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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.

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The permeability of the iron is usually assumed to be infinite by the linear subdomain technique, leading to the neglect of magnet saturation. This study presents an analytical model of a segmented Halbach array permanent magnet machine by considering the iron B-H curve and saturation effects. Firstly, the entire field problem is divided into six regions in the radial direction according to the excitation source. Then, Poisson's and Laplace's equations are solved in each region to obtain the magnetic vector potential. Specifically, in our approach, the teeth and slots' permeability variation is solved by Cauchy's product theorem. An iterative algorithm incorporates the nonlinearity of the iron. Subsequently, the electromagnetic performance, such as air-gap magnetic flux density, electromagnetic torque, and unbalanced magnetic force, is predicted by the analytical method. The analytical results are shown in line with those obtained from finite element analysis, and a prototype was fabricated to further verify the accuracy of the analytical method. Besides, the proposed method can also be used to evaluate the performance of the Halbach array machines with any number of segmented magnets. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.