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1、Design considerations for an automotive magnetorheological brake Kerem Karakoca, Edward J. Park, a, and Afzal SulemanaaDepartment of Mechanical Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6Received 10 October 2007; accepted 22 February 2008. Available onli
2、ne 11 April 2008. AbstractIn this paper, design considerations for building an automotive magnetorheological (MR) brake are discussed. The proposed brake consists of multiple rotating disks immersed in a MR fluid and an enclosed electromagnet. When current is applied to the electromagnet, the MR flu
3、id solidifies as its yield stress varies as a function of the magnetic field applied. This controllable yield stress produces shear friction on the rotating disks, generating the braking torque. In this work, practical design criteria such as material selection, sealing, working surface area, viscou
4、s torque generation, applied current density, and MR fluid selection are considered to select a basic automotive MR brake configuration. Then, a finite element analysis is performed to analyze the resulting magnetic circuit and heat distribution within the MR brake configuration. This is followed by
5、 a multidisciplinary design optimization (MDO) procedure to obtain optimal design parameters that can generate the maximum braking torque in the brake. A prototype MR brake is then built and tested and the experimental results show a good correlation with the finite element simulation predictions. H
6、owever, the braking torque generated is still far less than that of a conventional hydraulic brake, which indicates that a radical change in the basic brake configuration is required to build a feasible automotive MR brake.Keywords: Mechatronic design; Magnetorheological fluid; Automotive brake; Mag
7、netic circuit; Finite element analysis; Multidisciplinary design optimization; Brake-by-wireArticle Outline1. Introduction2. Analytical modeling of MR brake3. Design of MR brake3.1. Magnetic circuit design 3.2. Material selection 3.2.1. Magnetic properties3.2.2. Structural and thermal properties3.3.
8、 Sealing 3.4. Working surface area 3.5. Viscous torque generation 3.6. Applied current density 3.7. MR fluid selection4. Finite element modeling of the MR Brake5. Design optimization6. Overview of experimental setup7. Experimental results7.1. Discussions8. ConclusionReferences1. IntroductionThe auto
9、motive industry has demonstrated a commitment to build safer, cheaper and better performing vehicles. For example, the recently introduced “drive by wire” technology has been shown to improve the existing mechanical systems in automobiles. In other words, the traditional mechanical systems are being
10、 replaced by improved electromechanical systems that are able to do the same tasks faster, more reliably and more accurately. In this paper, an electromechanical brake (EMB) prototype suitable for “brake-by-wire” applications is presented. The proposed brake is a magnetorheological brake (MRB) that
11、potentially has some performance advantages over conventional hydraulic brake (CHB) systems. A CHB system involves the brake pedal, hydraulic fluid, transfer lines and brake actuators (e.g. disk or drum brakes). When the driver presses on the brake pedal, the master cylinder provides the pressure in
12、 the brake actuators that squeeze the brake pads onto the rotors, generating the useful friction forces (thus the braking torque) to stop a vehicle. However, the CHB has a number limitations, including: (i) delayed response time (200300ms) due to pressure build up in the hydraulic lines, (ii) bulky
13、size and heavy weight due to its auxiliary hydraulic components such as the master cylinder, (iii) brake pad wear due to its frictional braking mechanism, and (iv) low braking performance in high speed and high temperature situations.The MRB is a pure electronically controlled actuator and as a resu
14、lt, it has the potential to further reduce braking time (thus, braking distance), as well as easier integration of existing and new advanced control features such as anti-lock braking system (ABS), vehicle stability control (VSC), electronic parking brake (EPB), adaptive cruise control (ACC), as wel
15、l as on-board diagnostic features. Furthermore, reduced number of components, simplified wiring and better layout are all additional benefits. In the automotive industry, companies such as Delphi Corp. and Continental Automotive Systems have been actively involved in the development of commercially
16、available EMBs as next generation brake-by-wire technology. These are aimed at passenger vehicles with conventional powertrains, as well as vehicles with advanced power sources, like hybrid electric, fuel cell and advanced battery electric propulsion (e.g. 42V platform). For example, Delphi has rece
