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Design considerations for an automotive magnetorheological brake
Mechatronics 18 (2008) 434–447
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Design considerations for an automotive magnetorheological brake Kerem Karakoc, Edward J. Park *, Afzal Suleman Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6
a r t i c l e
i n f o
Article history: Received 10 October 2007 Accepted 22 February 2008
Keywords: Mechatronic design Magnetorheological fluid Automotive brake Magnetic circuit Finite element analysis Multidisciplinary design optimization Brake-by-wire
a b s t r a c t In 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 fluid 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, viscous 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 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. However, 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. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The automotive 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 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 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 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 (200–300 ms) due to pressure build up in the hydraulic lines, (ii) bulky size and heavy weight due to its auxiliary hydraulic components such as the master cylinder, (iii) brake pad wear due to its frictional braking mech-
* Corresponding author. Tel.: +1 250 721 7303; fax: +1 250 721 6051. E-mail address: [email protected] (E.J. Park). 0957-4158/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2008.02.003
anism, and (iv) low braking performance in high speed and high temperature situations. The MRB is a pure electronically controlled actuator and as a result, 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 well 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 available EMBs as next generation brakeby-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. 42 V platform). For example, Delphi has recently 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 that 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 shown in Fig. 1, in this configuration,
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Fig. 1. Cross-section of basic automotive MRB design [3].
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 generated, 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. The literature presents a number of MR fluid-based brake designs, e.g. [3–8]. In [4,5], 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 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 analysis. Our previous work [3] was 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 [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 to increase its braking torque capacity, is then prototyped for experimental verification. 2. Analytical modeling of MR brake
where sH is the yield stress due to applied magnetic field, lp is the no-field plastic viscosity of the fluid and c_ is the shear rate. The braking torque for the geometry shown in Fig. 1 can be defined as follows: Z Z z Tb ¼ sr dA ¼ 2pN ðsH sgnð_cÞ þ lp c_ Þr2 dr ð2Þ where A is the working surface area (the domain where the fluid is activated by applied 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. 1 mm), the shear rate can be obtained by c_ ¼
rw h
s ¼ sH sgnð_cÞ þ lp c_
ð1Þ
ð3Þ
assuming linear 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, sH, can be approximated in terms of the magnetic field intensity applied specifically onto the MR fluid, HMRF, and the MR fluid dependent constant parameters, k and b, i.e. b
sH ¼ kHMRF
ð4Þ
By substituting Eqs. (3) and (4), the braking torque equation in Eq. (2) can be rewritten as Z z rw 2 b r dr T b ¼ 2pN kHMRF sgnð_cÞ þ lp ð5Þ h j Then, Eq. (5) can be divided into the following two parts after the integration 2p b NkHMRF ðr3z r3j Þ 3 p Nl ðr4 r4j Þw Tl ¼ 2h p z
TH ¼ The idealized characteristics of the MR fluid can be described effectively by using the Bingham plastic model [9–12]. According to this model, the total shear stress s is
j
A
ð6Þ ð7Þ
where TH is the torque generated due to the applied magnetic field and Tl is the torque generated due to the viscosity of the fluid.
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Finally, the total braking torque is Tb = Tl + 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 configuration 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 brake In this paper, the proposed MRB was designed 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 design 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 design optimization in the subsequent sections. The corresponding dimensional design parameters are shown in Fig. 3. (i) (ii) (iii) (iv) (v) (vi) (vii)
Magnetic circuit design Material selection Sealing Working surface area Viscous torque generation Applied current density MR fluid selection
3.1. Magnetic circuit design
magnet 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 generating magnetomotive force or mmf), and the flux carrying path. The path provides resistance over the flux flow, and such resistance is called reluctance ðRÞ. 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 fluid and the shear disk (see Fig. 2). Then, the flux generated (u) in a member of the magnetic circuit in Fig. 4 can be defined as u¼
ni mmf ¼ R R
where R¼
l lA
ð9Þ
In Eq. (8), n is the number of turns in the coil winding and i is the current applied; in Eq. (9), l is the permeability of the member, A is its cross-sectional area, 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 decreased or/and l and A can be increased according to Eq. (9). However, since the magnetic fluxes in the gap (ugap) and in the core (ucore) are different, the magnetic fluxes cannot be directly calculated as the ratio between the mmf and the total reluctance of the magnetic circuit. Note that magnetic flux can be written in terms of magnetic flux density B Z Z u¼ B n dA ¼ lH n dA ð10Þ A
The main goal of the magnetic circuit analysis is to direct the maximum amount of the magnetic flux generated by the electro-
ð8Þ
A
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 l and A of the member. Note that H in Eq. (10) can be
Fig. 2. Chosen MRB based on the design criteria.
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Fig. 3. Dimensional parameters related to magnetic circuit design.
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. l) for the circuit members and their geometry (l and A). 3.2. Material selection The material selection is another critical part of the MRB design process. Materials used in the MRB have crucial influence on the magnetic circuit (i.e. via l) 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 properties.
Fig. 4. Magnetic circuit representation of the MRB.
obtained by writing the steady-state Maxwell–Ampere’s Law (see Eq. (13)) in an integral form, i.e. I j H j dl ¼ ni ð11Þ 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 as I I I j Hcore j dlcore j Hdisk j dldisk ð12Þ j HMRF j dlMRF ¼ ni where jHcorej, jHdiskj and jHMRFj 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 parts are omitted.
3.2.1. Magnetic properties The property that defines a material’s magnetic characteristic is the permeability (l). 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 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
Table 1 Examples of ferromagnetic and non-ferromagnetic materials Ferromagnetic materials (lr > 1.1)
Non-ferromagnetic materials (lr < 1.1)
Alloy 225/405/426 Iron Low carbon steel Nickel 42% nickel 52% nickel 430 stainless steel
Aluminum Copper Molybdenum Platinum Rhodium 302–304 stainless steel Tantalum Titanium
lr is the relative permeability.
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is difficult to accurately measure the permeability of materials, in this work, only materials with known properties were considered as possible candidates. Considering the cost, permeability and availability, low carbon steel, AISI 1018 was selected as the magnetic material in the magnetic circuit (i.e. the core and disks). Corresponding B–H curve of steel 1018 with the saturation effect is shown in Fig. 5. 3.2.2. Structural and thermal properties In terms of structural considerations, there are two critical parts: the shaft and the shear disk. The shaft should be non-ferromagnetic in order to keep the flux far away from the seals that enclose the MR fluid (to avoid from MR fluid being solidified, see Section 3.3). In Table 1, 304 stainless steel is a suitable material for the shaft due to its high yield stress and availability. For the shear disk material, already chosen AISI 1018 has a high yield stress. The remaining parts are not under any considerable structural loading. Thermal properties of the materials are another important factor. Due to the temperature dependent permeability values of the ferromagnetic materials and the MR fluid viscosity, heat generated in the brake should be removed as quickly as possible. In terms of material properties, in order to increase the heat flow from the brake, a material with high conductivity and high convection coefficient has to be selected as materials for the non-magnetic brake components. Aluminum is a good candidate material for the thermal considerations. 3.3. Sealing Sealing of the MRB is another important design criterion. Since MR fluid is highly contaminated due to the iron particles in it, the risk of sealing failure is increased. In addition, in the case of dynamic seals employed between the static casing and the rotating shaft (see Fig. 6), MR fluid leakage would occur if the fluid was repetitively solidified (due to the repetitive braking) around the vicinity of the seals.
