Aiming at small magnetic force and the complexity of magnetic force numeral calculation for previous research of radial magnetic force model on APAM(axial placement and axial magnetization) bi-annular-shaped PMB(permanent magnetic bearings),the new construction of APAM multi-annular -shaped PMB was designed,which can make good use of magnetic energy and have greater radial magnetic force. Based on analysis of the gap magnetic conductance of multi -annular-shaped PMB,connected with rare earth permanent material property and the principle of magnetic-flux equivalency in flux paths as well as linearity adding, this paper adopted the differential coefficient of magnetic energy to virtual displacement method to derive a magnetic force analytical calculation formula of APAM multi- annular-shaped PMB. This formula indicates that the radial magnetic force of APAM multi-annular-shaped PMB is in positive proportion to the second power of residual magnetism induction density,and that the radial magnetic force increases with an increment in the magnetic annular radial size, average radius,the number of permanent magnetic annular and total magnetic conductance of magnetic circuit,and that the radial magnetic force decreases with an increment in the axial and radial gap.Test validation employed experimental device refitted by triaxial vertical milling machine and triaxial ergometer,the model calculation values are basically in agreement with those actually-measured.
