Ultra-low magnetic fields have drawn lots of attention due to their important role in scientific and technological research. The combination of a magnetic shield and an active compensation coil is adopted in most high performance magnetically shielded rooms. Special consideration needs to be taken in the coil design since the magnetic shield significantly affects the uniformity of the magnetic field that is generated by the coil. An analytical model for the magnetic field calculation of the coil inside a cubic magnetic shield is proposed based on the generalized image method, which is validated by finite element analysis. A novel design method of the coil used in a cubic magnetic shield with a large homogeneous volume is proposed. The coil parameters are optimized to obtain a large cubic uniform volume with desired total deviation rate by discretizing the central volume in the coil. In the desired total deviation rate, the normalized usable volume of the new coil increases by 70% when compared with the Merritt coil. A coil system is developed according to the parameters obtained based on this method. The magnetic flux density and practical deviation rate of the coil are measured to validate the accuracy of this model and the feasibility of the design method. The experimental magnetic flux density agrees well with the analytical value. The maximum practical deviation rate of uniform volume of 0.8 × 0.8 × 0.8 m is in good agreement with the theoretical design value, taking into account the experiment errors.

In this article, a uniform magnetic field coil with a magnetic shield is presented and designed to cancel the geomagnetic field and the surrounding magnetic noises. First, an analytical model of the uniform magnetic field coil with the magnetic shield is developed, based on the Biot–Savart law and the traditional images method. Second, in order to improve the model accuracy, the influence of the noninfinite shield thickness on the magnetic field produced by the uniform magnetic coil is considered using the multireflection theory, and an improved analytical model is obtained. The improved analytical model is verified by the three-dimensional finite-element method, and its accuracy is significantly improved compared to the previous analysis model. Then, the characteristic analysis of the uniform magnetic field coil is carried out using the improved analytical model, and design criteria of the uniform magnetic field coils are given to obtain a large uniform field area. Finally, the uniform magnetic field coil with the magnetic shield was constructed and the resulting magnetic field was tested. The test results show that the improved analytical model can accurately predict the performance of such magnetic field coils with magnetic shields, and can be used for its preliminary design.

In this paper, the thermal analysis of a hybrid excitation Linear eddy current brake is presented. The air gap flux of the hybrid excitation linear eddy current brake is provided by the excitation windings and the permanent magnets. Therefore, the braking force produced by the eddy current brake is large and controllable. But on the other hand there is a high heating value in the excitation windings and conductor plate, hence, it is necessary to analyze thermal characteristics of the eddy current brake to avoid the declination of braking performance or even damage of device. Firstly, the working principle of the eddy current brake is described, then, the thermal network model of the eddy current brake is built taking the actual air flow around the eddy current brake into consideration. Finally, the validity of the thermal network model is verified by steady and dynamic thermal experimental measurements, respectively.

This paper presents a novel parallel magnetic path hybrid excitation linear eddy current brake. The eddy current brake using parallel magnetic path scheme with the presence of the PMs, whose flux lines in the primary are oppositely directed with respect to the flux lines by the excitation windings, has the effect of mitigating the saturation of the iron in the teeth of the primary. This allows the brake to be fed with more intense currents improving the braking force. The structure and working principle are introduced. The analytical model was found using the equivalent magnetic circuit method and the layer theory approach. The design method of the eddy current brake was studied using the finite element method. Compared with traditional induction motors and synchronous motors, the design method of the eddy current brake has not been proposed. Therefore, in this paper, the design parameters of the hybrid excitation linear eddy current brake were gradually determined by consulting the design method of the linear induction motor and linear synchronous motor, and a design flowchart was proposed. Finally, a prototype of hybrid excitation linear eddy current brake was created and an experimental study of the eddy current brake was conducted.

A novel cylindrical magnetic levitation gravity compensator (MLGC) with low-stiffness and vacuum-compatible characteristics is proposed in this paper. This compensator can be used as the out-of-plane electromagnetic actuator for the 6-DOF fine stage in certain high-precision positioning applications, for example, the wafer stage in a lithography machine. Compared with conventional actuators such as the electromagnet and voice coil motor, the heat and the resulting temperature rise that degrade the stage positioning accuracy can be reduced by using passive magnetic gravity compensation. Based on the equivalent current method, the analytical equations for the magnetic field, static levitation force, vertical stiffness, and dynamic levitation force are derived. However, the static levitation force-vertical displacement characteristic from the traditional analytical model is not sufficiently accurate for the low-stiffness applications when compared with the finite-element model. Therefore, the main reason for the model error is analyzed, and an improved semianalytical method based on a single-point magnetostatic field simulation is proposed. This method offers a theoretical basis for the analysis and design of the low-stiffness MLGC.