In this work, the dynamic seals were kept away from the magnetic circuit by introducing a non-ferromagnetic shaft and shear disk support outside the circuit which holds the magnetic shear disks (see Fig. 2). Also the surface finishes were improved and the tolerances were kept tight for better interface between the seals and the counterpart surfaces. In Fig. 6, the sealing types used in the MRB and their locations are shown. In our MRB, Viton Orings were used for both static and dynamic applications. In addition, a sealant, Loctite 5900Ò Flange Sealant, was also used. 3.4. Working surface area A working surface is the surface on the shear disks where the MR fluid is activated by applied magnetic field intensity. It is where the magnetic shear, sH, is generated. According to Eq. (6), the braking torque is increased when the working surface area is increased by modifying the dimensional parameters shown in Fig. 3 (which affects ðr3z r3j Þ as well as HMRF), and by introducing additional shear disks (i.e. increasing N). Hence, the proposed MRB has two shear disks (N = 2) attached to the shaft, as well as optimized dimensional parameters for higher braking torque generation. 3.5. Viscous torque generation According to Eq. (7), viscous torque is generated due to the viscosity of the fluid l, the angular velocity w of the shear disk(s), and the MR fluid gap thickness h. In order to decrease the amount of viscous torque that impedes with the free shaft rotation, an MR fluid with low viscosity was selected, and the fluid gap thickness was optimized along with the other dimensional parameters for better brake performance. 3.6. Applied current density Coil is another important design criterion, as it is the source (i.e. mmf) in the magnetic circuit. The current density that can be applied to the electromagnet coil is limited, which depends on the
Fig. 5. B–H curve of steel 1018 for initial magnetic loading.
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Fig. 6. Different seals on proposed MRB design.
cross-sectional area of the coil, its material, and the saturation flux densities of the magnetic materials used in the MRB. When the saturation flux value of a magnetic material has been reached, it will behave as non-magnetic material (i.e. lr becomes 1), affecting the corresponding reluctance in the magnetic circuit. Thus, it is beneficial to keep the flux in the unsaturated region for that material. In order to maximize the amount of applied current density, the dimensional space of where the coil is located is also optimized along with the other dimensional parameters. In addition, a wire size that can generate the highest current density was selected: AWG 21 (£ 0.77 mm). 3.7. MR fluid selection There is a number of commercial MR fluids available from Lord Corporation. No-field viscosity of the MR fluid, operating temperature range and shear stress gradient are some of the key properties that have to be considered when making a selection. According to our previous work [3], MRF-132DGÒ is the best candidate for the automotive braking application due to its broad operating temperature range. In Table 2, the properties of MRF-132DGÒ are shown and its relationship between the magnetic field intensity and the generated shear stress is shown in Fig. 7. 4. Finite element modeling of the MR Brake To solve Eq. (5), the magnetic field intensity distribution in the MRB has to be calculated. For this purpose, a finite element analysis (FEA) was carried out using a commercial package, COMSOL MultiphysicsÒ. The following governing magnetostatic equations [14] are used by the COMSOL electromagnet module rH¼J
ð13Þ
rB¼0
ð14Þ
where H is the magnetic field intensity, B is the magnetic flux density and J is the electric current density. By solving these equations
Table 2 Properties of MRF-132DGÒ Property
Value/limits
Base fluid Operating temperature Density Color Weight percent solid Coefficient of thermal expansion (calculated values) 0–50 (°C) 50–100 (°C) 100–150 (°C) Specific heat at 25 (°C) Thermal conductivity at 25 (°C) Flash point Viscosity (slope between 800 and 500 Hz at 40 °C) k b
Hydrocarbon 40 to 130 (°C) 3090 (kg/m3) Dark gray 81.64 (%) Unit volume per °C 5.5e4 6.6e4 6.7e4 800 (J/kg K) 0.25–1.06 (W/m K) 150 (°C) 0.09(±0.02) Pa s 0.269 (Pa m/A) 1
over a defined domain with proper boundary conditions, the magnetic field intensity distribution (H) generated by the modeled MRB can be calculated. Subsequently, the braking torque in Eq. (6) can be calculated. In order to solve the above magnetostatic equations, a 2-D MRB finite element model (FEM) was created. The FEM is a quasi-static magnetic model, which simulates the in-plane induction currents and vector potentials, needed to obtain the magnetic field intensity distribution (H) over the defined MRB geometry. First, the geometry of the proposed MRB was generated using the sketch function in COMSOL and the non-linear material properties of the MR fluid and AISI 1018 were defined as functions of the magnetic flux density B. Then, a magnetically isolated boundary that includes the MRB geometry was selected. After the mesh was generated, the FEM was solved using a parametric non-linear solver and the magnetic field distribution onto the MR fluid (i.e. HMRF) was obtained which is equal to the magnitude of the magnetic field distribution, jHj. Finally, the braking torque in Eq. (6) was calculated using a boundary integration post processing function in COMSOL that
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Fig. 7. Shear stress versus magnetic field intensity for MRF-132DGÒ.
Fig. 8. Magnetic field intensity distribution.
integrates the shear calculated by the magnetic field intensity distribution, over the shear disk surfaces. Fig. 8 shows the resulting magnetic field intensity distribution and magnetic flux density distribution in the MRB is shown in Fig. 9. Next, a simplified heat transfer model for the above configuration was generated to provide a quick monitoring of the temperature distribution inside the MRB. Note that there are two main heat sources within the MRB: (i) the Joule heating of the coil due to the electrical current flow and (ii) the frictional heating generated between the MR fluid and stator/rotor surfaces. Our study [15] showed that the latter is a much more significant heat source, and thus the Joule heating was not considered here. The following two cases were considered for the frictional heating: (i) heat generated when there is no applied magnetic field and (ii) heat generated when magnetic field is present (thus changing the rheology of the MR fluid). To simplify our heat transfer analysis, we assumed
that the flow of the MR fluid within the gap between the stator and the rotor is laminar. We also assumed that the MR fluid particles are under pure shear stress (i.e. no axial stress), dissipating the following amount of heat [16] U ¼ lp ½c2xy þ c2yz þ c2xz
ð15Þ
where lp is replaced by l0p ¼ lp þ sH =cxz when the magnetic field is present and cxy, cyz and cxz are the shear strains in the x y, y z and x z coordinate planes, respectively. In order to carry out the heat transfer analysis, the magnetic field intensity distribution simulated by the electromagnetic FEA was used calculate the above shear strains and changing MR fluid viscosity l0p due to the presence of the magnetic field. As for the boundary conditions of the heat transfer analysis, convective boundaries were defined between the fluid and its surrounding material (forced convection), and between the casing and the ambient air (free convection).
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441
Fig. 9. Magnetic flux density distribution.
