as is shown for power-sensitive Omnimagnets. Using this methodology, non-experts can use a figure of merit to streamline the design of Omnimagnets for new or existing use cases. The methodology is broadly applicable for the design of similar electromagnetic devices such as electrical motors, generators, and electromagnets.

Predicting thermal and electromagnetic performance of omndirectional magnetic field generators via figure of merit

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2025年8月28日

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Mason Pratt,
Tim Ameel,
Sameer R. Rao

摘要

Omnidirectional magnetic field generators, or Omnimagnets, are electromagnetic devices used for non-contact manipulation tasks. Supplying current to an Omnimagnet generates a magnetic field and generates Joule heating, which can cause overheating. Omnimagnets are thermally limited. Omnimagnet design currently relies on advanced thermal-electromagnetic simulations, which can vary widely between applications. Currently, there is no generalized understanding for coupled thermal-electromagnetic effects. This work addresses this knowledge gap by developing a universal framework for estimating Omnimagnet performance directly from the design and operating conditions. Scaling analysis is used to determine the coupling between thermal and electromagnetic effects in terms of design variables and base principles. The scaling relationships are used to define a figure of merit \(\eta\) where a higher \(\eta\) indicates a superior design. Equations are fitted to simulated Omnimagnet performance for multiple cooling mechanisms (convection, radiation) and different electromagnetic priorities (dipole moment m, m/mass). Quantitative relationships are developed that can predict Omnimagnet performance across a spectrum of designs without requiring advanced thermal and electromagnetic simulations (i.e. \(m =\) 530 \(\eta _{conv}\) for convectively-cooled Omnimagnets, where \(\eta _{conv} = h^{0.5}(T_{max}-T_{\infty })^{0.5}L_{max}^{3.5}\) is the figure of merit). The figure of merit \(\eta\) can also be used to gauge Omnimagnet performance for new applications, as is shown for power-sensitive Omnimagnets. Using this methodology, non-experts can use a figure of merit to streamline the design of Omnimagnets for new or existing use cases. The methodology is broadly applicable for the design of similar electromagnetic devices such as electrical motors, generators, and electromagnets.