汽车磁流变制动器设计的多学科设计优化【中文8000字】
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汽车磁流变制动器设计的多学科设计优化【中文8000字】,中文8000字,汽车,流变,制动器,设计,学科,优化,中文
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Multidisciplinary design optimization of an automotive magnetorheological brake design Edward J. Park, Luis Falca o da Luz, Afzal Suleman * Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6 Available online 3 April 2007 Abstract This paper presents the development of a new electromechanical brake system using magnetorheological (MR) fl uid. The proposed brake system consists of rotating disks immersed in a MR fl uid and enclosed in an electromagnet, where the yield stress of the fl uid varies as a function of the magnetic fi eld applied by the electromagnet. The controllable yield stress causes friction on the rotating disk surfaces, thus generating a retarding torque. The braking torque can be precisely controlled by simply changing the current applied to the elec- tromagnet. Key issues involved in the initial design of the automotive MR brake are presented such as the MR fl uid selection, magnetic circuit design, torque requirements, weight constraints, dimensions and temperature. A multidisciplinary fi nite element analysis is per- formed involving magnetostatics, fl uid fl ow, and heat transfer analysis to study the behaviour of the system, and to serve as basis for a multidisciplinary design optimization procedure. The results of the optimization procedure are presented and the fi nal design obtained is discussed in detail. ? 2007 Elsevier Ltd. All rights reserved. Keywords: Magnetorheological fl uid; Automotive brake; Finite element analysis; Computational fl uid dynamics; Multidisciplinary design optimization; Electric brake actuator 1. Introduction This work is concerned with the development of a new brake-by-wire system for automotive vehicles, using an electromechanical brake (EMB) that employs magnetorhe- ological (MR) fl uid. Brake-by-wire replaces the mechanical connection between the brake actuator on each wheel and the brake pedal with electrical components. There are many advantages of using a pure electronically controlled brake system over a conventional hydraulic brake (CHB) system. The properties and behaviour of the brake will be easy to adapt by simply changing software parameters and electrical outputs instead of adjusting mechanical com- ponents. This also allows easier integration of existing and new control features such as anti-lock braking system (ABS), vehicle stability control (VSC), electronic parking brake (EPB), etc., as well as vehicle chassis control (VCC) and adaptive cruise control (ACC). Diagnostic fea- tures and the elimination of the water polluting brake fl uids are additional benefi ts 1, as well as a small number of components, simplifi ed wiring and generalized optimized layout. In this paper, we propose a MR actuator design for the brake in each wheel. The actuator consists of a rotating disk immersed in a MR fl uid, enclosed in an electromagnet. In principle, the brake torque can be controlled by changing the DC current applied to the electromagnet. Magnetorhe- ological fl uid a compound containing fi ne iron particles in suspension stiff ens in the presence of a magnetic fi eld. Two important characteristics of MR fl uids are: (i) they exhibit approximately linear response, i.e., the increase in stiff ness is directly proportional to the strength of the applied mag- netic fi eld and (ii) they provide fast response, i.e., MR fl uid changes from a fl uid state to a near-solid state within milli- seconds of exposing a magnetic fi eld. CHB systems exhibit about 200300 ms of delay between the time the brake pedal 0045-7949/$ - see front matter ? 2007 Elsevier Ltd. All rights reserved. doi:10.1016/pstruc.2007.01.035 * Corresponding author. Tel.: +1 250 721 6039; fax: +1 250 721 6051. E-mail address: sulemanuvic.ca (A. Suleman). /locate/compstruc Available online at Computers and Structures 86 (2008) 207216 is pressed by the driver and the corresponding brake response is observed at the wheels due to pressure build- up within the hydraulic lines. An electric brake system has the potential to drastically reduce this time delay, conse- quently bringing a reduction in braking distance. Recently, Delphi 2 introduced an EMB with performance similar to the existing disk brakes, with the brake pads actuated by an electrical motor, instead of the hydraulic actuator. While the application of MR fl