5. Design optimization As a next step, the chosen design configuration shown in Fig. 2 was optimized for higher braking torque and lower weight. In setting up such an optimization problem for the MRB, a cost function was defined by including the braking torque and weight as functions of the dimensional parameters of the magnetic circuit (see Fig. 3). The objective function of the MRB optimization problem is defined as Minimize : f ðdÞ ¼ kW
W T kT W ref T ref
where kW þ kT ¼ 1 subject to : W < 180 N
ð16Þ ð17Þ
and
dbrake < 240 mm
ð18Þ
where W (N) is the weight of the actuator, T (Nm) is the braking torque (equal to TH in Eq. (6)) generated due to applied magnetic field, d = [d1, d2, . . . , d12]T is the design variable vector that consists of the dimensional parameters shown in Fig. 3, and kW and kT are the weighting coefficients. The FEM was used to obtain W and T in the cost function for various brake designs. The block diagram in Fig. 10 shows the process of calculating W and T via COMSOL in the cost function for an arbitrary design. In order to solve the objective function, kW and kT were set to be 0.1 and 0.9, respectively, as the maximum torque generation is of our primary concern. In addition, the reference weight value was obtained considering the overall system weight of the CHB that consists of the on wheel components as well as the extra weight contributed by the hydraulic components: the master cylinder, brake fluid lines, and pump. Since an MRB would not have these extra components, each MRB can potentially have heavier on-wheel weight than that of a CHB. Moreover, since the braking torque generated by the proposed configuration of the MRB is comparably less than that of the CHB, Tref was selected to be 20 Nm. This reference torque value was selected by checking a number of random designs which satisfied the constraints. As the constraints for the optimization problem, the weight of the actuator was set to be smaller than the weight of the CHB,
Fig. 10. Process of computing the cost function for a random design.
i.e. W < 180 N. Since the brake should fit into a standard automobile wheel, the diameter of the MRB is set to be smaller than the inner diameter of the wheel: for example, 13” wheel, the inner diameter is 240 mm, thus dbrake < 240 mm. The objective function was then solved using a random search algorithm called simulated annealing (SA). SA statistically
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Fig. 11. MRB optimization process.
guarantees to converge to a global optimum after adequate number of iterations [17,18]. Since SA is a random search algorithm, it cannot give the exact global optimum; instead it gives a design which is close to the global optimum. Therefore, a gradient based optimization algorithm called sequential quadratic programming (SQP) was also used on the dimensional parameters optimized by SA. The SQP algorithm searches for the optimum using the gradient data of the objective function, thus it guarantees to find an optimum design. The block diagram for the MRB optimization process is shown in Fig. 11. In order to solve the MRB optimization problem using SA, a design space was specified as the possible solution space Table 3 Optimum design parameters Parameter
Optimum value (mm)
LB–UB (mm)
d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12
17.11 18.05 1.03 47.34 5.08 14.57 2.07 10.00 10.34 3.08 0.91 2.04
20–80 5–15 2–4 10–80 5–10 4–15 2–20 10–30 5–20 3–10 0.91–3.79 1–4
LB: lower boundary and UB: upper boundary.
(lower and upper boundaries of this space were defined and shown in Table 3). Then, the solution of SA entered into the SQP algorithm to update the solution until an optimum design was found. The optimum dimensional parameters for the magnetic circuit are given in Table 3, with the corresponding illustration already shown in Fig. 3. 6. Overview of experimental setup After the optimum design was found for the proposed MRB, a 3D CAD model was generated using Pro/E (see Fig. 12(L)). Fig. 12(R) shows the subsequent prototype that was manufactured. The main specifications of the MRB prototype are given in Table 4. The MRB prototype was installed into the experimental setup shown in Fig. 13. A servo motor from CMC Inc. with a continuous torque of 5.13 Nm and with rotational speed of 5445 rpm was used to generate the shaft rotation. Since the torque generation capacity of the servo motor is relatively low, an ALPHA 0755-MC1-7 gear reducer (7:1) was used. The servo motor was connected to a Futek torque sensor (TRS605) which is a shaft-to-shaft rotary torque sensor with a torque measuring capacity up to 1000 Nm. The other end of the torque sensor was connected to the MRB prototype. An inertia dynamics magnetic clutch was installed between the torque sensor and the servo motor in order to release the load on the servo motor generated by the brake. In order to connect the various components, flexible couplings were used. A K-type thermocouple was also installed into the prototype in order to measure temperature changes during experiments.
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443
Fig. 12. CAD model (L) and prototype (R) of the proposed MRB.
Table 4 MRB prototype specifications Weight
11.8 (kg)
Diameter Number of disks Amount of MR fluid used Coil wire size Number of turns Maximum current applied Maximum current density applied Seals used Magnetic materials used Non-magnetic materials used Maximum braking torque
239.9 (mm) 2 205 (cm3) AWG 21 (£ 0.77 mm) 236 ± 2 (turns) 1.8 (A) 2.54 106 (A/m2) Static and synamic O-rings Steel 1018 Al T-6061 and SS 304 23 Nm at 1.8 A
The servo motor was controlled with a PID controller and the rotational speed of the brake was verified using an optical encoder embedded in the torque sensor. All input and output signals were connected to a dSPACE hardware-in-the-loop control board (DS1104). The control signal from the dSPACE board to the servo motor was amplified using an Advanced Motion Control Brushless PWM servo amplifier. In addition, a low-pass filter circuit was implemented into the setup in order to reduce any high frequency noise in the torque sensor readings. During experiments, the rotational speed was kept constant at various values and current was applied to the coil using an Agilent
Technologies high current power supply (N5766A). Whenever the brake was actuated, since the system was at steady-state, the relative torque measured between the shafts on each side of the torque sensor was recorded as the braking torque generated by the brake prototype. After the braking torque data was obtained, the magnetic clutch was turned on in order to release the load on the servo motor. 7. Experimental results Initially, we measured the no-field torque generated by the viscosity of the MR fluid (plus the mechanical friction torque). In Fig. 14, the torque generated due to viscosity of the fluid at various rotational speeds is shown. As one can see, the relationship between the viscous torque and rotational speed is linear, as described by Eq. (7). After the viscous torque was calculated, current was applied to the electromagnet coil and corresponding changes in the torque readings were recorded. The total braking torques (Tb) generated with respect to the increasing speeds are shown in Fig. 15. The difference between the three torque curves is directly due to the varying viscous torques (Fig. 14) at different speeds. The plots shown in Fig. 15 contain the viscous effects and the frictional effects. In order to compare the experimental results with the simulation results, the viscous and the friction effects have to
Fig. 13. Picture of experimental setup.
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Fig. 17. Comparison between experimental and simulation results at 200 rpm. Fig. 14. Viscous torque versus velocity.
