Levitated optomechanics has great potential in precision measurements, thermodynamics, macroscopic quantum mechanics, and quantum sensing. Here we synthesize and optically levitate silica nanodumbbells in high vacuum. With a linearly polarized laser, we observe the torsional vibration of an optically levitated nanodumbbell. This levitated nanodumbbell torsion balance is a novel analog of the Cavendish torsion balance, and provides rare opportunities to observe the Casimir torque and probe the quantum nature of gravity as proposed recently. With a circularly polarized laser, we drive a 170-nm-diameter nanodumbbell to rotate beyond 1 GHz, which is the fastest nanomechanical rotor realized to date. Smaller silica nanodumbbells can sustain higher rotation frequencies. Such ultrafast rotation may be used to study material properties and probe vacuum friction.

In this study, a novel time–frequency (TF) analysis method, referred to as the scaling-basis chirplet transform (SBCT), is developed by extending the conventional chirplet transform. This method includes a replacement kernel function that can vary the chirp rate with frequency and time by scaling the TF basis at and around the corresponding time center. This enables the corresponding chirplets to accurately match the targeted slopes for every trajectory of a multicomponent signal and within any window length. Therefore, the TF representation obtained via the SBCT can achieve significantly higher energy concentrations even for multicomponent signals with close-spaced frequencies and high levels of background noise. The effectiveness of the proposed SBCT approach was demonstrated by analyzing a numerical multicomponent signal and a vibration signal obtained from a gearbox test rig. Both numerical and experimental results showed that the SBCT can satisfactorily handle multicomponent signals with nonlinear frequency trajectories, close-spaced frequencies, and noisy backgrounds, demonstrating its superiority.

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.

Stator current modeling for defective planetary gearboxes based on magnetic equivalent circuits (MEC) is conducted in this study. A lumped parameter torsional model of the motor-planetary gearbox coupling system is established to obtain the nonlinear time-variable torsional response of the rotor numerically. A MEC model of an induction motor is established by connecting the equivalent flux tubes with nodes. After considering the time-variable rotor torsional response, the nonlinear magnetic field intensity of the iron material and magnetic saturation, an iterative numerical integration method is presented to solve the MEC model. Both a finite element analysis and dynamic tests on a planetary gearbox driven by an induction motor are carried out for verification. Based on these, the fault characteristic components in the stator current spectra are, respectively, identified when the tooth chipping defect appears at sun/planet/ring gears. Fault-related frequencies are essentially represented by the combinations between the meshing frequency, sun/planet/ring gear fault passing frequency, its harmonics, and the power supply frequency. Owing to the electromechanical coupling effect, high-order harmonics of the power supply frequency also participate in the fault-related frequencies of the planet and ring gears. By quantitatively analyzing the influence of chipping size on the amplitudes of fault characteristic frequencies, suitable spectra for planetary gearbox condition monitoring are recommended.