Non-linear Isolator for Vibration and Force Transmission Control of Unbalanced Rotating Machines

Purpose: The objective of this paper is to investigate with simulations how non-linear spring and non-linear damper components of isolators can be employed to effectively reduce both the oscillations and the force transmitted to ground in the whole spinning range of unbalanced rotating machines. Methods: The principal goal of this paper is twofold. First, to present a concise and consistent formulation based on the harmonic balance approach for the vibration response of spinning machines mounted on linear/non-linear, softening/hardening, un-tensioned/pre-tensioned springs and linear/non-linear dampers. Second, to provide a comprehensive overview of the vibration and force transmission control with non-linear isolators specifically tailored to unbalanced machines. Results: The study has shown that, the best vibration isolation is provided by a pre-tensioned linear and cubic softening spring combined with a linear and negative quadratic damper. The pre-tensioned spring should be designed in such a way as it holds the weight of the machine and thus produces on the vibrating machine a symmetric elastic restoring force proportional to the linear and cubic powers of the displacement. The cubic softening stiffness should then be tuned to minimise the frequency, and thus the amplitude, of the resonant response of the fundamental mode of the machine and elastic suspension system, while preserving stability and a desired static deflection. In parallel, to reduce the force transmission to ground above the fundamental resonance frequency, the negative quadratic damping effect should be tailored to maximize the energy absorption at higher frequencies. Conclusion: The study has shown that non-linear spring and non-linear damper components can be effectively employed to control the vibration and force transmission in the whole spinning range of the machine. In particular, a pre-tensioned softening cubic non-linear spring can be used to mitigate the vibration and force transmission at low frequencies, close to the fundamental natural frequencies of the elastically suspended machine. Also, a negative quadratic non-linear damper can be used to tailor the energy dissipation of the isolator in such a way as to have high damping at low frequencies and low damping at higher frequencies, which enhances the vibration and force transmission control at low frequencies and, rather importantly, mitigates the force transmission at higher frequencies.