Design of a Washing Machine with a Stochastic Approach
DOI:
https://doi.org/10.70567/mc.v41i5.30Keywords:
Washing machine, Nonlinear dynamics, Uncertain unbalance, Shooting method, Monte Carlo simulationAbstract
A washing machine is a household appliance that has an interesting and complex dynamicalbehavior, which can be well described by a set of nonlinear differential equations. When analyzing the dynamics of a washing machine, the steady state motion (periodic solution) is an important response to consider and can be evaluated as a solution of a periodic boundary-valueproblem. The unbalance generated by the unevenly distribution of clothes during centrifugationis highly random and, therefore, a stochastic model is necessary to take this characteristic intoaccount. The novelty of this paper consists in the analysis of a washing machine dynamics considering the uncertainty in the unbalance. Therefore, a stochastic model is proposed for the dynamics of a washing machine. The steady state solutions are calculated using the shootingmethod combined with a sequential continuation to evaluate it across all the spin speeds of the machine. The probability distributions of the washing machine vibration at those different spin speeds are approximated using Monte Carlo simulations. The impact of the random unbalance in the vibration amplitude of the washing machine is also investigated and consists in a keyinput for the fatigue design of many components.
References
Bae S., Lee J., Kang Y., Kang J., and Yun J. Dynamic analysis of a automatic washing machine with hydraulic balancer. Journal of Sound and Vibration, 257:3-18, 2002. https://doi.org/10.1006/jsvi.2001.4162
Chen H. and Zhang Q. Stability analyses of a vertical axis automatic washing machine without balancer. Journal of Sound and Vibration, 329:2177-2192, 2010. https://doi.org/10.1016/j.jsv.2009.12.012
Chen H., Zhang Q., and Fan S. Study on steady-state response of a vertical axis automatic washing machine with a hydraulic balancer using a new approach and a method for getting a smaller deflection angle. Journal of Sound and Vibration, 330:2017-2030, 2011. https://doi.org/10.1016/j.jsv.2010.11.006
Conrad D. and Soedel W. On the problem of oscillatory walk of automatic washing machines. Journal of Sound and Vibration, 188:301-314, 1995. https://doi.org/10.1006/jsvi.1995.0595
Cursi E. and Sampaio R. Uncertainty Quantification and Stochastic Modeling with Matlab. Elsevier, Oxford, UK, 2015.
Lima R. and Sampaio R. What is uncertainty quantification? Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40:1-8, 2018. Mecánica Computacional Vol XLI, págs. 299-308 (2024) 307
Wagner G., Sampaio R., and Lima R. Uma introdução aos modos normais não-linear de sistemas mecânicos, volume 95 of Notas em matemática aplicada. SBMAC, São Carlos, Brazil, 2023.
Wagner G. and Sampaio R.L.R. A versatile strategy to compute nonlinear normal modes of flexible beams. Nonlinear Dynamics, 111:9815-9837, 2023. https://doi.org/10.1007/s11071-023-08418-6
Wagner G. and Sampaio R.L.R. Dynamics of vertical axis washing machines with uncertain unbalance. Mechanical Systems and Signal Processing, 211:111231, 2024. https://doi.org/10.1016/j.ymssp.2024.111231
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Argentine Association for Computational Mechanics
This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.