Fig. 15. Torque (Tb) versus current applied.
be subtracted from the experimental data. The resulting plot between the torque (TH) generated due to the applied magnetic field and the current applied is shown in Fig. 16. Three plots are almost identical, which shows that this quantity is not speed dependent, as described by Eq. (6). Finally, the simulation and the experimental results are compared in Fig. 17. While the initial (at 0 A) and final (at 1.8 A) values
Fig. 16. Torque (TH) generated due to magnetic field (without viscous and friction torques).
match, there is deviation in the middle values (104% difference at 0.2 A and 12% difference at 1.6 A). The main reason behind this deviation is probably due to the lack of accurate information on the material properties that were used in the simulations. Another minor factor is the varying temperature. Since the temperature variation has an effect on both the viscosity and magnetic properties of the MR fluid, the heat build-up is a major concern in the actual implementation of such a brake. Due to the lack of detailed information, however, our FEM does not account for temperature effects on material properties. In Figs. 18 and 19, the temperature distribution within the MRB is shown for the two cases described in Section 4. In the first case (see Fig. 18), the disks were freely rotated at 400 rpm for 20 s without applying a magnetic field. In the second case (see Fig. 19), 1.8 A was applied to the coil, generating a magnetic field across the brake that was rotating at 200 rpm. Fig. 20 shows the heat buildup for the above two cases. The solid lines represent the actual temperature variation at the location of the thermocouple (see Fig. 12(R)), while the dotted lines represent the corresponding simulation results. It can be seen that the experimental and simulation results are reasonably in good agreement for the 20 s cruising or braking period that we considered. 7.1. Discussions Note that in order to stop a 1000 kg passenger vehicle with a deceleration of 6 m/s2, which is the typical requirement for measuring braking performance of a fully loaded passenger vehicle with burnished brakes, each brake has to generate around 500 Nm. The prototyped MRB can generate only 5% of this torque value. This indicates that a radical change in the basic brake configuration is required in order to build a feasible automotive MRB. For example, the following design improvements can be made in the basic configuration to further increase the braking torque capacity: (i) In Fig. 21, the simulated improvement in the braking torque with additional disks is shown for the same design configuration proposed in this work. Note that 20% (i.e. 100 Nm) of the required torque can be generated with an MRB with 7 disks. (ii) The braking torque capacity can also be increased significantly by relaxing the size and the weight constraints defined in Eq. (18). Note from Table 4 that the weight of the prototyped MRB is still relatively light (especially considering that of the overall CHB system), 11.8 kg; hence there is still some room to allow increases in the overall size/weight of the MRB. For example, in our previous paper [3], the size and weight constraints were greatly relaxed,
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Fig. 18. Temperature distribution within MRB: no magnetic field applied.
Fig. 19. Temperature distribution within MRB: magnetic field applied.
which resulted in a 27.8 kg two-disk MRB design that can generate up to 1000 Nm of braking torque in numerical simulations. While the current work shows that this level of torque cannot be generated in practice when the limitations in space/weight and current density, as well as sealing and magnetic saturation considerations (Section 3) are taken into account, some relaxation of the constraints is still possible. For example, Fig. 22(L) shows such an MRB design with a thicker single disk that can generate about 55 Nm at 1.8 A (see Fig. 22(R)).
Once an improved MRB configuration is suggested, one can repeat the design process presented in this paper to maximize the braking torque capacity. Another critical design criteria that one must further consider is the long term temperature effects (due to heat build-up) on the degradation of the MR fluid properties. Note that in the case of Fig. 19, the temperature rises by almost 25 °C in just 20 s of continuous braking. In addition, in [15], a dynamic finite element analysis was also performed to study the effects of applying repeated cycles of pressing and releasing the brake on the heat build-up, and showed that the operating
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Fig. 20. Temperature change at measurement location: (L) no magnetic field applied and (R) magnetic field applied.
8. Conclusion
Fig. 21. Simulation plot of braking torque (TH) generated with respect to the number of disks (at 1.8 A).
temperature can intermittently reach outside the recommended temperature range of the MR fluid. These results show a need for the design of an effective passive or active cooling mechanism, as the MR fluid degradation would be the ultimate limiting factor on the performance and life cycle of the MRB. However, if the above problems cannot be overcome, a hybrid electromechanical brake (HEMB) system [19] that combines with a CHB system may be an alternate solution.
In this paper, a magnetorheological brake (MRB) design has been introduced as a viable alternative to the current conventional hydraulic brake (CHB) device. Since the MRB is an electromechanical device, it has several advantages over the CHB, such as reduced actuation delay, ease of software control implementation and lower system weight. The design process was started with an analytical model of the MRB. Then, the MRB device was designed with a focus on magnetic circuit optimization and material selection. A two-dimensional finite element model of the MRB was created to simulate the steady-state magnetic flux flow within the MRB domain using COMSOL Electromagnetic Module and solve for the magnetic field intensity distribution. In addition to the detailed electromagnetic analysis, a simple heat transfer analysis was carried out to monitor the heat build-up within the brake. The FEM was then used to optimize the magnetic circuit design in order to maximize the braking torque and minimize the weight of the MRB. The optimization problem was solved using a hybrid optimization procedure that included simulated annealing and sequential quadratic programming algorithm. A 3-D CAD model of the optimum MRB design was generated and a MRB prototype of the optimum design was manufactured. The MRB braking performance was tested using an experimental apparatus that consisted of a torque sensor and a servo motor.
Fig. 22. An MRB with different magnetic circuit configuration (L) and corresponding simulation plot of braking torque (TH) versus applied currents (R).
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The experimental results showed that the braking torque increases with applied current, reaching more than 20 Nm at 1.8 A, thus confirming the theoretical predictions. There were discrepancies with respect to the simulation results due to estimated material properties used in the simulations. However, the proposed MRB configuration was not able to generate sufficient braking torque to stop a vehicle. Therefore, an improved MRB design should be suggested (e.g. by increasing the number of disks or completely redesigning the magnetic circuit configuration) in future designs, taking into account the temperature effects and more accurate description of the material properties as well. References [1] Kolde H, Omekanda AM, Lequesne B, Golpalakrishnan S, Khalil A, Underwood S, et al. The potential of switched reluctance motor technology for electromechanical brake applications. In: Proceedings of the SAE world congress, Detroit, MI; April 3–6, 2006. 2006-01-0296. [2] Lee KJ, Park KH. Optimal robust control of a contactless brake system using an eddy current. Mechatronics 1999;9:615–31. [3] Park EJ, Stoikov D, Falcao da Luz L, Suleman A. A performance evaluation of an automotive magnetorheological brake design with a sliding mode controller. Mechatronics 2006;16:405–16. [4] Carlson JD, LeRoy DF, Holzheimer JC, Prindle DR, Marjoram RH. Controllable brake. US Patent No. 5842547. United States Patent Office; December 1, 1998. [5] Carlson JD. Magnetorheological brake with integrated flywheel. US Patent No. 6186290 B1. United States Patent Office; February 13, 2001.
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[6] Lord Corporation Material Division. MR Brake Product Bulletin MRB-2107-3. Cary, NC; 2003. [7] Webb GM. Exercise apparatus and associated method including rheological fluid brake. US Patent No. 5810696. United States Patent Office; September 22, 1998. [8] Liu B, Li WH, Kosasih PB, Zhang XZ. Development of an MR brake based haptic device. Smart Mater and Struct 2006;15:1960–6. [9] Phillips RW. Engineering applications of fluids with a variable yield stress. PhD thesis. University of California: Berkeley, CA; 1969. [10] An J, Kwon DS. Modeling of a magnetorheological actuator including magnetic hysteresis. J Intel Mater Syst Struct 2003;14(9):541–50. [11] Kordonsky W. Elements and devices based on magnetorheological effect. J Intel Mater Syst Struct 1993;4(1):65–9. [12] Weiss KD, Carlson JD, Nixon DA. Viscoelastic properties of magnetoand electrorheological fluids. J Intel Mater Syst Struct 1994;5(11): 772–5. [13] ASTM International. Magnetic properties. Annual book of ASTM standards, vol. 4(3); 2005. [14] Ida N. Engineering electromagnetics. New York: Springer-Verlag; 2000. [15] Park EJ, Falcao da Luz L, Suleman A. Multidisciplinary design optimization of an automotive magnetorheological brake design. Comput Struct 2008; 86(3–5):207–16. [16] Pai Shih-i. Viscous flow theory: 1-Laminar flow. Princeton, NJ: D. Van Nostrand Company, Inc.; 1956. [17] Arora J. Introduction to optimum design. 2nd ed. San Diego, CA: Elsevier Academic Press; 2004. [18] van Laarhoven PJM, Aarts EHL. Simulated annealing: theory and applications. Dordrecht, Holland: D. Reidel Publishing Co.; 1987. [19] Song J. Performance evaluation of a hybrid electric brake system with a sliding mode controller. Mechatronics 2005;15:339–58.
