This paper presents an analytical method for calculating the magnetic field in a new linear permanent-magnet vernier (LPMV) machine, thus predicting the electromagnetic vibration. The main vibration source is the normal
force between the mover and the stator of the LPMV machine. Firstly, the air-gap flux density is calculated and analyzed using the rotor permeance to modulate the magneto-motive force, and is verified by the
finite element (FE) results. Then, the harmonics of the normal force density is calculated, the normal force and thrust force are analyzed. Secondly, the natural vibration modes and the transient displacement of the mover
are predicted by FE method, and the relationship between the normal force density and the vibration is determined. Finally, experimental results are given for verification. This study is instructive for the design of a
high-precision and low-vibration LPMV machine.