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Vibration isolation is one of the most efficient approaches to protecting host structures from harmful vibrations, especially in aerospace, mechanical, and architectural engineering, etc. Traditional linear vibration isolation is hard to meet the requirements of the loading capacity and isolation band simultaneously, which limits further engineering application, especially in the low-frequency range. In recent twenty years, the nonlinear vibration isolation technology has been widely investigated to broaden the vibration isolation band by exploiting beneficial nonlinearities. One of the most widely studied objects is the “three-spring” configured quasi-zero-stiffness (QZS) vibration isolator, which can realize the negative stiffness and high-static-low-dynamic stiffness (HSLDS) characteristics. The nonlinear vibration isolation with QZS can overcome the drawbacks of the linear one to achieve a better broadband vibration isolation performance. Due to the characteristics of fast response, strong stroke, nonlinearities, easy control, and low-cost, the nonlinear vibration with electromagnetic mechanisms has attracted attention. In this review, we focus on the basic theory, design methodology, nonlinear damping mechanism, and active control of electromagnetic QZS vibration isolators. Furthermore, we provide perspectives for further studies with electromagnetic devices to realize high-efficiency vibration isolation.

Electrical machines are important devices that convert electric energy into mechanical work and are widely used in industry and people’s life. Undesired vibrations are harmful to their safe operation. Reviews from the viewpoint of fault diagnosis have been conducted, while summaries from the perspective of dynamics is rare. This review provides systematic research outlines of this field, which can help a majority of scholars grasp the ongoing progress and conduct further investigations. This review mainly generalizes publications in the past decades about the dynamics and vibration of electrical machines. First the sources of electromagnetic vibration in electrical machines are presented, which include mechanical and electromagnetic factors. Different types of air gap eccentricity are introduced and modeled. The analytical methods and numerical methods for calculating the electromagnetic force are summarized and explained in detail. The exact subdomain analysis, magnetic equivalent circuit, Maxwell stress tensor, winding function approach, conformal mapping method, virtual work principle and finite element analysis are presented. The effects of magnetic saturation, slot and pole combination and load are discussed. Then typical characteristics of electromagnetic vibration are illustrated. Finally, the experimental studies are summarized and the authors give their thoughts about the research trends.

Torque ripple and radial electromagnetic (EM) vibration can lead to motor vibration and noise, which are crucial to the motor’s NVH (Noise, Vibration, and Harshness) performance. Researchers focus on two main aspects: motor body design and control strategy, employing various methods to optimize the motor and reduce torque ripple and radial EM vibration. Rotor notching and segmented rotor skewing are frequently used techniques. However, determining the optimal notch and skew strategy has been an ongoing challenge for researchers. In this paper, an 8-pole, 36-slot ISG motor is optimized using a combination of Q-axis and magnetic bridge notching (QMC notch) as well as segmented rotor skewing to reduce torque ripple and radial EM vibration. Three skewing strategies—step skew (SS), V-shape skew (VS), and zigzag skew (ZS)—along with four segmentation cases are thoroughly considered. The results show that the QMC notch significantly reduces torque ripple, while skewing designs greatly diminish radial EM vibrations. However, at 14 fe, the EM vibration frequency is close to the motor’s third-order natural frequency, leading to mixed results in vibration reduction using skewing techniques. After a comprehensive analysis of all skewing strategies, four-segment VS and ZS are recommended as the optimal approaches.

In order to solve the defect that the intrinsic frequency ω 0 of the diamagnetic levitation electromagnetic vibration energy harvester cannot be adjusted, a pulling magnet with downward attraction to the floating magnet is added below the floating magnet of the original structure. The simulation found multiple ω 0 exist in the structure with the pulling magnet, and the relationship between ω 0 and the vertical distance L L from the lifting magnet’s lower surface to the floating magnet’s upper surface is determined. It is found that ω 0 can be varied from 2.36 to 12.3 Hz by adjusting L L . The dynamic characteristics of the floating magnet is studied to obtain its amplitude-frequency curve. The output performance of the energy harvester at different ω 0 is calculated and the simulation results are well verified experimentally. The experiments show that the effective voltages can all reach their maximum after arranging the induction coil when the excitation frequency is from 2.2 to 6.1 Hz. The frequency band width for effective voltages greater than 400 mV is made up to 7.6 Hz. The maximum effective voltage of the structure with the pulling magnet is 749 mV, which is 1.98 times larger than the structure without a pulling magnet; the maximum power is 779 µW, which is 7.9 times larger than the structure without a pulling magnet. Experiments show that the structure with the pulling magnet not only significantly broadens the effective bandwidth of the energy harvester, but also significantly improves the output performance of the energy harvester. In addition, the nonlinear characteristics of the system make it possible to obtain good output performance even when the vibration frequency is far from ω 0 .