Contents lists available at ScienceDirect
Mechatronics journal homepage: www.elsevier.com/locate/mechatronics
Design considerations for an automotive magnetorheological brake Kerem Karakoc, Edward J. Park *, Afzal Suleman Department of Mechanical Engineering, University of Victoria, P.O. Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6
a r t i c l e
i n f o
Article history: Received 10 October 2007 Accepted 22 February 2008
Keywords: Mechatronic design Magnetorheological fluid Automotive brake Magnetic circuit Finite element analysis Multidisciplinary design optimization Brake-by-wire
a b s t r a c t In 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 fluid 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, viscous 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 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. However, 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. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The automotive 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 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 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 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 (200–300 ms) due to pressure build up in the hydraulic lines, (ii) bulky size and heavy weight due to its auxiliary hydraulic components such as the master cylinder, (iii) brake pad wear due to its frictional braking mech-
* Corresponding author. Tel.: +1 250 721 7303; fax: +1 250 721 6051. E-mail address: [email protected] (E.J. Park). 0957-4158/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechatronics.2008.02.003
anism, and (iv) low braking performance in high speed and high temperature situations. The MRB is a pure electronically controlled actuator and as a result, 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 well 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 available EMBs as next generation brakeby-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. 42 V platform). For example, Delphi has recently 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 that 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 shown in Fig. 1, in this configuration,
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Fig. 1. Cross-section of basic automotive MRB design [3].
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 generated, 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. The literature presents a number of MR fluid-based brake designs, e.g. [3–8]. In [4,5], 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 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 analysis. Our previous work [3] was 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 [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 to increase its braking torque capacity, is then prototyped for experimental verification. 2. Analytical modeling of MR brake
where sH is the yield stress due to applied magnetic field, lp is the no-field plastic viscosity of the fluid and c_ is the shear rate. The braking torque for the geometry shown in Fig. 1 can be defined as follows: Z Z z Tb ¼ sr dA ¼ 2pN ðsH sgnð_cÞ þ lp c_ Þr2 dr ð2Þ where A is the working surface area (the domain where the fluid is activated by applied 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. 1 mm), the shear rate can be obtained by c_ ¼
rw h
s ¼ sH sgnð_cÞ þ lp c_
ð1Þ
ð3Þ
assuming linear 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, sH, can be approximated in terms of the magnetic field intensity applied specifically onto the MR fluid, HMRF, and the MR fluid dependent constant parameters, k and b, i.e. b
sH ¼ kHMRF
ð4Þ
By substituting Eqs. (3) and (4), the braking torque equation in Eq. (2) can be rewritten as Z z rw 2 b r dr T b ¼ 2pN kHMRF sgnð_cÞ þ lp ð5Þ h j Then, Eq. (5) can be divided into the following two parts after the integration 2p b NkHMRF ðr3z r3j Þ 3 p Nl ðr4 r4j Þw Tl ¼ 2h p z
TH ¼ The idealized characteristics of the MR fluid can be described effectively by using the Bingham plastic model [9–12]. According to this model, the total shear stress s is
j
A
ð6Þ ð7Þ
where TH is the torque generated due to the applied magnetic field and Tl is the torque generated due to the viscosity of the fluid.
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Finally, the total braking torque is Tb = Tl + 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 configuration 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 brake In this paper, the proposed MRB was designed 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 design 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 design optimization in the subsequent sections. The corresponding dimensional design parameters are shown in Fig. 3. (i) (ii) (iii) (iv) (v) (vi) (vii)
Magnetic circuit design Material selection Sealing Working surface area Viscous torque generation Applied current density MR fluid selection
3.1. Magnetic circuit design
magnet 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 generating magnetomotive force or mmf), and the flux carrying path. The path provides resistance over the flux flow, and such resistance is called reluctance ðRÞ. 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 fluid and the shear disk (see Fig. 2). Then, the flux generated (u) in a member of the magnetic circuit in Fig. 4 can be defined as u¼
ni mmf ¼ R R
where R¼
l lA
ð9Þ
In Eq. (8), n is the number of turns in the coil winding and i is the current applied; in Eq. (9), l is the permeability of the member, A is its cross-sectional area, 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 decreased or/and l and A can be increased according to Eq. (9). However, since the magnetic fluxes in the gap (ugap) and in the core (ucore) are different, the magnetic fluxes cannot be directly calculated as the ratio between the mmf and the total reluctance of the magnetic circuit. Note that magnetic flux can be written in terms of magnetic flux density B Z Z u¼ B n dA ¼ lH n dA ð10Þ A
The main goal of the magnetic circuit analysis is to direct the maximum amount of the magnetic flux generated by the electro-
ð8Þ
A
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 l and A of the member. Note that H in Eq. (10) can be
Fig. 2. Chosen MRB based on the design criteria.
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Fig. 3. Dimensional parameters related to magnetic circuit design.
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. l) for the circuit members and their geometry (l and A). 3.2. Material selection The material selection is another critical part of the MRB design process. Materials used in the MRB have crucial influence on the magnetic circuit (i.e. via l) 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 properties.
Fig. 4. Magnetic circuit representation of the MRB.
obtained by writing the steady-state Maxwell–Ampere’s Law (see Eq. (13)) in an integral form, i.e. I j H j dl ¼ ni ð11Þ 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 as I I I j Hcore j dlcore j Hdisk j dldisk ð12Þ j HMRF j dlMRF ¼ ni where jHcorej, jHdiskj and jHMRFj 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 parts are omitted.
3.2.1. Magnetic properties The property that defines a material’s magnetic characteristic is the permeability (l). 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 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
Table 1 Examples of ferromagnetic and non-ferromagnetic materials Ferromagnetic materials (lr > 1.1)
Non-ferromagnetic materials (lr < 1.1)
Alloy 225/405/426 Iron Low carbon steel Nickel 42% nickel 52% nickel 430 stainless steel
Aluminum Copper Molybdenum Platinum Rhodium 302–304 stainless steel Tantalum Titanium
lr is the relative permeability.
