Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 http://www.apjcen.com/content/1/1/3 RESEARCH Open Access Optimal design and performance evaluation of a flow-mode MR damper for front-loaded washing machines Quoc Hung Nguyen1*, Ngoc Diep Nguyen1 and Seung Bok Choi2 *Correspondence: Abstract [email protected] 1DepartmentofMechanical It is well known that thevibration ofwashing machines is a challenging issue to be Engineering,IndustrialUniversityof HoChiMinhCity,Hochiminh-12 considered. This research work focuses onthe optimal design of a flow-mode NVBao,Vietnam magneto-rheological (MR) damperthat can replace the conventional passivedamper Fulllistofauthorinformationis for a washing machine. Firstly, rigid mode vibration of the washing machine due to availableattheendofthearticle an unbalanced mass is analyzed and an optimal positioning of thesuppression system for thewashing machine is considered. AnMR damper configuration for the washer is thenproposed considering available space for thesystem. The damping force of the MR damper is derived based onthe Bingham rheological behavior of the MR fluid. Anoptimal design problem for the proposed MR brake is then constructed.The optimization is to minimize thedamping coefficient of theMR damperwhile themaximum value of the damping force is kept being greater than a required value. An optimization procedure based onfinite element analysis integrated with an optimizationtool is employed to obtain optimal geometric dimensionsof the MR damper. The optimal solution of theMR damperis then presentedwith remarkable discussions onits performance. The results are then validatedby experimentalworks. Finally, conclusions on the research work are given and future works for developmentof the research is figured out. Keywords:Magneto-rheological; MR damper; Washing machine; Vibration control Background 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-dryingstage, because thedrumspinsat arelatively high speed causingthe 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 themachine. 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 ©2014Nguyenetal.;licenseeSpringer.ThisisanopenaccessarticledistributedunderthetermsoftheCreativeCommons AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproductioninany medium,providedtheoriginalworkisproperlycited. Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page2of14 http://www.apjcen.com/content/1/1/3 tub balance to eliminate the source of vibration [1,2]. In this approach, one type of dy- namic 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 automatic- ally due to the inherent nature of fluids when the rotational speed is higher than the critical speed of the spinning drum [1]. Another dynamic balancer that counteracts vi- brations 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[2].Itisprovedthatthe vibration ofthewashingmachinecanbesignificantly 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 ap- proach. In the second approach, the vibration of the washing machine is suppressed based on damping control of a suspension system [3]. It is noted that during the spin- ning 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 sideandrearpanelsoftheframemayexperienceresonanceswhichcausenoisesandvi- bration 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 re- duce 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 asamagneto-rheological(MR) damper shouldbeemployed. 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 op- timal 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 con- structed 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.Theresultsarethen validatedbyexperimentalworks. Methods VibrationcontrolofwashingmachineusingMRdamper The washing machine object of this work is a prototype based on the LG F1402FDS washer manufactured by LG Electronics (Seoul, South Korea). A three-dimensional (3D) schematic diagram ofthewasherisshowninFigure 1.Itischaracterized bya sus- pended tub (basket) to store the water for washing linked to the cabinetby two springs Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page3of14 http://www.apjcen.com/content/1/1/3 Figure13Dschematicoftheprototypewashingmachine. and two dampers. The rotor is directly connected with the drum which rotates against the tub while the stator is fixed on the back of the tub. When the drum is rotating, the unbalanced mass due to the eccentricity of laundry causes the vibration of the tub as- sembly. The vibration