An experimental and analytical approach while predicting damped vibration responses of machine tool installed on a tuneable-damper foundation (TDF) via dimension theory

[Display omitted] •Attenuating residual vibration in machine tools enhances accuracy and productivity.•Early prediction of vibration response is vital in optimising quality attributes.•An optimum value of static and dynamic stiffness at support structure is crucial.•Tuneable damping at machine tool foundation is a novel concept & possible via ERF.•DA & soft computing tools simplify the system to a functional mathematical model.•Visible attenuation of residual vibration in machine tool achieved through a TDF. This study proposes a novel tuneable-damper foundation (TDF) that isolates a machine tool and prevents transmission of dynamic excitation from machine to ground or vice versa. Electrorheological fluid (ERF) facilitates the development of TDF. TDF is a motion-controlled piston that utilises electrical potential to regulate ERF's rheological characteristics. Then, TDF was exposed to the excitation of a medium-duty lathe machine operating at idle and during turning. An experimental-database model (EDBM) uses trial data to develop a mathematical equation for forecasting vibration response and surface quality using dimensional analysis (DA) and multivariable regression (MVR). A mathematical model of DA and MVR, the mechanism of TDF, the characteristics of ERF, experimentation, and novel analytical models are all documented in the paper. The experiment-driven controlled damping confirms the efficacy of TDF, attaining 60% attenuation at 1–100 Hz. Similarly, the developed analytical model accurately forecasts vibration response and surface finish, boosting the quality parameters.