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Purpose This study aims to accurately calculate the magnetic field distribution, which is a prerequisite for pre-design and optimization of electromagnetic performance. Accurate calculation of magnetic field distribution is a prerequisite for pre-design and optimization. Design/methodology/approach This paper proposes an analytical model of permanent magnet machines with segmented Halbach array (SHA-PMMs) to predict the magnetic field distribution and electromagnetic performance. The field problem is divided into four subdomains, i.e. permanent magnet, air-gap, stator slot and slot opening. The Poisson’s equation or Laplace’s equation of magnetic vector potential for each subdomain is solved. The field’s solution is obtained by applying the boundary conditions. The electromagnetic performances, such as magnetic flux density, unbalanced magnetic force, cogging torque and electromagnetic torque, are analytically predicted. Then, the influence of design parameters on the torque is explored by using the analytical model. Findings The finite element analysis and prototype experiments verify the analytical model’s accuracy. Adjusting the design parameters, e.g. segments per pole and air-gap length, can effectively increase the electromagnetic torque and simultaneously reduce the torque ripple. Originality/value The main contribution of this paper is to develop an accurate magnetic field analytical model of the SHA-PMMs. It can precisely describe complex topology, e.g. arbitrary segmented Halbach array and semi-closed slots, etc., and can quickly predict the magnetic field distribution and electromagnetic performance simultaneously.

It is generally assumed that the stator core and rotor core are infinitely permeable in conventional analysis methods. Therefore, magnetic saturation is easily overlooked and the magnetic flux density is overestimated. This article introduces the analysis model of a permanent magnet (PM) machine with a segmented Halbach array (PMMSHA). It considers the finite permeability of the stator teeth and tooth tips and can study the saturation effect of the teeth. Therefore, the electromagnetic performance is calculated, including the magnetic field distribution, excitation force density, cogging torque, and electromagnetic torque in all areas. The results of finite element analysis (FEA) show that the analysis model is highly accurate.

A six degree of freedom nonlinear passive vibration isolator is proposed based on Stewart platform configuration with the quasi-zero-stiffness structure as its legs. Due to the high static stiffness and low dynamic stiffness of each leg, the proposed six degree of freedom system can realize very good vibration isolation performance in all six directions while keeping high static load-bearing capacity in a pure passive manner. The mechanic model of the proposed six degree of freedom isolator and the dynamic equation of the isolator are established successively. Theoretical analysis on cross coupling stiffness reveals that the system can demonstrate quasi-zero-stiffness property in all six degree of freedom. Moreover, an analysis on stability shows that the condition of structural parameters for the isolator to realize quasi-zero-stiffness is also the stability boundary of the system. A series of numerical simulations on displacement transmissibilities in coupled degree of freedoms, the coupling effects of transmissibility, and a dynamic response in random excitation are carried out to show the effectiveness of the proposed six degree of freedom isolator, as well as the influence of structural parameters on vibration attenuation performance. Considering its high performance in a simple passive manner, it can be foreseen that the proposed six degree of freedom isolator will be applied in various engineering practices with multi-degree of freedom vibration isolation.

In this paper, a novel 3-axis torsion quasi-zero-stiffness (TQZS)-based sensor system is proposed for absolute rotation measurement in vibration systems. Analysis on the applied torque and structural parameters shows that the proposed mechanism with two concentric spheres connected by six symmetry distributed springs could approximately achieve TQZS features in three rotational degrees of freedom simultaneously, thus a remarkable torsional vibration measurement performance can be guaranteed. Although due to high stiffness, the mechanism also has high anti-interference ability about force or vibration in translational directions. Mathematical modeling and numerical simulations are carried out to show the effectiveness of the proposed 3-axis sensor system in different base vibrations. In consideration of its feasibility and high performance, it can be foreseen that the proposed TQZS-based sensor will get more and more implementations in various engineering practices with torsional vibration measurements.

A permanent magnet motor with auxiliary slots in the stator teeth is taken as the research object in this article. In the two-dimensional polar coordinate system, the Fourier series method is used to establish an analytical model of the electromagnetic field of surface-mounted permanent magnet motors. The motor solution domain is divided into five sub-domains: permanent magnet, air gap, stator slot, stator slot opening, and auxiliary slot. The electromagnetic properties such as air gap magnetic density, no-load back-EMF, cogging torque, and electromagnetic torque of the motor are calculated. The analytic model is used to analyze the electromagnetic characteristics of surface-mounted permanent magnet motors under no load and load.