The use of limited power motors fixed to flexible structures is widely used in engineering and has seen a significant increase in published studies. These components form a non-ideal system, which can cause undesirable phenomena throughout its execution, such as the capture of parametric oscillation by resonance, studied by Sommerfeld, whose effect bears his name. One study, on a vibration absorber in a non-ideal system, was done in Petrocino et al., Meccanica, v. 58, n. 1, p. 287-302, 2023, on a model that represents a fixed beam and at the free end a motor with its unbalanced shaft. In this work, based on the equations that govern the movement, an analytical development was carried out, using the average method, to obtain an approximate solution and numerical simulations with the absorber on and off. The results demonstrated a reduction in parametric excitation, an effect caused by the electromagnetic absorber. Based on the parameters of this revisited work, a prototype was built to carry out experimental tests. A beam was fixed at one end and at the free end a DC motor was fixed with an unbalance on its axis, a magnet fixed at the free end immersed in the core of a coil as a damping actuator. When the motor is accelerated, it causes a parametric excitation in the beam and is captured by resonance, where the damping action is evident. The results of the tests were compared with the results of the models from the revisited work, validating the performance of the passive electromagnetic vibration absorber.

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

In recent years, distributed energy power supply systems have been widely used in remote areas and extreme environments. However, the intermittent and uncertain output power may cause power grid fluctuations, leading to higher harmonics in electromechanical equipment, especially motors. For permanent magnet synchronous motor (PMSM) systems, an electromagnetic (EM) vibration can cause problems such as energy loss and mechanical wear. Therefore, it is necessary to design control algorithms that can effectively suppress EM vibration. To this end, a vibration suppression algorithm for fractional-slot permanent magnet synchronous motors based on a d-axis current injection is proposed in this paper. Firstly, this paper analyzes the radial electromagnetic force of the fractional-slot PMSM to identify the main source of EM vibration in fractional-slot PMSMs. Based on this, the intrinsic relationship between the EM vibration of fractional-slot PMSMs and the d-axis and q-axis currents is explored, and a method for calculating the d-axis current to suppress the vibration is proposed. Experimental verification shows that the proposed algorithm can effectively suppress EM vibration.

Electromagnetic Vibration Energy Harvesting (EM-VEH) is an attractive alternative to batteries as a power source for wireless sensor nodes that enable intelligence at the edge of the Internet of Things (IoT). Industrial environments in particular offer an abundance of available kinetic energy, in the form of machinery vibrations that can be converted into electrical power through energy harvesting techniques. These ambient vibrations are generally broadband, and multi-modal harvesting configurations can be exploited to improve the mechanical-to-electrical energy conversion. However, the additional challenge of energy conditioning (AC-to-DC conversion) to make the harvested energy useful brings into question what specific type of performance is to be expected in a real industrial application. This paper reports the operation of two practical IoT sensor nodes, continuously powered by the vibrations of a standard industrial compressor, using a multi-modal EM-VEH device, integrated with customised power management. The results show that the device and the power management circuit provide sufficient energy to receive and transmit data at intervals of less than one minute with an overall efficiency of about 30%. Descriptions of the system, test-bench, and the measured outcomes are presented.

This paper addresses the multi-physical field coupling problem of electromagnetic vibration in permanent magnet synchronous motors (PMSMs), and presents a fast calculation method for multi-harmonic decoupling of electromagnetic forces based on subdomain analysis and an equivalent ring model. This method breaks through the simplifying assumptions of traditional models regarding the non-uniform distribution of tangential electromagnetic forces and high-frequency nonlinear effects. By introducing a modified modal participation factor and an orthogonal anisotropic stiffness superposition criterion, it achieves a low-order modal frequency error of <7% for the stator-winding system and constructs a nonlinear mapping model between tangential forces and high-frequency vibrations. Compared with existing studies that neglect the non-uniform distribution of tooth surface forces and end constraint effects, the proposed method exhibits spectral localization accuracy better than 5% in the low-frequency band (<3 kHz) and improves computational efficiency by 80%. It significantly alleviates the modeling complexity of traditional finite element methods under multi-speed conditions and high-frequency prediction deviations. Experimental verification shows that this method can accurately characterize the electromagnetic vibration characteristics of motors, providing an effective technical approach for the early suppression of motor vibration and noise.

In this paper, a new method is proposed to suppress the vibration caused by the modulation effect of high-order electromagnetic forces in permanent magnet (PM) motors. Firstly, the modulation effect of the radial force was investigated, which indicated that the higher-order electromagnetic force could cause modulated vibrations through the modulation effect. Then, auxiliary slots on the magnet surface and their effect on vibration reduction were investigated. The optimal shape of the auxiliary slot was found to minimize the noise of motor vibration. Finally, the method was verified experimentally.