[[abstract]]In this paper, a multibody dynamic model is developed for a front loading type washing machine in details.
This model is constructed for verifying the bearing model
between the tub and drum, and for analyzing the suspension
system composed by two springs and magnetorheological
dampers between the case and basket. The obtained results
help engineers to design washing machines efficiently.[[sponsorship]]National Taipei University of Technology[[conferencetype]]國際[[conferencedate]]20091127~20091129[[iscallforpapers]]Y[[conferencelocation]]Taipei, Taiwa

[[corresponding]]Tyan, Feng

Tyan, Feng

In this paper, a multibody dynamic model is developed for a front loading type washing machine in details.
This model is constructed for verifying the bearing model
between the tub and drum, and for analyzing the suspension
system composed by two springs and magnetorheological
dampers between the case and basket. The obtained results
help engineers to design washing machines efficiently.National Taipei University of Technology國際20091127~20091129YTaipei, Taiwa

Tamkang University Institutional Repository

Proceedings of 2009 CACS International Automatic Control ConferenceNational Taipei University of Technology, Taipei, Taiwan, Nov. 27-29, 2009Modeling and Vibration Control of a Drum-Type Washing Machinevia MR Fluid DampersFeng Tyan and Chung-Ta ChaoComputational Dynamics and Control LabDepartment of Aerospace EngineeringTamKang UniversityTamshui, Taipei County 25147, Taiwan, R.O.C.email: tyanfeng@mail.tku.edu.twShun-Hsu TuSky Leading CorportationChupei, Hsin Chu County, Taiwan 30204, R. O. C.Abstract— In this paper, a multibody dynamic model isdeveloped for a front loading type washing machine in details.This model is constructed for verifying the bearing modelbetween the tub and drum, and for analyzing the suspensionsystem composed by two springs and magnetorheologicaldampers between the case and basket. The obtained resultshelp engineers to design washing machines efficiently.Keywords – drum type washing machine, MR fluid damperI. INTRODUCTIONWashing machines had been developed to be automaticmachines with several milestones. Automatic washing ma-chines can be characterized into two types according toloading types, namely, top loading model with vertical axisand front loading type with horizontal axis. Front loadingtype had become standard in Europe, and top loading modelswere popular in America and Asia. Recently, front loadingtype has been increased in the United States and Asia.To reduce vibration and oscillatory walk, one type ofdynamic balancer that can be used of washing machines is ahydraulic balancer, which contains salt water and is attachedat the upper rim of the basket. The liquid in the balancermoves to the opposite side of unbalance automatically due toinherent nature of fluids when the rotational speed is higherthan the critical speed of the spinning drum [1]. Anotheractive balancing that counteracts vibrations is to use twobalancing masses. In this method, two balancing massesmove along the rim of the basket. The rotation plane of thebalancing masses can be easily chosen to be wherever judgedsuitable, always targeting at the reduction of the inducedmoments [2].For the vibration caused by the imbalance of clothes dur-ing the varying spin-drying stage in a drum-type washing ma-chine requiring the varying damping force to be reduced toget the results of vibration reduction that we need. Recently, anew way of using low-cost, controllable magnetorheological(MR) sponge dampers was developed [3], which is appro-priate for the next-generation high-performance horizontal-axis washing machines when a moderate-force is desired.The control system is implemented via a semi-active mag-netorheological (MR) damper located on the suspension thatlinks the basket to the cabinet. The suspension is to damp thebasket movements and to reduce the vibrations transmittedto the chassis, which are strictly related to the perceivedacoustic noise. The idea is to use electronically-controlledMR dampers to adapt the on-line damping characteristics toreduce vibration level of the washing machine panels wasproposed in [4].This paper is organized as follows. Section 2 describes...II. WASHING MACHINE MODELA model of a horizontal-axis washing machine is shown inFig. 