Research on mathematical modeling of the servo valve torque motor considering the variation of working air-gaps leakage flux

In the current research of the magnetic circuit model of the servo valve torque motor, the magnetic flux leaking from working air-gaps is regarded as constant. However, the working air-gaps leakage flux varies with the armature rotation angle, which affects the accuracy of the existing mathematical model of the torque motor. To solve this problem, a new mathematical model of the torque motor with two working air-gaps is built. First, different from the previous model, the variation of the working air-gaps leakage flux is considered in the magnetic circuit model. A more detailed mathematical model of the torque motor is established based on the magnetic circuit model. Second, the finite element method is used to reveal that there is a linear relationship between working air-gaps leakage flux and armature rotation angle in a certain range of rotation angles. Then, the new model is validated by numerical calculation, which indicates that the theoretical results calculated by this new model show better agreement with the simulation results compared to the previous model when the armature rotation angle increases. Further, the theoretical results of the electromagnetic torque constant and magnetic spring stiffness acquired by the new model and the previous model are compared. The comparison shows that the variation of the working air-gaps leakage flux has the greatest influence on the magnetic spring stiffness. Finally, the experiments on the torque motor are conducted to verify the accuracy of the new model. The theoretical results obtained by this new model are better consistent with the experimental results than that obtained by the previous model. This study shows that considering the variation of working air-gaps leakage flux is valuable to improve the accuracy of the magnetic circuit model of the torque motor, which provides an effective guidance for the structural optimization and performance prediction of the torque motor.

Influence of saturation levels on transformer equivalent circuit model

This paper presents a modelling approach for a transformer with different saturation levels. First, the magnetic field distributions at different saturation levels in the transformer are analyzed by using numerical simulations. Then, the characteristics of the leakage magnetic flux are analyzed, and the magnetic circuits with varying leakage reluctance topologies are modeled. Finally, based on the mature duality relationship between electric and magnetic circuits, the equivalent electric circuit models are obtained. These kinds of models embody the effect of different saturation levels on the connection points of the leakage flux branches, and it can fully reflect the various working states of the transformer. The accuracy of the models is verified by comparing the circuit simulation results with those of FEM transient simulations.

Analytical calculation of leakage permeance of coreless axial flux permanent magnet generator

Purpose This paper aims to study the relationship between leakage flux coefficient and the coreless axial magnetic field permanent magnet synchronous generator (AFPMSG) size and obtain the expressions of leakage flux coefficient. Design/methodology/approach In this paper, a magnetic circuit model of coreless AFPMSG is proposed. Four kinds of leakage permeances of permanent magnet (PM) are considered, and the expression of no-load leakage flux coefficient is obtained. Solving the integral region of leakage permeances by generator size, which improves the accuracy of the solution. Findings Finite element method and magnetic circuit method are used to obtain the no-load leakage flux coefficient and its variation trend charts with the change of pole arc coefficient, air gap length and PM thickness. The average errors of the two methods are 2.835%, 0.84% and 1.347%, respectively. At the same time, the results of single-phase electromotive force obtained by magnetic circuit method, three dimensional finite element method and prototype experiments are 19.36 V, 18.82 V and 19.09 V, respectively. The results show that the magnetic circuit method is correct in calculating the no-load leakage flux coefficient. Originality/value The special structure of the coreless AFPMSG is considered in the presented equivalent magnetic circuit and equations, and the equations in this paper can be applied for leakage flux evaluating purposes and initial parameter selection of the coreless AFPMSG.

Numerical simulation of a squirrel cage motor including magnetic wedges and radial vents

This work is a proposal of a finite element model to obtain the electromagnetic performance of a squirrel cage motor considering the magnetic wedges and radial vents. To analyze the electromagnetic performance at the design stage, without the need to build a prototype, the paper proposes a simple two dimensions finite element model, which includes components as magnetic wedges used to hold the windings in the stator slots, radial vents in the core, which are part of motor cooling system, and edge effects to improve the model. The stator and rotor cores are modeled with an equivalent homogeneous permeability, obtained from the combination of the radial air vents of rotor and stator and the magnetic core material. The permeability of magnetic wedges is also considered. Edge effects considered are the end winding leakage inductance, representing the leakage flux in the end coils of the stator, and an equivalent impedance between rotor bars due to conductivity and leakage flux in the rings of the squirrel cage. The results obtained are compared with experimental tests performed in steady state to validate the model. Furthermore, no-load, and blocked-rotor tests are simulated to estimate the equivalent circuit parameters and draw the typical induction motor torque-speed curve, which is compared with the obtained curve by means of Thevenin’s theorem. With this proposed model, the results are close to the ones obtained experimentally. The implementation of a 3D model is complex, and the computational cost can be much higher, compared to the 2D model developed here.