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is difficult to accurately measure the permeability of materials, in this work, only materials with known properties were considered as possible candidates. Considering the cost, permeability and availability, low carbon steel, AISI 1018 was selected as the magnetic material in the magnetic circuit (i.e. the core and disks). Corresponding B–H curve of steel 1018 with the saturation effect is shown in Fig. 5. 3.2.2. Structural and thermal properties In terms of structural considerations, there are two critical parts: the shaft and the shear disk. The shaft should be non-ferromagnetic in order to keep the flux far away from the seals that enclose the MR fluid (to avoid from MR fluid being solidified, see Section 3.3). In Table 1, 304 stainless steel is a suitable material for the shaft due to its high yield stress and availability. For the shear disk material, already chosen AISI 1018 has a high yield stress. The remaining parts are not under any considerable structural loading. Thermal properties of the materials are another important factor. Due to the temperature dependent permeability values of the ferromagnetic materials and the MR fluid viscosity, heat generated in the brake should be removed as quickly as possible. In terms of material properties, in order to increase the heat flow from the brake, a material with high conductivity and high convection coefficient has to be selected as materials for the non-magnetic brake components. Aluminum is a good candidate material for the thermal considerations. 3.3. Sealing Sealing of the MRB is another important design criterion. Since MR fluid is highly contaminated due to the iron particles in it, the risk of sealing failure is increased. In addition, in the case of dynamic seals employed between the static casing and the rotating shaft (see Fig. 6), MR fluid leakage would occur if the fluid was repetitively solidified (due to the repetitive braking) around the vicinity of the seals.
In this work, the dynamic seals were kept away from the magnetic circuit by introducing a non-ferromagnetic shaft and shear disk support outside the circuit which holds the magnetic shear disks (see Fig. 2). Also the surface finishes were improved and the tolerances were kept tight for better interface between the seals and the counterpart surfaces. In Fig. 6, the sealing types used in the MRB and their locations are shown. In our MRB, Viton Orings were used for both static and dynamic applications. In addition, a sealant, Loctite 5900Ò Flange Sealant, was also used. 3.4. Working surface area A working surface is the surface on the shear disks where the MR fluid is activated by applied magnetic field intensity. It is where the magnetic shear, sH, is generated. According to Eq. (6), the braking torque is increased when the working surface area is increased by modifying the dimensional parameters shown in Fig. 3 (which affects ðr3z r3j Þ as well as HMRF), and by introducing additional shear disks (i.e. increasing N). Hence, the proposed MRB has two shear disks (N = 2) attached to the shaft, as well as optimized dimensional parameters for higher braking torque generation. 3.5. Viscous torque generation According to Eq. (7), viscous torque is generated due to the viscosity of the fluid l, the angular velocity w of the shear disk(s), and the MR fluid gap thickness h. In order to decrease the amount of viscous torque that impedes with the free shaft rotation, an MR fluid with low viscosity was selected, and the fluid gap thickness was optimized along with the other dimensional parameters for better brake performance. 3.6. Applied current density Coil is another important design criterion, as it is the source (i.e. mmf) in the magnetic circuit. The current density that can be applied to the electromagnet coil is limited, which depends on the
Fig. 5. B–H curve of steel 1018 for initial magnetic loading.
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Fig. 6. Different seals on proposed MRB design.
cross-sectional area of the coil, its material, and the saturation flux densities of the magnetic materials used in the MRB. When the saturation flux value of a magnetic material has been reached, it will behave as non-magnetic material (i.e. lr becomes 1), affecting the corresponding reluctance in the magnetic circuit. Thus, it is beneficial to keep the flux in the unsaturated region for that material. In order to maximize the amount of applied current density, the dimensional space of where the coil is located is also optimized along with the other dimensional parameters. In addition, a wire size that can generate the highest current density was selected: AWG 21 (£ 0.77 mm). 3.7. MR fluid selection There is a number of commercial MR fluids available from Lord Corporation. No-field viscosity of the MR fluid, operating temperature range and shear stress gradient are some of the key properties that have to be considered when making a selection. According to our previous work [3], MRF-132DGÒ is the best candidate for the automotive braking application due to its broad operating temperature range. In Table 2, the properties of MRF-132DGÒ are shown and its relationship between the magnetic field intensity and the generated shear stress is shown in Fig. 7. 4. Finite element modeling of the MR Brake To solve Eq. (5), the magnetic field intensity distribution in the MRB has to be calculated. For this purpose, a finite element analysis (FEA) was carried out using a commercial package, COMSOL MultiphysicsÒ. The following governing magnetostatic equations [14] are used by the COMSOL electromagnet module rH¼J
ð13Þ
rB¼0
ð14Þ
where H is the magnetic field intensity, B is the magnetic flux density and J is the electric current density. By solving these equations
Table 2 Properties of MRF-132DGÒ Property
Value/limits
Base fluid Operating temperature Density Color Weight percent solid Coefficient of thermal expansion (calculated values) 0–50 (°C) 50–100 (°C) 100–150 (°C) Specific heat at 25 (°C) Thermal conductivity at 25 (°C) Flash point Viscosity (slope between 800 and 500 Hz at 40 °C) k b
Hydrocarbon 40 to 130 (°C) 3090 (kg/m3) Dark gray 81.64 (%) Unit volume per °C 5.5e4 6.6e4 6.7e4 800 (J/kg K) 0.25–1.06 (W/m K) 150 (°C) 0.09(±0.02) Pa s 0.269 (Pa m/A) 1
over a defined domain with proper boundary conditions, the magnetic field intensity distribution (H) generated by the modeled MRB can be calculated. Subsequently, the braking torque in Eq. (6) can be calculated. In order to solve the above magnetostatic equations, a 2-D MRB finite element model (FEM) was created. The FEM is a quasi-static magnetic model, which simulates the in-plane induction currents and vector potentials, needed to obtain the magnetic field intensity distribution (H) over the defined MRB geometry. First, the geometry of the proposed MRB was generated using the sketch function in COMSOL and the non-linear material properties of the MR fluid and AISI 1018 were defined as functions of the magnetic flux density B. Then, a magnetically isolated boundary that includes the MRB geometry was selected. After the mesh was generated, the FEM was solved using a parametric non-linear solver and the magnetic field distribution onto the MR fluid (i.e. HMRF) was obtained which is equal to the magnitude of the magnetic field distribution, jHj. Finally, the braking torque in Eq. (6) was calculated using a boundary integration post processing function in COMSOL that
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Fig. 7. Shear stress versus magnetic field intensity for MRF-132DGÒ.
Fig. 8. Magnetic field intensity distribution.
integrates the shear calculated by the magnetic field intensity distribution, over the shear disk surfaces. Fig. 8 shows the resulting magnetic field intensity distribution and magnetic flux density distribution in the MRB is shown in Fig. 9. Next, a simplified heat transfer model for the above configuration was generated to provide a quick monitoring of the temperature distribution inside the MRB. Note that there are two main heat sources within the MRB: (i) the Joule heating of the coil due to the electrical current flow and (ii) the frictional heating generated between the MR fluid and stator/rotor surfaces. Our study [15] showed that the latter is a much more significant heat source, and thus the Joule heating was not considered here. The following two cases were considered for the frictional heating: (i) heat generated when there is no applied magnetic field and (ii) heat generated when magnetic field is present (thus changing the rheology of the MR fluid). To simplify our heat transfer analysis, we assumed
that the flow of the MR fluid within the gap between the stator and the rotor is laminar. We also assumed that the MR fluid particles are under pure shear stress (i.e. no axial stress), dissipating the following amount of heat [16] U ¼ lp ½c2xy þ c2yz þ c2xz
ð15Þ
where lp is replaced by l0p ¼ lp þ sH =cxz when the magnetic field is present and cxy, cyz and cxz are the shear strains in the x y, y z and x z coordinate planes, respectively. In order to carry out the heat transfer analysis, the magnetic field intensity distribution simulated by the electromagnetic FEA was used calculate the above shear strains and changing MR fluid viscosity l0p due to the presence of the magnetic field. As for the boundary conditions of the heat transfer analysis, convective boundaries were defined between the fluid and its surrounding material (forced convection), and between the casing and the ambient air (free convection).
