The most important characteristic of a passive vibration isolator is its natural frequency and load capacity. The vibration isolation performance of a passive vibration isolator in low input frequencies is considerably improved by reducing its natural frequency. This paper presents a negative stiffness magnetic suspension vibration isolator (NSMSVI) using a magnetic spring combined with rubber membranes to obtain lower natural frequency. To study the vibration isolation performance of the NSMSVI, the stretching force of the rubber membrane is measured through experiments. The stiffness of the rubber membrane comes from the derivative of the stretching force. A parametric study of load capacity, axial magnetic stiffness, and natural frequency of the magnetic spring is also performed. Consequently, as a case study, the size dimensions of the magnetic spring are determined. An NSMSVI table is set up for experimental validation, after which the transmissibility curves of the NSMSVI are calculated and tested. Experimental results show that the lowest natural frequency of the NSMSVI reaches 1.5 Hz with a maximum attenuation of -40 dB between 0 Hz and 100 Hz, whereas the NSMSVI has the maximum load capacity at the lowest stiffness. This paper essentially provides an efficient method to construct a negative stiffness vibration isolator for practical applications.

This study concerns the analysis and minimisation of the force ripples existing in ironless permanent magnet planar motors. The force ripples is one of the key factors for moving accuracy of the planar motors. One of the main sources of the force ripples, the neglected higher harmonics of the magnetic flux density distribution, is analysed for synthesis of real-time control model in this study. An analytical model of the planar motor is firstly developed, which illustrates that the force ripples part caused by some higher harmonics can cancel each other when the length of the coil is an even multiple of the pole pitch of the magnet array. As a result, the force ripples caused by the higher harmonics can be basically eliminated with a selected coil. Finally, the analysis results are both validated by comparative simulation and experiment of two partial motors.

Ironless permanent magnet planar motors have significant potential for accurate positioning systems. The higher harmonics of the magnetic flux density distribution, which is ignored in the analytical model for real-time control, is usually one of the main reasons for the force ripples of the ironless permanent magnet planar motors. The force ripples cased by the higher harmonics is analyzed and minimized in this paper. An analytical model of the force ripples cased by the higher harmonics is developed first. Then it can be derived from the analytical model that the force ripples cased by some higher harmonics can cancel each other when the length of the coil is an even multiple of the pole pitch of the magnet array. Furthermore, the winding factors of the ironless permanent magnet planar motors are also derived and can be used to eliminate dominating components of the force ripples cased by the left higher harmonics. As a result, the force ripples cased by the higher harmonics can be basically eliminated with a selected coil length and winding factors. Finally, it is validated by comparison of the planar motors with finite element (FE) analysis that most of force ripples cased by higher harmonics can cancel each other when the length of the coil is an even multiple of the pole pitch of the magnet array.

This paper presents novel overlapping ironless windings for permanent magnet planar motors, which have high winding factors and make full use of the magnetic field of the magnet array in the planar motor. A simple analytical model of the planar motors is developed and validated by finite-element method first. Then the winding factors of the ironless windings are derived and used to simplify the analytical model. Furthermore, the design rules of the ironless windings for the planar motor are obtained from the analytical model with winding factors and the ironless windings are optimized for maximum steepness of the planar motor. Compared with the nonoverlapping ironless windings, the novel overlapping ironless windings have a much (up to 25%) larger force with the same copper loss and nearly the same size when the coils of the windings have a large length/width ratio.

Linear flat switched flux permanent magnet (SFPM) brushless machines have significant potential for many applications including transportation, automobile and aerospace. Novel E-core and C-core linear SFPM machines are proposed and optimized by individual parameter optimization, when the copper loss and volume is fixed, in this paper by finite element (FE) analysis. Then, the results of the individual parameter optimizations are examined by a global optimization with genetic algorithm. Furthermore, the magnet thickness of all the machines and the middle teeth of the E-core machines are analyzed individually. Finally, the electromagnetic performance of the novel machines are analyzed and compared with the conventional machine. It shows that both E-core and C-core machines require significantly smaller magnet volume since only about half the number of permanent magnets is required. Furthermore, the C-core machines have the largest back-EMF and force density due to the largest slot area, and the E-core machines are suitable for fault-tolerant operations while the 6/11 mover/stator pole E-core SFPM machine has the smallest cogging force.

Linear planar flux-switching permanent magnet (FSPM) brushless machines have significant potential for transportation application. A 6-slot/5-pole linear FSPM motor is optimized in this paper for maximum thrust force at a fixed copper loss and also for minimum cogging force by finite element (FE) analysis. The influence of major design parameters, such as the split ratio between the mover and stator, the stator pole width, the stator pole height, the mover back-iron thickness and the mover tooth width, on the thrust force, when the copper loss is fixed, is firstly investigated by individual parameter optimization. The results are then compared to a global optimization of thrust force obtained by genetic algorithm. It is shown that their differences are very small and hence the individual parameter optimization may be employed in optimizing such linear FSPM motor. Finally, the peak-to-peak value of the cogging force is reduced by ~40% via optimizing the slot opening and width associated with the end teeth.

This paper presents a new 2-D permanent-magnet array for a planar motor, in which the angle between the magnetization directions of any two adjacent magnets is 45°. The harmonic model for flux density distribution of the array is solved by the scalar magnetic potential equation and validated by the finite-element method. An analytical model for real-time control is derived by taking the first harmonic of the magnetic flux density distribution. The ignored higher harmonics in z-component of the magnetic flux density distribution is minimized by the genetic algorithm such that the analytical model becomes more accurate. Compared with the well-known Halbach magnet array, the proposed magnet array has lower higher harmonic components and higher z -component of the magnetic flux density, which will reduce the force ripples of the planar motor.