Equations for the approximate calculation of forces between cuboid magnets

Schomburg, Werner Karl; Reinertz, Olivier; Sackmann, Johannes; Schmitz, Katharina

doi:10.1016/j.jmmm.2020.166694

Cited by 19 publications

(13 citation statements)

References 30 publications

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“…Better approximation is achieved in case of large distance between the magnets. A possible improvement, from an energetic point of view, is the approach of Schomburg et al [29] in which the interaction is more spread in the space domain with respect to the inverse square formula. However, this formula is quite poor in the representation of the F y component and it requires two fitting parameters ( F 0 and d e ) making necessary experimental data or finite element simulations.…”

Section: Discussionmentioning

confidence: 99%

“…Given the analogy between the magnetic and the electrostatic problems, Pillatsch et al in [16] introduced an additional semplification and assumed an inverse square relationship between the magnetic force and the relative distance between the magnets. Similarly, Schomburg et al in [29] assumed a sort of inverse square relationship but with two fitting parameters instead of the single parameter of the classical inverse square.…”

Section: Magnetic Interaction: Analytical Formulasmentioning

confidence: 99%

“…Moreover, the y-component can be computed with the following expression [29] (under the assumption that A ≥ a):…”

Section: Fig 1 Schematization Of Interacting Magnets In the Yonnet An...mentioning

confidence: 99%

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Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

2022

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The purpose of this work is to improve the modelling process for the application of permanent magnets in a frequency up-conversion (FuC) mechanism for piezoelectric energy harvesters. More specifically, the aim is to avoid the burdensome finite element analyses (FEA) in the framework of electromechanical devices design. The analytical calculations are compared with experimental tests conducted by an ad-hoc set up and with FEA. After investigations on the interaction, an application of FuC mechanism is proposed on a meso-scale case study in which a low frequency seismic mass (LFM) interacts non-linearly, due to magnetic field, with an high frequency piezoelectric vibration energy harvester (PVEH). Numerical simulations have been carried out in the time domain (step-by-step analysis) under a harmonic low-frequency input acceleration signal. The peculiar behavior, due to non-linear dynamics, is investigated in both the repulsive and the attractive configurations of the magnets. The results confirm the effectiveness of magnetic FuC and show that the repulsive case allows the device to recover a larger amount of energy than the attractive configuration.

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Section: Discussionmentioning

confidence: 99%

Section: Magnetic Interaction: Analytical Formulasmentioning

confidence: 99%

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Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

2022

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“…To approximate the normal force F normal between two magnets for a specific gap size z and the maximum lateral force F lateral,m at the same distance, equations (1) and (2) published in [7]. Variable L 1 and L 2 is the length parallel to the lateral force vector, equal for both selected magnets.…”

Section: A Magnet Calculation and Placementmentioning

confidence: 99%

Multi-actuated AUV Body for Windfarm Inspection: Lessons from the Bio-inspired RoboFish Field Trials

Wright

Gorma

Post

et al. 2020

2020 IEEE/OES Autonomous Underwater Vehicles Symposium (AUV)

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An innovative magnetic joint design has been developed as part of the construction of a bio-inspired Autonomous Underwater Vehicle (AUV) for wind farm inspection. This paper presents our design solutions for a jointed watertight AUV body made using current 3D printing techniques to achieves watertightness and resilient composite metal-polymer bonding. The design avoids dynamic interfaces and the need for rotary seals yet achieves robustness and strength. Test results prove a successful implementation of the magnetic connection between a freely rotating inner shaft and a driven outer shaft in a fish-like jointed AUV body.

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“…The calculations have also been extended to magnets in arrays and devices [9,10]. In addition to analytic solutions, magnetic field distributions have increasingly been simulated by the finite element method for permanent magnets of a variety of geometries such as cuboid [11] ring [12] and disk [13].…”

Section: Introductionmentioning

confidence: 99%

Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

Cheedket

Sirisathitkul

2021

Eureka: PE

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The force between permanent magnets implemented in many engineering devices remains an intriguing problem in basic physics. The variation of magnetic force with the distance x between a pair of magnets cannot usually be approximated as x-4 because of the dipole nature and geometry of magnets. In this work, the force between two identical cylindrical magnets is accurately described by a closed-form solution. The analytical model assumes that the magnets are uniformly magnetized along their length. The calculation, based on the magnetic field exerted by one magnet on the other along the direction of their orientation, shows a reduction in the magnetic force with the distance x and a dependence on the size parameters of magnets. To verify the equation, the experiment was set up by placing two cylindrical neodymium iron boron type magnets in a vertical tube. The repulsive force between the identical upper and lower magnets of 2.5 cm in diameter and 7.5 cm in length was measured from the weight on the top of the upper magnet. The resulting separation between the magnets was recorded as x. The forces measured at x=0.004-0.037 m differ from the values calculated using the analytic solution by -0.55 % to -13.60 %. The calculation also gives rise to a practical remnant magnetic field of 1.206 T. When x is much large than the equation of force is approximated as a simple form proportional to 1/x-4. The finding can be directly used in magnetic levitation as well as applied in calculating magnetic fields and forces in other systems incorporating permanent magnets.

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Equations for the approximate calculation of forces between cuboid magnets

Cited by 19 publications

References 30 publications

Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

Numerical and experimental evaluation of the magnetic interaction for frequency up-conversion in piezoelectric vibration energy harvesters

Multi-actuated AUV Body for Windfarm Inspection: Lessons from the Bio-inspired RoboFish Field Trials

Comparison of closed-form solutions to experimental magnetic force between two cylindrical magnets

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