This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

In the case of rotating electrical machines, the magnetic forces acting on the stator teeth are the principal electromagnetic cause of vibrations. Based on this fact, this paper presents a method to compute the vibrations of an induction motor with the aid of magnetic nodal forces. An accurate computation of local or nodal forces is essential in problems pertaining to vibration and noise analysis of electrical machines. Virtual work method is utilized here to compute the nodal forces as the local derivative of magnetic energy from the Finite Element (FE) solution of the magnetic field problem. The magnetic problem is then coupled to an elasticity solver to calculate the displacement due to these forces. The nodal force method is implemented in an open source finite element software Elmer and the entire magneto-mechanical computation is carried out in the same open source tool. The calculated results are then compared to vibration measurements of the motor.

This paper presents the vibration analysis and results of an induction motor through two kinds of magneto-mechanical coupling methods. The computation results are validated by comparing them with the vibration measurements of the motor. The role of both the magnetic forces and magnetostriction are examined and distinguished based on their contribution to the vibration behavior of the machine. It was found that the pole pair number of an induction machine can affect the way the vibrations caused by magnetostriction and magnetic forces either add up or oppose each other.

Paired associative stimulation (PAS) is a stimulation technique combining transcranial magnetic stimulation (TMS) and peripheral nerve stimulation (PNS) that can induce plastic changes in the human motor system. A PAS protocol consisting of a high-intensity single TMS pulse given at 100% of stimulator output (SO) and high-frequency 100-Hz PNS train, or “the high-PAS” was designed to promote corticomotoneuronal synapses. Such PAS, applied as a long-term intervention, has demonstrated therapeutic efficacy in spinal cord injury (SCI) patients. Adding a second TMS pulse, however, rendered this protocol inhibitory. The current study sought for more effective PAS parameters. Here, we added a third TMS pulse, i.e., a 20-Hz rTMS (three pulses at 96% SO) combined with high-frequency PNS (six pulses at 100 Hz). We examined the ability of the proposed stimulation paradigm to induce the potentiation of motor-evoked potentials (MEPs) in five human subjects and described the safety and tolerability of the new protocol in these subjects. In this study, rTMS alone was used as a control. In addition, we compared the efficacy of the new protocol in five subjects with two PAS protocols consisting of PNS trains of six pulses at 100 Hz combined with (a) single 100% SO TMS pulses (high-PAS) and (b) a 20-Hz rTMS at a lower intensity (three pulses at 120% RMT). The MEPs were measured immediately after, and 30 and 60 min after the stimulation. Although at 0 and 30 min there was no significant difference in the induced MEP potentiation between the new PAS protocol and the rTMS control, the MEP potentiation remained significantly higher at 60 min after the new PAS than after rTMS alone. At 60 min, the new protocol was also more effective than the two other PAS protocols. The new protocol caused strong involuntary twitches in three subjects and, therefore, its further characterization is needed before introducing it for clinical research. Additionally, its mechanism plausibly differs from PAS with high-frequency PNS that has been used in SCI patients.

This paper presents an efficient method to calculate the magnetic forces on bodies in contact. The forces are computed through the local application of the virtual work principle on degenerated air-gap elements. The results from this method are compared with those from other software and validated with measurements on a permanent magnet setup. Not only is this technique very accurate, but it also reduces the computational burden related to the problematic meshing of thin layers. The implementation of this method in an open source finite element software having facilities for higher order elements and parallel computation unlocks a cost effective and effectual platform for an electromechanical computation of electromechanical devices and magnetic materials.

Introduction: Transcranial magnetic stimulation (TMS) is widely employed to treat various psychiatric and neurological disorders. However, TMS protocols typically rely on generalizations, particularly in selecting stimulation intensities, leading to suboptimal and variable outcomes. Combining TMS with electroencephalography (EEG) offers a potential solution by allowing direct monitoring of stimulation effects. In this study, we investigate how features of the TMS–EEG signal change with intensity to identify thresholds implying qualitative shifts in the brain response. Methods: We stimulated eight subjects at both the primary motor cortex (M1) and the pre-supplementary motor area (pre-SMA) with navigated TMS at 15 closely spaced intensities and measured TMS-evoked EEG responses (TMS-evoked potential, TEP) with 60 trials per intensity. TEP thresholds were identified with three methods: by selecting the intensity where the TEP peak-to-peak exceeds 6 μV, or by fitting either piecewise-linear or sigmoid curves into the power spectral density (PSD) frequency components to identify nonlinear intensity behavior. Results: The identified TEP thresholds varied depending on subject, target, and identification method. In M1, the thresholds attained with the fixed-amplitude and piecewise PSD fit methods averaged around the motor threshold, and in pre-SMA around 120% of the motor threshold. The TEP thresholds yielded by the sigmoid fit method were higher in intensity, and least consistent between subjects. Conclusions: Our findings support the hypothesis that detectable changes in EEG patterns occur at specific TMS intensities. These results provide a basis for individualized stimulation dosing, potentially enhancing therapeutic efficacy and reliability. Future research should focus on refining these methods and validating their clinical applicability across diverse conditions and patient populations.