Analysis and Correction of Zero Stiffness Point Shift in Magnetic Levitation Gravity Compensator

Abstract

In the field of ultra-precision manufacturing, zero stiffness magnetic levitation gravity compensators (ZSMLGCs) are widely employed as passive vibration isolation devices to mitigate ground-induced disturbances. However, the asymmetry of the magnetic repulsive and attractive forces, induced by the relative permeability of the permanent magnets, results in a shift of the zero stiffness point away from the geometric center, significantly impairing isolation performance. This article proposes a novel ZSMLGC topology that addresses this issue. Both analytical and numerical models (NMs) are developed to evaluate magnetic force and stiffness characteristics, and a comprehensive comparison is conducted in terms of computational accuracy and efficiency. Based on the modeling results, a design method is introduced that effectively balances speed and accuracy while eliminating the zero stiffness point shift by optimizing the geometry of the compensating magnets. Simulation results demonstrate that the proposed design achieves zero stiffness point precisely at the geometric center, with vertical stiffness below 5 N/m within a ±2 mm stroke and a levitation force exceeding 20 N to compensate for the gravitational loads.