uid in automotive vehi- cles has been promising for years, it is only recent that MR fl uid-based electromechanical devices have started to displace all-mechanical or hydraulic counterparts. For instance, General Motors recently introduced the Magnetic Ride Control 3, which is a MR fl uid-based suspension control system developed by Delphi, on the Corvette and Cadillac Seville STS and XLR. The signifi cance with these new systems is that the vehicle control is quickly evolving away from the limitations of traditional mechanical com- ponents, such as springs, brakes, shocks and steering gear. Instead, real-time sensors and high-speed, direct electric actuation can now adjust all these systems depending on driving conditions 4. In this regard, a MR brake (MRB) actuator is a promising technology for the automotive industry with high commercial values. The outline of this paper is as follows. In Section 2, the MR fl uid phenomenon is explained in detail. In Section 3, our proposed automotive MRB design is described and modelled. Sections 4 and 5 present the multidisciplinary fi nite element analysis and subsequent design optimization of the proposed MRB. Section 6 presents design optimiza- tion results, along with transient temperature simulations, and the resulting dimensions and parameters of the fi nal MRB design. Section 7 concludes the paper. 2. MR fl uids MR fl uids are created by adding micron-sized iron par- ticles to an appropriate carrier fl uid such as oil, water or sil- icon. Their rheological behaviour is nearly the same as that of the carrier fl uid when no external magnetic fi eld is pres- ent. However, when exposed to a magnetic fi eld, the iron particles acquire a dipole moment aligned with the applied magnetic fi eld to form linear chains parallel to the fi eld 6. This reversibly changes the free fl owing liquid to semi-sol- ids that have a controllable yield strength, which depends on the magnitude of the applied magnetic fi eld. Although MR fl uids have been known for decades, they had been experiencing stability and longevity issues for commercial applications. Recently, however, these prob- lems have been solved and commercial applications are starting to appear, most notably as controllable dampers in the afore-mentioned car suspensions 4 and in civil engi- neering applications for seismic response control 5. In the literature, it is found that the essential magnetic fi eld dependent fl uid characteristics of MR fl uids can be described by a simple Bingham plastic model 6. As illus- trated in Fig. 1, in this model, the total shear stress s is given by s syH g_ c1 where sy is the yield stress due to the applied magnetic fi eld H, g is the constant plastic viscosity, which is considered equal to the no-fi eld viscosity of the fl uid, and _ c is the shear-strain rate. Here, the plastic viscosity is defi ned as the slope between the shear stress and shear-strain rate, which is the traditional relationship for Newtonian fl uids. True behaviour of MR fl uids exhibits some signifi cant departures from the Bingham model in the absence of a Shear Strain Rate (s-1) Total Shear Stress (Pa) y 1 Fig. 1. Bingham plastic model. Fig. 2. Shear stress as a function of shear-strain rate with no magnetic fi eld applied: (a) MRF-132AD and (b) MRF-241ES. 208E.J. Park et al. / Computers and Structures 86 (2008) 207216 magnetic fi eld (i.e., lp lp_ c;H) 7. Other researchers have tried more elaborate models such as the Herschel Bulkely model 8,9 to accommodate the shear-strain rate dependent shear thinning and shear thickening phenomena in the fl uid. However, if used properly Eq. (1) provides a useful basis for the design of MR fl uid-based devices 10, and the simple Bingham model is still very suitable for the initial design phase 5. In addition, the Lord Corpora- tions hydrocarbon-based MRF-132AD and water-based MRF-241ES, which are analyzed and compared in this paper, have nearly linear experimental stress-shear rate curves (see Fig. 2) that are well approximated by the Bing- ham model. Table 1 summarizes some of the key properties of these two MR fl uids that are most suitable for the auto- motive brake application. As can be seen from the table, the water-based MRF-241ES has a higher yield stress than MRF-132AD, but lower magnetic permeability. 