High-performance magnetic circuit offering uniform magnetic flux density (MFD) along ultra-long stroke is the key to develop a vibration exciter for ultra-low-frequency (ULF) vibration calibration. In this paper, a rectangular closed double magnetic circuit (RCDMC) offering ultra-long stroke up to 1.2 m is modeled and optimized. In order to overcome the modeling difficulty arising from the long stroke, a high-accuracy theoretical model is established taking advantage of the structural symmetry of the RCDMC through lumped parameter magnetic equivalent circuit method. Matrix equations are derived based on Kirchhoff’s law and solved by iteration calculation to deal with the strong nonlinear characteristics of the yoke material. The deviations between the model and finite element method (FEM) analysis results are less than 1% for non-saturated yokes and ~10% for saturated yokes. Theoretically, an MFD up to 122 mT and an acceleration waveform harmonic distortion (AWHD) as low as 0.45% are achieved through model-based optimization. Experiments are carried out using an RCDMC prototype assembled in a horizontal vibration exciter. The experimental results show that an MFD of 102 mT and an AWHD of 0.27% along 1.2 m stroke are achieved, making the proposed RCDMC a solution for ULF vibration exciter.
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