17、ntly proposed a switched reluctance (SR) motor 1 as one possible actuation technology for EMB applications. Another type of passenger vehicle EMBs that a number research groups and companies have been developing is eddy current brakes (ECBs), e.g. 2. While an ECB is a completely contactless brake th
18、at is perfectly suited for braking at high vehicle speeds (as its braking torque is proportional to the square of the wheel speed), however, it cannot generate enough braking torque at low vehicle speeds.A basic configuration of a MRB was proposed by Park et al. 3 for automotive applications. As sho
19、wn in Fig. 1, in this configuration, a rotating disk (3) is enclosed by a static casing (5), and the gap (7) between the disk and casing is filled with the MR fluid. A coil winding (6) is embedded on the perimeter of the casing and when electrical current is applied to it, magnetic fields are genera
20、ted, and the MR fluid in the gap becomes solid-like instantaneously. The shear friction between the rotating disk and the solidified MR fluid provides the required braking torque.Full-size image (49K)Fig. 1.Cross-section of basic automotive MRB design 3.View Within ArticleThe literature presents a n
21、umber of MR fluid-based brake designs, e.g. 3, 4, 5, 6, 7 and 8. In 4 and 5, Carlson of Lord Corporation proposed and patented general purpose MRB actuators, which subsequently became commercially available 6. In 7, an MRB design was proposed for exercise equipment (e.g. as a way to provide variable
22、 resistance to exercise bikes). More recently, an MRB was designed and prototyped for a haptic application as well 8. In this work, using the Bingham plastic model for defining the MR fluid behavior, its braking torque generation capacity was investigated using an electromagnetic finite element anal
23、ysis. Our previous work 3 E.J. Park, D. Stoikov, L. Falcao da Luz and A. Suleman, A performance evaluation of an automotive magnetorheological brake design with a sliding mode controller, Mechatronics 16 (2006), pp. 405416. Article | PDF (547 K) | View Record in Scopus | Cited By in Scopus (21)3 was
24、 a feasibility study based on a conceptual MRB design that included both electromagnetic finite element and heat transfer analysis, followed by a simulated brake-by-wire control (wheel slip control) of a simplified two-disk MRB design.Now, the current paper is a follow up study to our previous work
25、3. Here the MRB design that was proposed in 3 is further improved according to additional practical design criteria and constraints (e.g. be able to fit into a standard 13” wheel), and more in-depth electromagnetic finite element analysis. The new MRB design, which has an optimized magnetic circuit
26、to increase its braking torque capacity, is then prototyped for experimental verification.2. Analytical modeling of MR brakeThe idealized characteristics of the MR fluid can be described effectively by using the Bingham plastic model 9, 10, 11 and 12. According to this model, the total shear stress
27、is(1)where H is the yield stress due to applied magnetic field, p is the no-field plastic viscosity of the fluid and is the shear rate. The braking torque for the geometry shown in Fig. 1 can be defined as follows:(2)where A is the working surface area (the domain where the fluid is activated by app
28、lied magnetic field intensity), z and j are the outer and inner radii of the disk, N is the number of disks used in the enclosure and r is the radial distance from the centre of the disk.Assuming the MR fluid gap in Fig. 1 to be very small (e.g. 1mm), the shear rate can be obtained by(3)assuming lin
29、ear fluid velocity distribution across the gap and no slip conditions. In Eq. (3), w is the angular velocity of the disk and h is the thickness of the MR fluid gap. In addition, the yield stress, H, can be approximated in terms of the magnetic field intensity applied specifically onto the MR fluid,
30、HMRF, and the MR fluid dependent constant parameters, k and , i.e.(4)By substituting Eqs. (3) and (4), the braking torque equation in Eq. (2) can be rewritten as(5)Then, Eq. (5) can be divided into the following two parts after the integration(6)(7)where TH is the torque generated due to the applied
31、 magnetic field and T is the torque generated due to the viscosity of the fluid. Finally, the total braking torque is Tb=T+TH. From the design point of view, the parameters that can be varied to increase the braking torque generation capacity are: the number of disks (i.e. N), the dimensions and con
32、figuration of the magnetic circuit (i.e. rz, rj, and other structural design parameters shown in Fig. 3), and HMRF that is directly related to the applied current density in the electromagnet and materials used in the magnetic circuit.3. Design of MR brakeIn this paper, the proposed MRB was designed
33、 considering the design parameters addressed in the previous section. In addition, some of the key practical design considerations were also included during the design process, e.g. sealing of the MR fluid and the viscous torque generated within the MRB due to MR fluid viscosity. Below, the main des
