Load-position decoupled quasi-zero stiffness vibration isolation via translation-scaling coordinated transformation

The performance sensitivity of quasi-zero-stiffness (QZS) isolators to load-position mismatches poses significant challenges and hinders their practical implementation. Herein, a translation-scaling coordinated transformation method is proposed for decoupled adjustment of the rated load and equilibrium position. By coordinating translation and scaling transformations of negative and positive stiffnesses, the rated load and equilibrium position can be independently tuned, thereby mitigating performance sensitivity under time-varying operating conditions. Based on this method, a load-position decoupled QZS isolator (LPD-QZS) is developed and systematically investigated. A liftable nested magnet-coil pair is employed to generate translatable and scalable negative stiffness, while an end-to-end magnet-coil pair combined with a membrane spring pair provides nonuniformly scalable positive stiffness. Analyses reveal and verify the tunable stiffness characteristics and the effectiveness of the translation-scaling coordinated transformation in achieving load-position decoupled adjustment, as well as the distinctive behavior arising from it. Finally, offline and online tests are conducted to evaluate the robustness of the LPD-QZS under varying rated loads and equilibrium positions. Sweep excitation tests indicate that the LPD-QZS exhibits excellent low-frequency vibration isolation performance, with a low isolation frequency starting from 3.3 Hz, in drastic contrast with the degraded performance without load-position decoupled adjustment under load-position mismatches. Significantly, through translation-scaling coordinated transformation, the LPD-QZS preserves its QZS characteristic across various applied loads and operating positions, highlighting its potential for practical engineering applications, particularly in multi-leg QZS platforms.