1. Three coordinate systems are adopted in this system:XY Z: inertial coordinate system, attached to the groundat the initial position of center of mass of washingmachine, G (see Fig. 1).xbybzb: body coordinate system, attached to the basket atits center of mass, Gb (Fig. 2).xdydzd: body coordinate system, attached to the drum atits center of mass, Gd (see Fig. 3).Fig. 1. Schematic View of a Horizontal-axis Washing MachineFig. 2. Body Coordinate System for BasketFig. 3. Body Coordinate System for DrumIn this washing machine system model, we assume thatthe basket is a thin cylinder with the front end opened, therear side sealed with a thin disk, and the motor is attached tothe rear side. We also assume that the drum is a thin cylinderwith a similar structure as the basket.A. Bearing between Basket and DrumThe bearing system installed between the tub and the drumwas modeled with three degrees of freedom (see Fig. 4) [5],that is,1) the first one is for the vertical motion in planar joint,2) the second one is for horizontal motion in planar joint,and3) the third one is for rotation of the drum.Although this bearing model does not correctly predict theacceleration in the vertical direction as was pointed out in[5] when the drum is loaded with unbalanced laundary, thismodel is adopted in this work for simplicity.Fig. 4. Schematic View of Bearing Model between Basket andDrumB. Contact Force between Tub and DrumTo present real motions between the drum and bearings,contact force was used. The algorithm of contact was selectedas shown in equation (2.1). This makes normal force Fn andtangential force Ft when the drum impacts the front bearingas shown in Fig. 5.Normal force Fn was calculated from equation (2.1), andtangential force Ft was applied with assumption of Coulombfriction [5].Fn = k × ge + Step (g, 0, 0, dmax, cmax)dgdt, (2.1)wherek is the stiffness of boundary surface,g is the gap size between two boundaries,Fig. 5. Contact Force between Tub and Drum [5]dmax means the penetration depth, andcmax is the damping coefficient.III. THREE WALK MODES FOR A WASHING MACHINEIt has been shown in [2] that the minimum critical spinspeed of the impending rotational slipωrot =√fg(mc x1x2 +mL)mL(rd − rL)√1 + f2. (3.1)whererd and rL are the radius of drum and laundry, respec-tively,f is a constant Coulomb friction coefficient,and the other variables are defined in Fig. 6. In the meantime, as x1x2 = 1, the washer will not rotate, the critical spinspeed becomes for the impending translational slipωtra =√fg(mc +mL)mL(rd − rL)√1 + f2. (3.2)Fig. 6. (a) Laundry Forces on The Drum (b) The Front View of a HorizontalAxis Washing Machine (c) The Free Body Diagram of The Horizontal AxisWashing Machine in The Bird’s Eye View [2]From [6] the critical spin speed of the impending tippingcondition isωtip =√ahg(mc +mL)mL(rd − rL)√1 + ( ah )2, (3.3)where the variables are defined in Fig. 6 (b). A washingmachine in three dimensions can in principle have three walkmodes : tip, rotational slip and translational slip. With thecomparisons among euqations (3.1), (3.2) and (3.3), we canfind the relationship among ωrot, ωtra and ωtip as ωrot <ωtra < ωtip under two conditions as followingsx1x2≤ 1, f ≤ ah.When the laundry is rotated across the angle α, three walkmodes for a washing machine will be induced under theseconditions as followingsWhen ωtra < ω < ωtip, the washing machine will bemoved along the positive x-direction axis,When ωtip < ω, the washing machine will be movedup and down heavily and