34、ign criteria considered for the brake are listed, which will be discussed in detail in this section. Note that Fig. 2 shows the cross-section of the MRB which was designed according to the listed design criteria. This is the basic configuration that will be considered for finite element analysis and
35、 design optimization in the subsequent sections. The corresponding dimensional design parameters are shown in Fig. 3. (i) Magnetic circuit design (ii) Material selection(iii) Sealing(iv) Working surface area(v) Viscous torque generation(vi) Applied current density(vii) MR fluid selectionFull-size im
36、age (79K)Fig. 2.Chosen MRB based on the design criteria.View Within ArticleFull-size image (38K)Fig. 3.Dimensional parameters related to magnetic circuit design.View Within Article3.1. Magnetic circuit designThe main goal of the magnetic circuit analysis is to direct the maximum amount of the magnet
37、ic flux generated by the electromagnet onto the MR fluid located in the gap. This will allow the maximum braking torque to be generated.As shown in Fig. 4, the magnetic circuit in the MRB consists of the coil winding in the electromagnet, which is the magnetic flux generating “source” (i.e. by gener
38、ating magnetomotive force or mmf), and the flux carrying path. The path provides resistance over the flux flow, and such resistance is called reluctance . Thus, in Fig. 4, the total reluctance of the magnetic circuit is the sum of the reluctances of the core and the gap, which consists of the MR flu
39、id and the shear disk (see Fig. 2). Then, the flux generated () in a member of the magnetic circuit in Fig. 4 can be defined as(8)where(9)In Eq. (8), n is the number of turns in the coil winding and i is the current applied; in Eq. (9), is the permeability of the member, A is its cross-sectional are
40、a, and l is its length. Recall that in order to increase the braking torque, the flux flow over the MR fluid needs to be maximized. This implies that the reluctance of each member in the flux path of the flux flow has to be minimized according to Eq. (8), which in turn implies that l can be decrease
41、d or/and and A can be increased according to Eq. (9).Full-size image (19K)Fig. 4.Magnetic circuit representation of the MRB.View Within ArticleHowever, since the magnetic fluxes in the gap (gap) and in the core (core) are different, the magnetic fluxes cannot be directly calculated as the ratio betw
42、een the mmf and the total reluctance of the magnetic circuit. Note that magnetic flux can be written in terms of magnetic flux density B(10)where n is the normal vector to the surface area A. Eq. (10) implies that the magnetic flux is a function of the magnetic field intensity as well as and A of th
43、e member. Note that H in Eq. (10) can be obtained by writing the steady-state MaxwellAmperes Law (see Eq. (13) in an integral form, i.e.(11)which implies that H depends on the mmf (or ni) and l of the member. Since maximizing the flux through the MR fluid gap is our goal, Eq. (11) can be rewritten a
44、s(12)where Hcore, Hdisk and HMRF are the magnitudes of field intensity generated in the magnet core, shear disk and MR fluid respectively and lcore, ldisk, and lMRF are the length/thickness of the corresponding members. In Eq. (12), the negligible losses due to the surrounding air and non-magnetic p
45、arts are omitted.Hence, in order to maximize the magnetic flux and field intensity through the MR fluid, the magnetic circuit should be optimized by properly selecting the materials (i.e. ) for the circuit members and their geometry (l and A).3.2. Material selectionThe material selection is another
46、critical part of the MRB design process. Materials used in the MRB have crucial influence on the magnetic circuit (i.e. via ) as well as the structural and thermal characteristics. Here, the material selection issue is discussed in terms of the (i) magnetic properties and (ii) structural and thermal
47、 properties.3.2.1. Magnetic propertiesThe property that defines a materials magnetic characteristic is the permeability (). However, permeability of ferromagnetic materials is highly non-linear. It varies with temperature and applied magnetic field (e.g. saturation and hysteresis). In Table 1, some
48、candidate examples of ferromagnetic and non-ferromagnetic materials are listed. As ferromagnetic material, there is a wide range of alloy options 13 that are undesirably costly for the automotive brake application. Therefore, a more cost-effective material with required permeability should be selected. In addition, since it is difficult to accurately measure the permeability of materials, in this work, only materials with known properties were considered as possible candidates.Table 1. Examples of ferromagnetic and non-ferromagnetic materials Ferromagneti
