Analysis and Design of Circular Plate MR Fluids Brake

第38卷增刊上海交通大学学报VolL,38 sup.2004年6月JOURNAL OF SHANGHAI JIAOTONG UNIVERSITYJun. 2004文章编号: 1006-2467(2004)S1-0152-03Analysis and Design of Circular Plate MR Fluids BrakeYang Yan',a , Lin Chang-Hua', Li Hui2c and Zhou Jing1d1 Department of Mechanic, Chongqing Institute of Technology, Chongqing, 400050 China,2 Department of Material, Chongqing Institute of Technology, Chongqing, 400050 Chinayangyan@cqit.edu.cn, 'linchanghua @cqit.edu.cn, "lihui @qit.edu.cn, Szhoujing@cqit.edu.cnAbstract: A magnetorheological (MR) fluids brake is a device to achieve brake by shear force of MRfluids. A MR rotary brake has the property that its braking torque changes quickly in response to anexternal magnetic field. In this study, the design method of the circular plate MR fluids brake isinvestigated theoretically. The equation of the torque transmitted by the MR fluids in the brake isderived to provide the theoretical foundation in the design of the brake. Based on this equation, aftermathematically manipulated, the calculations of the volume, thickness and width of the MR fluidswithin the circular plate MR fluids brake are yield.Key words: MR fluids; brake; design method1 IntroductionMagnetorheological(MR) fluids consist of stable suspensions of particles in a carrying fluid suchas silicone oils. They are smart materials that respond to an applied magnetic field in their rheologicalbehavior. In the absence of applied magnetic field, MR fluids exhibit Newtonian-like behavior. Uponapplication of a magnetic field, The suspended particles in the MR fluids become polarized and alignthemselves, like chains, with the direction of the magnetic field and the behavior of the fluids is oftenrepresented as semi-solids having a controllable yield stress in milliseconds. The yield stress of MRfluids increases as the applied magnetic field increases. The feature provides reversible, quiet, rapidresponse interfaces between electronic controls andmechanical systemsl"1.2 Operational Principle_ MR fluldsA magnetorheological (MR) fluids brake is adevice to achieve brake by shear force of MR fluids.人shaft 2A MR rotary brake has the property that its brakingtorque changes quickly in response to an externalmagnetic field. The operational principle of theFlux pa thcircular plate MR fluids brake is shown in Fig. 1.The MR fluids fil the gap between the fixed shaft2.and the rotary shaft 1. The shaft 1 rotates at rotaryspeedof w.Fig.1 The operational priciple of the MR brakeIn the absence of an applied magnetic field, thebrake torque is the viscous force of MR fluids inliquid state. When the external magnetic field is applied, the suspended particles in the MR fuidsbecome polarized and gathered to form chain-like structure. These chain-like structures restrict themovement of the MR fluids, thereby increasing the;中国煤化工le brake can beachieved by utiling the shear stress of the MR fu?YHCN MH Gan be adjusted .continuously by changing the magnetic field strength.增刊Yang Yan, et al: Analysis and Design of Circular Plate MR Fluids Brake .1533 The Shear Stress of MR FluidsMany constitutive equations were presented to exhibit the behavior of the MR fluidsk4. Butthose equations are too complex to apply.The behavior of the MR fluids is often represented as aBingham fluids. In this model, the constitutive equation is derived by 5y.τ=Tg +7Ywhere T is the stress; Tp is the dynamic yieldσ 60p✧0.17stress developed in response to the applied*---*-x- x+0.2Tmagnetic field, its value is dependent upon they 40-← ★★★→+0.4Tmagnetic induction B; η is the viscosity; Y is- *0.57the fluid shear rate.”20F+++景The relationship between shear stress ands110 tshear rate of a sort of MR fluid (manufactured by万050100 150 200 250 300ourselves) is shown in Fig. 2. As can be see, theshear stress of MR fluids increasing with theShear rate/s-Iapplied magnetic field strength. The shear rateFig. 