3. Automotive MR fl uid brake Shown in Fig. 3 is a three-dimensional illustration of the basic confi guration of the MR brake (MRB) actuator design that is proposed and analyzed in this paper. It con- sists of a disk rotating within MR fl uid enclosed in a static casing. In Fig. 3, a cut has been made to highlight the cross-section that was modelled and analyzed. The legend in the fi gure indicates the various components of the MRB with the exception of the MR fl uid, which is located in the narrow channel (part no. 7) surrounding the rotating disk (no. 3) and the stator (no. 5). Based on Eq. (1) and the given geometrical confi gura- tion shown in Fig. 1, the retarding torque or braking torque which is caused by the friction on the interfaces between the MR fl uid and the solid surfaces within the MRB can be written as 11 Tb 2pn Z rz rw sr2dr 2pn Z rz rw g_ c sHr2dr2 where n is the number of surfaces of the brake disk(s) in contact with the MR fl uid (e.g., 2 for 1 disk with MR fl uid covering the both sides, 4 for 2 disks, etc.); rzand rware the outer and inner radii of the brake disk, respectively; and _ c rx h andsy kHb where x is the angular velocity of the rotating disk, h is the thickness of the MR fl uid gap, H is the magnetic fi eld inten- sity, and k and b are constant parameters that approximate the relationship between the magnetic fi eld intensity and the yield stress for the MR fl uid. Then, Eq. (2) can be rewritten as Tb 2pn Z rz rw g rx h kHb ? r2dr3 Eq. (3) is a more accurate form than that of the Lord Cor- porations low torque MRB used in 12, because it can take into account non-constant magnetic fi eld distribu- tions. This improvement is necessary in order to use a greater amount of MR fl uid (which causes greater varia- tions in the magnetic fi eld intensity) than that of 12, which was used for AC induction motor braking. Eq. (3) provides some insight into the dynamics of an MRB and shows pos- sible ways to improve the braking torque, including the use of multiple disk surfaces (increasing n) or fl uids with high yield stresses (increasing k and/or b). Improving the brak- ing torque by amplifying the fi rst term in the integral, i.e., increasing the plastic viscosity g or decreasing the gap thickness h, is not desired as this would lead to a greater residual torque (increasing the drag even without the brakes applied). Eq. (3) indicates that, while carrying a one-disk confi gu- ration (hence, n = 2) would be ideal in terms of the simplic- ity of the design, manufacturing and weight of the MRB, having multiple disks generates more braking torque. Hence, a total of four confi gurations were selected for detailedanalysis, involving all possiblecombinations between two diff erent geometry confi gurations, one disk or two disks, and two diff erent MR fl uids, MRF-241ES or MRF-132AD fl uids. Given the number of disk surfaces, additional parameters that infl uence the performance of the MRB are the physical dimensions of its components. Now, the physical dimensions of the MRB shown in Fig. 4 can be optimized for performance and weight. How- ever, its overall dimensions must be restricted so that the Table 1 Key properties of Lords MRF-132AD and MRF-241ES PropertiesMRF-132ADMRF-241ES Base fl uidHydrocarbonWater Operating temperature?40 to +130 ?C?10 to +70 ?C Maximum yield stress, sy44.5 kPa69 kPa Viscosity, g (no magnetic fi eld applied) 0.09 0.02 Pa s between 500 and 800 s?1 2.2 0.4 Pa s 50 s?1 Fig. 3. Basic confi guration of the proposed MR brake. E.J. Park et al. / Computers and Structures 86 (2008) 207216209 brake can be fi tted inside a wheel rim as the typical CHB does. For example, considering the fact that the general recommended minimum clearance between the wheel rim and the brake is 3 mm, the maximum acceptable MRB radius for a 1600wheel is about 20 cm 11. In Section 6, the various dimensional parameters represented in Fig. 4 are optimized using a multidisciplinary design optimization (MDO) procedure described in Section 5. Finally, the applied magnetic fi eld H can be produced within the MRB when current i is supplied to the electro- magnet encircling the MR fl uid, i.e., H ai4 where a is a proportional gain. Then, the two contributions of the resulting braking torque, Tydue to the yield stress induced by the applied magnetic fi eld and Tldue to the friction and viscosity of the MR fl uid, can be derived by performing the integration in Eq. (3) and substituting Eq. (1), i.e., Ty 2p 3 nkar3 z ? r3 wi Tii 5 Tl p 2h nlpr4 z ? r4 w_ h Tv_h6 where _ h is the rotational speed of the disk(s) and b = 1. Note that the magnetomotive force which drives the mag- netic fl ux around the magnetic circuit within the MRB is given by 13 Ni I H dl Hfh HsLs7 where the subscripts ()fand ()s denote the MR fl uid and the steel parts, respectively; N is the number of turns in the coil; h is the length of the MR fl uid gap; and Lsis the average length of the fl ux path in the steel casing. Then to maximize the braking torque, Hfhas to be maximized (maximizing the magnetic fi eld energy in the MR fl uid gap), while Hshas to be minimized (minimizing the energy lost in the steel path). The proportional gain a in Eqs. (4) and (5) then can be obtained from Eq. (7). 