Analysis of Damped Vibrations in Washing Machine Drums Using Free-Decay, FRF, and Spin-Up Methods

This research presents a methodological framework for calculating and characterizing damped vibrations in washing machine drums based on a single-degree-of-freedom (SDOF) model. The system is described by the equation , representing unbalanced excitation caused by uneven distribution of laundry mass during spinning. Key parameters—natural frequency , damping ratio , stiffness , damping coefficient , and transmissibility  are identified through three complementary approaches: (i) free-decay analysis, determining via logarithmic decrement and deriving ; (ii) frequency response function (FRF) testing using an impact hammer to obtain and through the −3 dB bandwidth method; and (iii) operational spin-up testing, mapping the system response across resonance and computing . The procedure includes signal preprocessing, time- and frequency-domain parameter estimation, and formulation of key relationships and . Emphasis is placed on safety, reproducible sensor placement (at the drum housing and chassis), and structured reporting through schematics, calculation tables, and illustrative vibration curves. The main contribution of this study is to provide a consistent, measurable, and replicable methodology for vibration evaluation of washing machine drums, serving as a foundation for vibration isolation optimization, enhanced user comfort, and extended component lifespan.