of the tub assembly is then transmitted to the cabinet and the bottom through the springs and the dampers. In Figure 2, a two-dimensional (2D) sim- plified schematic of the machine is depicted. From the figure, the following governing equation ofthewashingmachine canbederived: (cid:1) (cid:3) (cid:1) (cid:3) mu€þcu_ sin2ðφþβ2Þþ sin2ðφ−β1Þ þku sin2ðφþα1Þþ sin2ðφ−α2Þ ¼FuðtÞ ð1Þ where m is the mass of the suspended tub assembly including the drum, laundry, shaft, counterweight,rotor,andstator.Fortheprototype washingmachine,misroughlyesti- mated about 40kg. cisthe dampingcoefficient ofeach damper,andkis thestiffnessof each spring which is assumed to be 8 kN/m in this study. φ is the angle of an arbitrary direction (u direction) in which the vibration is considered. Fu is the excitation force due to unbalanced mass in the u direction, Fu=F0cosωt=muω2Rucosωt, in which mu and Ru are the mass and radius from the rotation axis of the unbalanced mass. From Equation1,thedamped frequencyofthesuspendedtubassembly iscalculated by qffiffiffiffiffiffiffiffiffiffi ωd ¼ωn 1−ξ2 ð2Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where ωn ¼ k½sin2ðφþα1Þmþsin2ðφ−α2Þ(cid:2)andξ ¼2pc½ffimffisffikiffinffi½ffi2ffisffiðiffiφnffiffiþ2ffiðffiβffiφffi2þffiffiÞffiþαffiffi1ffisÞffiiffiþnffiffi2ffisðffiiffiφnffiffi−2ffiðffiβffiφ1ffi−ffiÞffi(cid:2)αffiffi2ffiffiÞffi(cid:2)ffi: It is seen that the damped frequency and natural frequency of the tub assembly in the u direction are a function of φ. Therefore, in general, in a different direction of vibration, the tub assembly exhibits different resonant frequency. This causes the Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page4of14 http://www.apjcen.com/content/1/1/3 Figure22Dsimplifiedschematicoftheprototypewashingmachine. vibration to become more severe and hard to control. In the design of the suspension system for the tub assembly, the frequency range of the resonance in all directions should be as small as possible. From the above, it is easy to show that, by choosing α +α =90° and β +β =90°, Equation 1 can be simplified to yield 1 2 2 2 mu€þcu_ þku¼Fu ð3Þ In this case, the damped frequency and natural frequency of the tub assembly do not dependonthedirectionofthe vibration.Wehave qffiffiffiffiffiffiffiffiffiffi ωd ¼ωn 1−ξ2 ð4Þ qffiffiffi where ωn ¼ mk andξ ¼2pcffimffiffikffiffi: Aninherentdrawbackofthe conventionaldamperisitshightransmissibilityof vibra- tion 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 areemployedtocontrol the vibrationofthetubassembly. Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page5of14 http://www.apjcen.com/content/1/1/3 Figure 3 shows the schematic configuration of a flow-mode MR damper proposed for theprototypewashingmachine.Fromthefigure,itisobservedthatanMRvalvestructure isincorporatedintheMRdamper.Theouterandinnerpistonsarecombinedtoformthe MR valve structure which divides the MR damper into two chambers: the upper and R s R L p R d R L c W c t d t h Figure3SchematicconfigurationoftheMRdamper. Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page6of14 http://www.apjcen.com/content/1/1/3 lower chambers.These chambers are fully filled with the MR fluid. As the piston moves, the MR fluid flows from one chamber to the other through the annular duct (orifice). The floating piston incorporated with a gas chamber functions as an accumulator to accommodatethepistonshaftvolumeasitentersandleavesthefluidchamber. By neglecting the frictional force and assuming quasi-static behavior of the damper, thedamping force canbe calculated by[7] (cid:5) (cid:6) Fd ¼PaAsþCvisx_pþFMRsgn x_p ð5Þ where Pa, cvis, and FMR, respectively, are the pressure in the gas chamber, the viscous coefficient,andtheyieldstressforceoftheMRdamperwhicharedeterminedasfollows: (cid:7) (cid:8) V γ Pa ¼P0 V þ0Ax ð6Þ 0 s p 12ηL (cid:5) (cid:6) Cvis ¼πR t3 Ap−As 2 ð7Þ d d FMR ¼2(cid:5)Ap−As(cid:6)2:8t5Lpτy ð8Þ d In the above, τy 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. Rd is the average radius of the annular duct given by Rd=R−th−0.5td. L and R are the overall length and outside radius of the MR valve, respectively. th is the valve housing thickness, td is the annular ductgap,andLpisthe magnetic pole length. In this work, the commercial MR fluid (MRF132-DG) made by Lord Corporation (Cary, NC, USA) is used. The post-yield viscosity of the MR fluid is assumed to be in- dependent on the applied magnetic field, η=0.1 Pas. The induced yield stress of the MR fluid as a function of the applied magnetic field intensity (H) is shown in Figure 4. Data Polynomial Curve Fit 50 40 ) a P k ( y30 s, s e r St 20 d =0.044+0.4769H el y Yi 10 -0.0016H2+1.8007E-6H3 0 0 50 100 150 200 250 300 Magnetic Field Intensity, H(kA/m) Figure4YieldstressofMRfluidasafunctionofmagneticfieldintensity. Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page7of14 http://www.apjcen.com/content/1/1/3 By applying the least squares curve fitting method, the yield stress of the MR fluid can beapproximatelyexpressedby τy ¼C0þC1H þC2H2þC3H3 ð9Þ In Equation 9,the unit ofthe yield stress is kilopascal while that ofthe magnetic field intensity is kA/m. The coefficients C , C , C , and C are respectively identified as 0 1 2 3 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 magneticproblemoftheproposedMRdamper. OptimaldesignoftheMRdamper Inthis study,the optimal designofthe proposedMRdamper is consideredbasedonthe quasi-static model of the MR damper and dynamic equation of the tub assembly devel- oped in the ‘Vibration control of washing machine using MR damper’ section. From Figure 2 and Equation 3, the force transmissibility of the tub assembly to the cabinet canbeobtainedasfollows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þð2ξrÞ2 TR¼ ð10Þ ð1−r2Þ2þð2ξrÞ2 where r is the frequency ratio, r=ω/ωn. The dependence of the force transmissibility on excitation frequency is presented in Figure 5. As shown from the figure, at low damping, the resonant transmissibility is relatively large, while the transmissibility at higher frequencies is quite low. As the damping is increased, the resonant peaks are at- tenuated, but vibration isolation is lost at high frequency. This illustrates the inherent trade-off between resonance control and high-frequency isolation associated with the design of passive suspension systems. It is also observed from the figure that when the 6 =0.05 5 =0.1 =0.2 y 4 t bili =0.3 ssi 3 =0.4 mi =0.5 s n a 2 =0.6 r T =0.7 1 0 0 10 20 30 40 Excitation Frequency [Hz] Figure5Transmissibilityofthetubassembly. Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page8of14 http://www.apjcen.com/content/1/1/3 damping ratio is 0.7 or greater, the resonant peaks are almost attenuated. Thus, the higher value of damping ratio is not necessary. It is noted that in Equation 5, the third term F is much greater than the other and the behavior of the MR damper can is MR similar to that of a dry friction damper. By introducing an equivalent damping coeffi- cient C such thattheworkpercycleduetothisequivalentdampingcoefficient equals eq that due to the yield stress damping force of the MR damper, the following equation holds [8]: 4jF j C ¼ MR ð11Þ eq Xωπ or pffiffiffiffiffiffiffi XωπC Xωπξ km kXπξr jF j¼ eq ¼ ¼ ð12Þ MR 4 2 2 Intheabove, Xisthemagnitudeofthetubvibrationwhich isdeterminedby sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X ¼F0 1 ¼mur2Ru 1 ð13Þ k ð1−r2Þ2þð2ξrÞ2 m ð1−r2Þ2þð2ξrÞ2 From Equations 12 and 13, the required value of F can be determined from a re- MR quiredvalueofthedampingratio ξasfollows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jF j¼kπξmur3Ru 1 ð14Þ MR 2m ð1−r2Þ2þð2ξrÞ2 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 mu= 10 kg located atpthffiffiffieffiffiffiffirffiaffiffidius Ru=0.15 m. With the required damping ratio ξ=0.7, at the resonance r ¼ 1−ξ2, the required value of F can be calculated from Equation 14 MR which isaround 150Ninthis study. Takingallaboveintoconsideration,theoptimaldesignoftheMRbrakeforthewash- ing machine can be summarized as follows: Find the optimal value of significant di- mensions of the MR damper such as the pole length Lp, the housing thickness th, the core radius Rc, the width of the MR duct td, the width of the coil Wc, and the overall length ofthe valvestructureLthat 12ηL (cid:5) (cid:6) MinimizetheviscouscoefficientðobjectivefunctionÞ;OBJ¼cvis ¼πR t3 Ap−As 2 d d Subjectedto:FMR ¼2(cid:5)Ap−As(cid:6)2:8t5Lpτy≥150N d In order to obtain the optimal solution, a finite element analysis code integrated with an optimization tool is employed. In this study, the first-order method with the golden section algorithm of the ANSYS optimization tool is used. Figure 6 shows the flow chart to achieve optimal design parameters of the MR damper. Firstly, an analysis ANSYS file for solving the magnetic circuit of the damper and calculating the objective function is built using ANSYS parametric design language (APDL). In the analysis file, the design variables (DVs) such as the pole length Lp, the housing thickness th, the core radius Rc, the width of the MR duct td, the width of the coil Wc, and the overall length Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page9of14 http://www.apjcen.com/content/1/1/3 Figure6FlowcharttoachieveoptimaldesignparametersoftheMRdamper. ofthevalvestructureLmustbecodedasvariablesandinitialvaluesareassignedtothem. The geometric dimensions of the valve structure are varied during the optimization process; the meshing size therefore should be specified by the number of elements per line rather than the element size. Because the magnetic field intensity is not constant along the pole length, it is necessary to define paths along the MR active volume where magnetic flux passes. The average magnetic field intensity across the MR ducts (H ) is mr calculated by integrating the field intensity along the defined path then divided by the pathlength.Thus,themagneticfieldintensityisdeterminedasfollows: ZLp 1 H ¼ HðsÞds ð15Þ mr L p 0 where H(s) is the magnetic flux density and magnetic field intensity at each nodal point onthedefined path. From the figure, it isobserved that the optimization isstartedwith the initialvalue of DVs. By executing the analysis file, first the magnetic field intensity is derived. Then the yield stress, yield stress damping force, and objective function are respectively cal- culated from Equations 9, 7, and 8. The ANSYS optimization tool then transforms the optimization problem with constrained design variables to an unconstrained one via Nguyenetal.AsiaPacificJournalonComputationalEngineering2014,1:3 Page10of14 http://www.apjcen.com/content/1/1/3 penalty functions. The dimensionless, unconstrained objective function f is formulated asfollows: Xn OBJ fðxÞ¼OBJ þ PxiðxiÞ ð16Þ 0 i¼1 where OBJ is the reference objective function value that is selected from the current 0 group ofdesignsets. Pxi is theexterior penalty functionfor the designvariable xi. For the initialiteration(j=0),thesearchdirectionofDVsisassumedtobethenegativeofthegra- dientoftheunconstrainedobjectivefunction.Thus,thedirectionvectoriscalculatedby (cid:9) (cid:10) dð0Þ ¼−∇f xð0Þ ð17Þ The values of DVs in the next iteration (j+1) is obtained from the following equation: xðjþ1Þ ¼xðjÞþsjdðjÞ ð18Þ where the line search parameter sj is calculated by using a combination of the golden section algorithm and a local quadratic fitting technique. The analysis file is then exe- cuted with the new values of DVs, and the convergence of the objective function is checked.Ifthe convergenceoccurs,the valuesofDVsatthisiteration aretheoptimum. If not, the subsequent iterations will be performed. In the subsequent iterations, the procedures are similar to those of the initial iteration except for that the direction vec- tors are calculated accordingtothePolak-Ribiererecursionformulaasfollows: (cid:9) (cid:10) dðjÞ ¼−∇f xðjÞ þrj−1dðj−1Þ ð19Þ (cid:1) (cid:5) (cid:6) (cid:5) (cid:6)(cid:3) (cid:5) (cid:6) ∇f xðjÞ −∇f xðj−1Þ T∇f xðjÞ whererj−1 ¼ j∇fðxðj−1ÞÞj2 : ð20Þ Results and discussion In this study, an optimal design of the MR damper for the washing machine is per- formed basedontheoptimization problem developedinthe‘OptimaldesignoftheMR damper’section. Itisassumedthatthepistonpartandhousingofthedamperaremade of commercial silicon steel, and the coil wires are sized as 21 gage (diameter= 0.511 mm) whose allowable working current is 2.5A. In the optimization, the applied current is assumed to be 2A. Figure 7 shows the optimal solution of the MR damper in case the pole length Lp, the housing thickness th, the core radius Rc, the width of the MRducttd, thewidth ofthe coil Wd,andthe overall length ofthe valve structure L are consideredasdesignvariables.Fromthefigure,itcanbefoundthatwithaconvergence tolerance of 0.5%, the optimal process is converged after 14 iterations and the solution at the 14th iteration is considered as the optimal one. The optimal values of Lp, th, Rc, td, Wd, and L, respectively, are 7.4, 2.5, 5.2, 2, 1.8, and 25 mm. It is noted that the opti- mal values of td and th are equal to their lower limits in this case. These limits are posed considering the stability and manufacturing cost of the damper. At the optimum, the viscous coefficient is significantly reduced up to 10 Ns/m from its initial value (290 Ns/m). When no current is applied to the coil, the damping ratio at the optimum is