turned over finally.Where ω is the spin speed of the drum. ωrot, ωtra, ωtip andω are all constant values. On the contrary, a washing machinehas no movements under this condition when the laundry isrotated across the angle αω < ωrot < ωtra < ωtip.In the practical analysis of walk, tipping is considered asafety hazard in the industry and is not allowed to occur.So, from equations (3.2) and (3.3), the design criterion for awashing machine becomes [6]f <ah.IV. CONTROL SCHEME FOR THE WASHING MACHINEA. Modified Bouc-Wen Model for MR DamperA modified Bouc-Wen model (see Fig. 7) for betterpredicting the response of the MR damper in the region ofthe yield point was proposed by [7] and is adopted in thiswork.The equations governing the force Frh exerted by the MRFdamper arex˙1 − y˙ = 1co + c1[−ko(x1 − y)− αz + c1x˙p1],z˙ = (x˙1 − y˙){δ − |z|n[β + γsgn(x˙1 − y˙)sgn(z)]}.Frh = −c1(x˙1 − y˙) + c1x˙p1 + k1(xp1 − x¯o),=c1co + c1[ko(x1 − y) + αz]+coc1co + c1x˙p1 + k1(xp1 − x¯o).The voltage dependent parameters are modeled byα = αa + αbu, co = coa + cobu, c1 = c1a + c1bu.Furthermore, the command voltage is accounted for throughthe firest-order filteru˙ = −η(u− v), u(0) = 0.The command input v is confined to be finite positive toreflect the real situation of the saturation of the magneticfield in the MR fluid damper [7].Fig. 7. Modified Bouc-Wen ModelB. Controller SynthesisIn this work the schematic of a semiactive control systembased on an MR fluid damper is illustrated in Fig. 8. TheMR damper based semiactive control system consists ofa system controller and a voltage algorithm. The systemcontroller generates the desired voltage according to thedynamic responses of the plant while the voltage algorithmadjusts the desired voltage to meet the range of the value forthe voltage between 0v ∼ 2.25v being under the saturationcondition.The two measurements ar and aL in Fig. 8 are asfollowingsar = atop · ~jr + aside · ~jr,aL = atop · ~jL + aside · ~jL.We present a PI control strategy to control the vibration ofthe suspension system. The values of the desired voltage forVrd and VLd in Fig. 8 can be defined as followingsVrd = KP · ar +KI ·∫ardt,VLd = KP · aL +KI ·∫aLdt.Fig. 8. Semi-active Control Systems for a Plant Integrated withMR Fluid DamperThe voltage algorithm for varying the applied voltage Vrand VL can be obtained in Fig. 8 as followingsIf Vrd > 2.25v, Vr = 2.25v. The same result is also forVLd.If 0v < Vrd < 2.25v, Vr = Vrd. The same result is alsofor VLd.If Vrd < 0v, we substitute Vrd with |Vrd| and thenfollows the above principles as followings.If |Vrd| > 2.25v, Vr = 2.25v. The same result isalso for |VLd|.If 0v < |Vrd| < 2.25v, Vr = |Vrd|. The same resultis also for |VLd|.V. NUMERICAL EXAMPLESIn this example, the PI controller synthesis is implementedto provide the desired voltages Vrd and VLd, and the voltagealgorithm is adopted to get the applied voltage Vr and VLfor two MR dampers in the range between 0v ∼ 2.25v. Thesystem parameters with Recurdyn are given in Table I, TableII and Table III for the washing machine, MR damper andcontact force, respectively. The parameters LE, W , H , MAmean the length, width, height and mass, respectively. Theparameters C, V , U mean the coefficient, value and unit,respectively.TABLE IPARAMETERS FOR WASHING MACHINEBody LE W, H MACase 500mm 500mm 100kgBasket 450mm 150mm 8kgDrum 300mm 100mm 4kgMotor 37.5mm 50mm 7kgLaundry 28.28727mm 28.28727mm 13kgTABLE IIPARAMETERS FOR MR DAMPER (LORD, RD-1005-3) IN MODIFIEDBOUC-WEN MODELC V U C V Ucoa 2.1 N s/mm αb 69.5 N/V mmcob 0.35 N s/V mm γ 3.63 mm−2c1a 28.3 N s/mm β 3.63 mm−2c1b 0.295 N s/V mm δ 301ko 4.69 N/mm n 2k1 30.425176 N/mm η 190 s−1αa 14 N/mm x¯o 0 mmTABLE IIIPARAMETERS FOR CONTACT FORCEC V U C V Uk 2.0E5 N/mm cmax 1 N s/mmg 20 mm β 2.5e 2.2 µs 0.3dmax 10 mm µk 0.1The parameters used in PI controller are chosen to beKP = 2.9, KI = 12.35.It is clear that the vibrations of the basket and case aresuppressed after two MR dampers work. The open-loop (left)and closed-loop (right) simulations are shown in Fig. 9 - 16for comparison purposes.Fig. 9. Horizontal Displacement of The BasketFig. 