4. Finite element modelling A fi nite element model (FEM) of the MRB was devel- oped using ANSYS?to accurately characterize the brakes behaviour. This model was a multiphysics model that accounted for magnetostatics, MR fl uid fl ow, heat transfer, structural response within the MRB. Due to the multidisci- plinary nature of the MRB, with the presence of nonlinear- ities such as magnetic saturation and non-newtonian fl uid behaviour and the absence of closed-form solutions, fi nite element modelling and analysis were an essential design step. Our fi nite element analysis procedure consisted of a magnetostatics study followed by a computational fl uid dynamics (CFD) simulation in ANSYS. The former gives the magnetic fi eld distribution throughout the MR brake, which allows the determination of the yield stress sy. The magnetic fi eld distribution is then supplied to the CFD model, which computes the wall shear stresses the friction exerted on the walls and disk surfaces and the tempera- ture distribution within the MRB. The fi rst step in the fi nite element modelling was to defi ne the basic brake geometry. Since our problem is axi- symmetric, meaning that the geometry, material properties and loads are all consistent along the tangential direction, only the cross-section was modelled. This way, the solution becomes that of a two-dimensional problem, allowing the use of ANSYS plane elements (i.e., the PLANE13 ele- ments for the magnetostatics modelling and the FLUID141 elements for the CFD modelling) with axisymmetric for- mulation, and thus greatly reducing the computational cost of each simulation. For the magnetostatics simulation, the BH (magnetic fl ux density vs. applied magnetic fi eld) curves for the two MR fl uids were obtained from the manufacturers specifi - cations and the BH curve for the steel element (SAE 1010 steel) that makes up the casing and disk(s) was obtained from the ANSYS material library. Steel is an ideal low reluctance (or high magnetic permeability) fl ux conduit that can guide and focus magnetic fl ux into the MR fl uid gap 13. Fig. 5 contains these BH curves, which show that both the MR fl uid (MRF-132AD as a represen- tative) and steel have a nonlinear magnetic characteristic (i.e., saturation). In the case of the steel, the knee of the sat- uration curve starts to occur at approximately 1.6 T, which should be the maximum operating point of the steel so that Hsin Eq. (7) is close to zero according to the BH curve of the steel in Fig. 5b, thus maximizing the braking torque. In the fi nite element modelling, the current in the coil was applied as an area load. Fig. 6 shows the magnetic fl ux Fig. 4. MR brake dimensional design parameters. 210E.J. Park et al. / Computers and Structures 86 (2008) 207216 density distribution in the one-disk confi guration using the MRF-241ES fl uid, with (a) thin casing and (b) thick casing, where the arrows that represent the direction of the mag- netic fl ux density follow the intended path around the steel casing. As Fig. 6 shows, based on the principle of continu- ity of magnetic fl ux, thicker casing exhibits lower magnetic fl ux density in the steel casing. Fig. 7a presents the distribu- tion of the magnetic fi eld intensity in the same confi gura- tion using the MRF-241ES fl uid. Fig. 6b illustrates the relationship between the applied magnetic fi eld H and the resulting yield stress sy . As the fi eld intensity (Hf) of the MR fl uid reaches about 130 kA/m, the yield stress starts to saturate. As a result, the increase in the braking torque of the MRB becomes limited. For heat transfer analysis of the CFD model, the veloc- ity of the moving disks was specifi ed, as well as the heat generated by the current fl ow in the coil (so-called the Joule eff ect). The heat generated by the friction between the fl uid and solid surfaces was computed by th
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