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Fig. 9. Magnetic flux density distribution.
5. Design optimization As a next step, the chosen design configuration shown in Fig. 2 was optimized for higher braking torque and lower weight. In setting up such an optimization problem for the MRB, a cost function was defined by including the braking torque and weight as functions of the dimensional parameters of the magnetic circuit (see Fig. 3). The objective function of the MRB optimization problem is defined as Minimize : f ðdÞ ¼ kW
W T kT W ref T ref
where kW þ kT ¼ 1 subject to : W < 180 N
ð16Þ ð17Þ
and
dbrake < 240 mm
ð18Þ
where W (N) is the weight of the actuator, T (Nm) is the braking torque (equal to TH in Eq. (6)) generated due to applied magnetic field, d = [d1, d2, . . . , d12]T is the design variable vector that consists of the dimensional parameters shown in Fig. 3, and kW and kT are the weighting coefficients. The FEM was used to obtain W and T in the cost function for various brake designs. The block diagram in Fig. 10 shows the process of calculating W and T via COMSOL in the cost function for an arbitrary design. In order to solve the objective function, kW and kT were set to be 0.1 and 0.9, respectively, as the maximum torque generation is of our primary concern. In addition, the reference weight value was obtained considering the overall system weight of the CHB that consists of the on wheel components as well as the extra weight contributed by the hydraulic components: the master cylinder, brake fluid lines, and pump. Since an MRB would not have these extra components, each MRB can potentially have heavier on-wheel weight than that of a CHB. Moreover, since the braking torque generated by the proposed configuration of the MRB is comparably less than that of the CHB, Tref was selected to be 20 Nm. This reference torque value was selected by checking a number of random designs which satisfied the constraints. As the constraints for the optimization problem, the weight of the actuator was set to be smaller than the weight of the CHB,
Fig. 10. Process of computing the cost function for a random design.
i.e. W < 180 N. Since the brake should fit into a standard automobile wheel, the diameter of the MRB is set to be smaller than the inner diameter of the wheel: for example, 13” wheel, the inner diameter is 240 mm, thus dbrake < 240 mm. The objective function was then solved using a random search algorithm called simulated annealing (SA). SA statistically
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Fig. 11. MRB optimization process.
guarantees to converge to a global optimum after adequate number of iterations [17,18]. Since SA is a random search algorithm, it cannot give the exact global optimum; instead it gives a design which is close to the global optimum. Therefore, a gradient based optimization algorithm called sequential quadratic programming (SQP) was also used on the dimensional parameters optimized by SA. The SQP algorithm searches for the optimum using the gradient data of the objective function, thus it guarantees to find an optimum design. The block diagram for the MRB optimization process is shown in Fig. 11. In order to solve the MRB optimization problem using SA, a design space was specified as the possible solution space Table 3 Optimum design parameters Parameter
Optimum value (mm)
LB–UB (mm)
d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12
17.11 18.05 1.03 47.34 5.08 14.57 2.07 10.00 10.34 3.08 0.91 2.04
20–80 5–15 2–4 10–80 5–10 4–15 2–20 10–30 5–20 3–10 0.91–3.79 1–4
LB: lower boundary and UB: upper boundary.
(lower and upper boundaries of this space were defined and shown in Table 3). Then, the solution of SA entered into the SQP algorithm to update the solution until an optimum design was found. The optimum dimensional parameters for the magnetic circuit are given in Table 3, with the corresponding illustration already shown in Fig. 3. 6. Overview of experimental setup After the optimum design was found for the proposed MRB, a 3D CAD model was generated using Pro/E (see Fig. 12(L)). Fig. 12(R) shows the subsequent prototype that was manufactured. The main specifications of the MRB prototype are given in Table 4. The MRB prototype was installed into the experimental setup shown in Fig. 13. A servo motor from CMC Inc. with a continuous torque of 5.13 Nm and with rotational speed of 5445 rpm was used to generate the shaft rotation. Since the torque generation capacity of the servo motor is relatively low, an ALPHA 0755-MC1-7 gear reducer (7:1) was used. The servo motor was connected to a Futek torque sensor (TRS605) which is a shaft-to-shaft rotary torque sensor with a torque measuring capacity up to 1000 Nm. The other end of the torque sensor was connected to the MRB prototype. An inertia dynamics magnetic clutch was installed between the torque sensor and the servo motor in order to release the load on the servo motor generated by the brake. In order to connect the various components, flexible couplings were used. A K-type thermocouple was also installed into the prototype in order to measure temperature changes during experiments.
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Fig. 12. CAD model (L) and prototype (R) of the proposed MRB.
Table 4 MRB prototype specifications Weight
11.8 (kg)
Diameter Number of disks Amount of MR fluid used Coil wire size Number of turns Maximum current applied Maximum current density applied Seals used Magnetic materials used Non-magnetic materials used Maximum braking torque
239.9 (mm) 2 205 (cm3) AWG 21 (£ 0.77 mm) 236 ± 2 (turns) 1.8 (A) 2.54 106 (A/m2) Static and synamic O-rings Steel 1018 Al T-6061 and SS 304 23 Nm at 1.8 A
The servo motor was controlled with a PID controller and the rotational speed of the brake was verified using an optical encoder embedded in the torque sensor. All input and output signals were connected to a dSPACE hardware-in-the-loop control board (DS1104). The control signal from the dSPACE board to the servo motor was amplified using an Advanced Motion Control Brushless PWM servo amplifier. In addition, a low-pass filter circuit was implemented into the setup in order to reduce any high frequency noise in the torque sensor readings. During experiments, the rotational speed was kept constant at various values and current was applied to the coil using an Agilent
Technologies high current power supply (N5766A). Whenever the brake was actuated, since the system was at steady-state, the relative torque measured between the shafts on each side of the torque sensor was recorded as the braking torque generated by the brake prototype. After the braking torque data was obtained, the magnetic clutch was turned on in order to release the load on the servo motor. 7. Experimental results Initially, we measured the no-field torque generated by the viscosity of the MR fluid (plus the mechanical friction torque). In Fig. 14, the torque generated due to viscosity of the fluid at various rotational speeds is shown. As one can see, the relationship between the viscous torque and rotational speed is linear, as described by Eq. (7). After the viscous torque was calculated, current was applied to the electromagnet coil and corresponding changes in the torque readings were recorded. The total braking torques (Tb) generated with respect to the increasing speeds are shown in Fig. 15. The difference between the three torque curves is directly due to the varying viscous torques (Fig. 14) at different speeds. The plots shown in Fig. 15 contain the viscous effects and the frictional effects. In order to compare the experimental results with the simulation results, the viscous and the friction effects have to
Fig. 13. Picture of experimental setup.