10. Vertical Displacement of The BasketFig. 11. Lateral Displacement of The BasketFig. 12. Horizontal Displacement of The CaseFig. 13. Vertical Displacement of The CaseVI. CONCLUSIONSIn this paper, a multibody dynamic model of a drum-typewashing machine with MR fluid dampers was generated ina commercial package “RecurDyn”, The resultant displace-ments from Recurdyn-Simulink simulation were conductedby utilizing this virtual system. The following conclusionswere obtained.1) Owing to this virtual system of a washing machine, weable change the parameters of the washing machine toFig. 14. Lateral Displacement of The CaseFig. 15. Case Acceleration in Right MR Damper DirectionFig. 16. Case Acceleration in Left MR Damper Directionwhat are required, and relocate the springs and MRdampers at the ours will efficiently.2) From the comparison of the above figures, we can seethat the PI control strategy is the best for reducing thevibrations of the bakset and the case at the same time.REFERENCES[1] S. Bae, J. M. Lee, Y. J. Kang, J. S. Kane, and J. R. Yun,“Dynamic analysis of an automatic washing machinewith a hydraulic balancer,” Sound and Vibration, vol. 257,no. 1, pp. 3–18, October 10 2002.[2] E. Papadopoulos and I. Papadimitriou, “Modeling, de-sign and control of a portable washing machine duringthe spinning cycle,” in IEEE/ASME International Confer-ence on Advanced Intelligent Mechatronics Systems, July2001, pp. 889–904.[3] M. J. Chrzan and J. D. Carlson, Eds., MR Fluid SpongeDevices and Their Use in Vibration Control of WashingMachines, Lord Corporation. SPIE 4331, 2001.[4] F. Previdi and C. Spelta, “Control of magnetorheologicaldampers for vibration reduction in a washing machine,”Mechatronics, September 16 2008.[5] N. Gyung-Hun, Y. Wan-Suk, C. Bo-Sun, K. Dong-Woo,and L. Jae-Cheol, “Matching of multibody dynamic sim-ulation and experiment of a drum-type washing machine,”in Proceedings of ACMD, no. A00662, 2006.[6] D. C. Conrad and W. Soedel, “On the problem ofoscillatory walk of automatic washing machines,” Soundand Vibration, vol. 188, no. 3, pp. 301–314, December1995.[7] F. Tyan, S. H. Tu, and W. S. Jeng, “Semi-active aug-mented h∞ control of vehicle suspension systems withmr dampers,” Journal of the Chinese Society of Mechan-ical Engineers, vol. 29, no. 3, pp. 249–255, 2008.APPENDIX: NOMENCLATUREPL center of mass of the laundry.m mass.φ, θ Euler angles.r, h radius and length, respectively.atop, aside acceleration in the center of top and leftlocation of the case, respectively.jr, jL direction of movements for the right andleft MR damper, respectively.k stiffness of the boundary surface interac-tion.c, f damping and friction coefficient.g gap size between two boundaries.σ gap size variation w.r.t. time.e spring force of restitution for non-linearcharacteristics, e ≥ 2.1 the results runbetter using this exponent value in theimpact function.β damping force of restitution for non-linearcharacteristics.x1−y, xp1,zinternal and external relative displacementand hysteretic component, respectively.x¯o initial displacement.η the delay time of the MR damper.v command voltage sent to the currentdriver.Subscripts,b, d, c basket, drum, case, respectively.L, m laundry and motor, respectively.cb, cd thin cylinder belonging to the basket anddrum, respectively.bp, dp thin disk belonging to the basket and drum,respectively.bf , df center point of the basket and drum in thefront side, respectively.

Modeling and Vibration Control of a Drum-Type Washing Machine via MR Fluid Dampers

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Modeling and Vibration Control of a Drum-Type Washing Machine via MR Fluid Dampers

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