2 Shear stress vesus shear ratehas lttle influence on the shear stress.4 Analysis of Braking TorqueFig. 3 shows the fluids in the circular plate brake. Whenthe magnetic field is applied, the braking torque developed by/Rxthe MR fluids can be calculated byT=2n”or'drdz(2)where R is radius of the circular plate, H is the effective of MR3zeffect developed by the MR fluids.The shear rate γ of discretional position in MR fluidscan be calculated byγ= @(z)H(3)Fig. 3 Analysis of braking torquewhere 0(z) is the rotate speeds of discretional position inMR fluids, r and h are the radius and thickness.Because the value of H is very smaller than the value of the R, we can think 0(z) is the linearequation. Applying the boundary conditions: 0(z)=0 at z= 0and 0(z)=0at z= H , we obtain@(z)= wH-z(4)Integrating Eq.(1)~(4), the braking torque T developed by the MR fluids can be calculated, toyieldT=πt,HR' +;πonR4(5)Eq. (5) shows that the braking torque developed in the circular plate MR fluid brake can bedivided into a magnetic field dependent induced yield stress component Tg and a viscous componentTπ.Tg=二πT中国煤化工(6):TYHCNMHGTr = nwpj.(7)The total torque T is the sum of Tp and Ty.154上海交通大学学报第38卷T=Tg +T,(8) .5 The Radius, Thickness and Volume of MR FluidsThe active volume of MR fluid in the circular plate MR brake can be obtained as follow:V=rR'H(9) .Eq.(6), Eq.(7), Eq.(9) can be further manipulated to yield the relationship between H and RH._3Tgηw(10)The Eq.(10) provides geometric constraints for MR fluid brake based on MR fluid materialproperties (η1rg), the desired control torque ratio (T/T ) and a given rotational speed 0.6 Design Example of the Circular Plate MR Fluids BrakeFor this example, the following parameters are given:Pm=1000W，wm =20(1/s)Based on the anticipated performance of brake and the properties of MR fluid, the desiredcontrol torque ratio (Tg/T,) may be chosen. For this example, the desired control torque ratio ischosen to be:T/T, =20The parameters (η/τp ) have something to do with the MR fluid material properties. In order toreduce the dimensions of the brake, a designer should select the highest yield stress developed inresponse to an applied magnetic field Tp under the MR fluid saturation magnetization and the lowestviscosity of MR fluid η possible. With this knowledge, For this example, assume that the MR fluidcan be magnetically saturated , the Tg and η are:τg= =40kPa, n=0.33Pa .sIntegrating all above, we obtain the H IR = 0.002475. Considering the value of the power, wewill know the size of brake will be small. We chose R=10mm, so H=0.2475mm, V=7771.5mm*.7 ConclusionThe geometric design method of circular plate MR fuid brake is investigated theoretically inthis paper. The braking torque developed by MR fluids within the brake under different magneticfield conditions was analyzed. The engineering design calculations of the volume, thickness andradius of the circular plate MR fluid within the brake are derived. The parameters of the thickness andradius of the fluid in the brake can be calculated from the obtained equations when the requiredmechanical power level, the rotational speed and the desired control torque ratio are specified.References:[1] D. JI. Carlson, M. D. Catanzarite, A. K. Clair: Comnercial magnetorheological fluid devices. Proceeding of the s$ IntemnationalConference on Electrorheological Fluids. Magnetorheological Suspensions and Associated Technology. Sheffeld, UK. July10~14,1995. P.20-28. (Copyright: World Scientifc Publishing, Co Pte, Ltd)[2] Z. P. Shulman, W.1. Kordonsky: Structure, Physical Properties and Dynamics of MR Suspen- sions. J. Muliphase Flow. (1986),12(6), p.935-955[3] R. Mark. Jolly, J. David. Carlson, C. Beth. Munoz: A Model of The Behavior of MR Materials. J. Smart Material and Structure.5(1996), p.607-614[4} Y. Yang, w. J. 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