Optimal design and performance evaluation of a flow-mode MR damper for front-loaded washing machines
© Nguyen et al.; licensee Springer. 2014
Received: 14 August 2013
Accepted: 9 December 2013
Published: 29 April 2014
It is well known that the vibration of washing machines is a challenging issue to be considered. This research work focuses on the optimal design of a flow-mode magneto-rheological (MR) damper that can replace the conventional passive damper for a washing machine. Firstly, rigid mode vibration of the washing machine due to an unbalanced mass is analyzed and an optimal positioning of the suppression system for the washing machine is considered. An MR damper configuration for the washer is then proposed considering available space for the system. The damping force of the MR damper is derived based on the Bingham rheological behavior of the MR fluid. An optimal design problem for the proposed MR brake is then constructed. The optimization is to minimize the damping coefficient of the MR damper while the maximum value of the damping force is kept being greater than a required value. An optimization procedure based on finite element analysis integrated with an optimization tool is employed to obtain optimal geometric dimensions of the MR damper. The optimal solution of the MR damper is then presented with remarkable discussions on its performance. The results are then validated by experimental works. Finally, conclusions on the research work are given and future works for development of the research is figured out.
KeywordsMagneto-rheological MR damper Washing machine Vibration control
It is well known that the vibration of washing machines is a challenging issue to be considered. The vibration of the washing machine is mainly due to the unbalanced mass of clothes distributed in the washing drum. This occurs most frequently in the spin-drying stage, because the drum spins at a relatively high speed causing the clothes to be pressed against the inner wall of the spin drum, and these can become a large unbalanced mass until the end of the stage. Particularly, in a front-loaded washing machine (drum-type washing machine), the unbalanced mass of clothes easily occurs and very severe due to the effect of gravity. The vibration of the washing machine is transferred to the floor causing noises, unpleasant feeling for humans, and failure of the machine.
There are many researches on vibration control of washing machines which can be classified into two main approaches. The first approach is based on the control of the tub balance to eliminate the source of vibration [1, 2]. In this approach, one type of dynamic balancer is used to self-balance the tub dynamics. A typical dynamic balancer is the hydraulic balancer containing salt water, which is attached to the upper rim of the basket. The liquid in the balancer moves to the opposite side of unbalance automatically due to the inherent nature of fluids when the rotational speed is higher than the critical speed of the spinning drum . Another dynamic balancer that counteracts vibrations is to use two balancing masses. In this method, two balancing masses move along the rim of the basket. The rotation plane of the balancing masses can be easily chosen to be wherever judged suitable, always targeting at the reduction of the induced moments . It is proved that the vibration of the washing machine can be significantly reduced by using a dynamic balancer. However, the complicated structure, high cost of manufacturing, and maintenance are a big obstacle for the wide application of this approach. In the second approach, the vibration of the washing machine is suppressed based on damping control of a suspension system . It is noted that during the spinning process, the washing machine usually experiences the first resonance at quite low frequency, around 100 to 200 rpm. This results from the resonance of the washing drum due to the unbalanced mass. When the rotating speed exceeds 1,000 rpm, the side and rear panels of the frame may experience resonances which cause noises and vibration transferred to the floor. If a passive damper is used to reduce the vibration of the drum at low frequency, it will cause the vibration of the washing machine at high frequencies more severe. The reason is that more excitation force from the drum is transferred to the frame via the passive damper. Therefore, in order to effectively reduce the vibration of the washing machine at low frequency while the vibration of the machine at high frequencies is insignificantly affected, a semi-active suspension system such as a magneto-rheological (MR) damper should be employed.
Although there have been several researches on the design and application of MR dampers to control the vibration of washing machines [4–6], the optimal design of such MR dampers was not considered. The main objective of this study is to achieve the optimal design of the semi-active suspension system for washing machines employing MR dampers. Firstly, rigid mode vibration of the washing machine due to an unbalanced mass is analyzed and an optimal positioning of the suppression system for the washing machine is considered. An MR damper configuration for the washer is then proposed. The damping force of the MR damper is then derived based on the Bingham model of the MR fluid. An optimal design problem for the proposed MR brake is then constructed considering the damping coefficient and required damping force of the MR damper. An optimization procedure based on finite element analysis integrated with an optimization tool is employed to obtain optimal geometric dimensions of the MR damper. The optimal solution of the MR damper is then presented with remarkable discussions. The results are then validated by experimental works.
Vibration control of washing machine using MR damper
An inherent drawback of the conventional damper is its high transmissibility of vibration at high excitation frequency. In order to solve this issue, semi-active suspension systems such as ER and MR dampers are potential candidates. In this study, two MR dampers are employed to control the vibration of the tub assembly.
In the above, τ y is the induced yield stress of the MR fluid which is an unknown and can be estimated from magnetic analysis of the damper and η is the post-yield viscosity of the MR fluid which is assumed to be field independent. R d is the average radius of the annular duct given by R d = R − t h − 0.5t d . L and R are the overall length and outside radius of the MR valve, respectively. t h is the valve housing thickness, t d is the annular duct gap, and L p is the magnetic pole length.
In Equation 9, the unit of the yield stress is kilopascal while that of the magnetic field intensity is kA/m. The coefficients C0, C1, C2, and C3 are respectively identified as 0.044, 0.4769, −0.0016, and 1.8007E-6. In order to estimate the induced yield stress using Equation 9, first the magnetic field intensity across the active MRF duct must be calculated. In this study, the commercial FEM software, ANSYS, is used to analyze the magnetic problem of the proposed MR damper.
Optimal design of the MR damper
In this study, it is assumed that the spring stiffness is k = 10 kN/m, the mass of the suspended tub assembly is m = 40 kg, and the equivalent unbalanced mass is m u = 10 kg located at the radius R u = 0.15 m. With the required damping ratio ξ = 0.7, at the resonance , the required value of FMR can be calculated from Equation 14 which is around 150 N in this study.
Results and discussion
In this research, optimal design of a flow-mode MR damper to suppress the vibration of front-loaded washing machines was undertaken. After a brief introduction, the general governing equation of the washing tub assembly is derived. The position of the two springs and the two dampers to suppress the machine vibration was then optimally determined based on the governing equation. A configuration of the MR damper for the washing machine was then proposed, and the damping force was obtained based on the Bingham rheological model of the MR brake. The optimization problem for the damper was constructed such that the viscous coefficient of the damper is minimized and the yield stress force of the damper is greater than a required value that attenuates almost the resonant peak of the tub mechanism. The optimal design of the MR damper for a prototype washing machine was obtained based on the ANSYS finite element analysis of the MR damper magnetic circuit and first-order optimization method. The results show that performances of the MR damper are significantly improved with the proposed optimal design. A prototype of the optimized MR damper was manufactured, and experimental results on the performance of the prototype damper were obtained and presented. It was shown that the experimental results well agreed with the modeling one obtained from finite element analysis. As the second phase of this study, dynamics of the whole prototype washing machine equipped with the MR damper will be obtained and experimental results on the prototype washer will be conducted to evaluate the effectiveness of the optimized MR damper.
This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 107.04.2011.07 and partially supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0015090).
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