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Fig. 17. Comparison between experimental and simulation results at 200 rpm. Fig. 14. Viscous torque versus velocity.
Fig. 15. Torque (Tb) versus current applied.
be subtracted from the experimental data. The resulting plot between the torque (TH) generated due to the applied magnetic field and the current applied is shown in Fig. 16. Three plots are almost identical, which shows that this quantity is not speed dependent, as described by Eq. (6). Finally, the simulation and the experimental results are compared in Fig. 17. While the initial (at 0 A) and final (at 1.8 A) values
Fig. 16. Torque (TH) generated due to magnetic field (without viscous and friction torques).
match, there is deviation in the middle values (104% difference at 0.2 A and 12% difference at 1.6 A). The main reason behind this deviation is probably due to the lack of accurate information on the material properties that were used in the simulations. Another minor factor is the varying temperature. Since the temperature variation has an effect on both the viscosity and magnetic properties of the MR fluid, the heat build-up is a major concern in the actual implementation of such a brake. Due to the lack of detailed information, however, our FEM does not account for temperature effects on material properties. In Figs. 18 and 19, the temperature distribution within the MRB is shown for the two cases described in Section 4. In the first case (see Fig. 18), the disks were freely rotated at 400 rpm for 20 s without applying a magnetic field. In the second case (see Fig. 19), 1.8 A was applied to the coil, generating a magnetic field across the brake that was rotating at 200 rpm. Fig. 20 shows the heat buildup for the above two cases. The solid lines represent the actual temperature variation at the location of the thermocouple (see Fig. 12(R)), while the dotted lines represent the corresponding simulation results. It can be seen that the experimental and simulation results are reasonably in good agreement for the 20 s cruising or braking period that we considered. 7.1. Discussions Note that in order to stop a 1000 kg passenger vehicle with a deceleration of 6 m/s2, which is the typical requirement for measuring braking performance of a fully loaded passenger vehicle with burnished brakes, each brake has to generate around 500 Nm. The prototyped MRB can generate only 5% of this torque value. This indicates that a radical change in the basic brake configuration is required in order to build a feasible automotive MRB. For example, the following design improvements can be made in the basic configuration to further increase the braking torque capacity: (i) In Fig. 21, the simulated improvement in the braking torque with additional disks is shown for the same design configuration proposed in this work. Note that 20% (i.e. 100 Nm) of the required torque can be generated with an MRB with 7 disks. (ii) The braking torque capacity can also be increased significantly by relaxing the size and the weight constraints defined in Eq. (18). Note from Table 4 that the weight of the prototyped MRB is still relatively light (especially considering that of the overall CHB system), 11.8 kg; hence there is still some room to allow increases in the overall size/weight of the MRB. For example, in our previous paper [3], the size and weight constraints were greatly relaxed,
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Fig. 18. Temperature distribution within MRB: no magnetic field applied.
Fig. 19. Temperature distribution within MRB: magnetic field applied.
which resulted in a 27.8 kg two-disk MRB design that can generate up to 1000 Nm of braking torque in numerical simulations. While the current work shows that this level of torque cannot be generated in practice when the limitations in space/weight and current density, as well as sealing and magnetic saturation considerations (Section 3) are taken into account, some relaxation of the constraints is still possible. For example, Fig. 22(L) shows such an MRB design with a thicker single disk that can generate about 55 Nm at 1.8 A (see Fig. 22(R)).
Once an improved MRB configuration is suggested, one can repeat the design process presented in this paper to maximize the braking torque capacity. Another critical design criteria that one must further consider is the long term temperature effects (due to heat build-up) on the degradation of the MR fluid properties. Note that in the case of Fig. 19, the temperature rises by almost 25 °C in just 20 s of continuous braking. In addition, in [15], a dynamic finite element analysis was also performed to study the effects of applying repeated cycles of pressing and releasing the brake on the heat build-up, and showed that the operating
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Fig. 20. Temperature change at measurement location: (L) no magnetic field applied and (R) magnetic field applied.
8. Conclusion
Fig. 21. Simulation plot of braking torque (TH) generated with respect to the number of disks (at 1.8 A).
temperature can intermittently reach outside the recommended temperature range of the MR fluid. These results show a need for the design of an effective passive or active cooling mechanism, as the MR fluid degradation would be the ultimate limiting factor on the performance and life cycle of the MRB. However, if the above problems cannot be overcome, a hybrid electromechanical brake (HEMB) system [19] that combines with a CHB system may be an alternate solution.
In this paper, a magnetorheological brake (MRB) design has been introduced as a viable alternative to the current conventional hydraulic brake (CHB) device. Since the MRB is an electromechanical device, it has several advantages over the CHB, such as reduced actuation delay, ease of software control implementation and lower system weight. The design process was started with an analytical model of the MRB. Then, the MRB device was designed with a focus on magnetic circuit optimization and material selection. A two-dimensional finite element model of the MRB was created to simulate the steady-state magnetic flux flow within the MRB domain using COMSOL Electromagnetic Module and solve for the magnetic field intensity distribution. In addition to the detailed electromagnetic analysis, a simple heat transfer analysis was carried out to monitor the heat build-up within the brake. The FEM was then used to optimize the magnetic circuit design in order to maximize the braking torque and minimize the weight of the MRB. The optimization problem was solved using a hybrid optimization procedure that included simulated annealing and sequential quadratic programming algorithm. A 3-D CAD model of the optimum MRB design was generated and a MRB prototype of the optimum design was manufactured. The MRB braking performance was tested using an experimental apparatus that consisted of a torque sensor and a servo motor.
Fig. 22. An MRB with different magnetic circuit configuration (L) and corresponding simulation plot of braking torque (TH) versus applied currents (R).
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The experimental results showed that the braking torque increases with applied current, reaching more than 20 Nm at 1.8 A, thus confirming the theoretical predictions. There were discrepancies with respect to the simulation results due to estimated material properties used in the simulations. However, the proposed MRB configuration was not able to generate sufficient braking torque to stop a vehicle. Therefore, an improved MRB design should be suggested (e.g. by increasing the number of disks or completely redesigning the magnetic circuit configuration) in future designs, taking into account the temperature effects and more accurate description of the material properties as well. References [1] Kolde H, Omekanda AM, Lequesne B, Golpalakrishnan S, Khalil A, Underwood S, et al. The potential of switched reluctance motor technology for electromechanical brake applications. In: Proceedings of the SAE world congress, Detroit, MI; April 3–6, 2006. 2006-01-0296. [2] Lee KJ, Park KH. Optimal robust control of a contactless brake system using an eddy current. Mechatronics 1999;9:615–31. [3] Park EJ, Stoikov D, Falcao da Luz L, Suleman A. A performance evaluation of an automotive magnetorheological brake design with a sliding mode controller. Mechatronics 2006;16:405–16. [4] Carlson JD, LeRoy DF, Holzheimer JC, Prindle DR, Marjoram RH. Controllable brake. US Patent No. 5842547. United States Patent Office; December 1, 1998. [5] Carlson JD. Magnetorheological brake with integrated flywheel. US Patent No. 6186290 B1. United States Patent Office; February 13, 2001.
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