周而复始英文版汽车资料

2021年1月16日发(作者：俞润)

英文版汽车资料
Design considerations for an automotive magnetorheological brake

Kerem Karakoca, Edward J. Park, a, and Afzal Sulemana
aDepartment of Mechanical Engineering, University of Victoria, P.O.
Box 3055, STN CSC, Victoria, BC, Canada V8W 3P6
Received 10 October 2007;
accepted 22 February 2008.
Available online 11 April 2008.

Abstract
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.
Keywords: Mechatronic design; Magnetorheological fluid; Automotive
brake; Magnetic circuit;
Finite element analysis; Multidisciplinary design optimization;
Brake-by-wire Article Outline
1.
Introduction
2.
Analytical modeling of MR brake
3.
Design of MR brake
3.1. Magnetic circuit design
3.2. Material selection
3.2.1. Magnetic properties
3.2.2. Structural and thermal properties
3.3. Sealing
3.4. Working surface area


3.5. Viscous torque generation
3.6. Applied current density
3.7. MR fluid selection
4.
Finite element modeling of the MR Brake
5.
Design optimization
6.
Overview of experimental setup
7.
Experimental results
7.1. Discussions
8.
Conclusion
References
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 mechanism, 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 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. 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, 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.



Full-size image (49K)
Fig. 1. Cross-section of basic automotive MRB design [3].
View Within Article
The literature presents a number 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
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] 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. 405–416. Article | PDF (547 K) | View
Record in Scopus | Cited By in Scopus (21)[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
The idealized characteristics of the MR fluid can be described
effectively by using the Bingham
[10], [11] and [12]. According to this model, the total shear stress
τ is plastic model [9],

(1)where τH is the yield stress due to applied magnetic field, μp
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 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

(3)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, τH,
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 β, i.e.

By substituting Eqs. (3) and (4), the braking torque equation in Eq.
(2) can be (4)
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 magnetic
field
and Tμ is the torque generated due to the viscosity of the fluid.
Finally, the total braking torque is Tb = Tμ + 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) Magnetic circuit design
(ii) Material selection
(iii) Sealing
(iv) Working surface area
(v) Viscous torque generation
(vi) Applied current density


(vii) MR fluid selection

Full-size image (79K)
Fig. 2. Chosen MRB based on the design criteria.
View Within Article

Full- size image (38K)
Fig. 3. Dimensional parameters related to magnetic circuit design.
View Within Article
3.1. Magnetic circuit design
The main goal of the magnetic circuit analysis is to direct the
maximum amount of the magnetic 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 generating 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 fluid and the shear disk (see Fig. 2). Then, the flux
generated (φ) 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), μ 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 μ and
A
can be increased according to Eq. (9).

Full-size image (19K)
Fig. 4. Magnetic circuit representation of the MRB.
View Within Article
However, since the magnetic fluxes in the gap (φgap) and in the
core (φcore) 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

(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 μ and A of the member. Note that H in Eq.
(10) can be obtained by writing the steady- state Maxwell–Ampere’s 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 as

(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 parts 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. μ) 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 μ) 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.
3.2.1. Magnetic properties
The property that defines a material’s magnetic characteristic is
the permeability (μ). 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 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
Ferromagnetic materials (μr > 1.1) Non-ferromagnetic materials (μr
< 1.1)


Alloy 225/405/426 Aluminum
Iron Copper
Low carbon steel Molybdenum
Nickel Platinum
42% nickel Rhodium
52% nickel 302–304 stainless steel
430 stainless steel Tantalum
Titanium
Full- size table
μr is the relative permeability.
View Within Article
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.

Full-size image (21K)
Fig. 5. B–H curve of steel 1018 for initial magnetic loading.
View Within Article
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.

Full-size image (43K)


Fig. 6. Different seals on proposed MRB design.
View Within Article
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 O-rings
were used for both static and dynamic applications. In addition, a
sealant, Loctite 5900? 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, τH, 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 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 μ, 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 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. μr 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-132DG? is the best candidate for the automotive braking
application due to its broad
operating temperature range. In Table 2, the properties of MRF-132DG?
are shown and its relationship between the magnetic field intensity and
the generated shear stress is shown in Fig. 7.
Table 2. Properties of MRF-132DG?
Property Value/limits
Base fluid Hydrocarbon
Operating temperature ?40 to 130 (?C)
Density 3090 (kg/m3)
Color Dark gray
Property Value/limits
Weight percent solid 81.64 (%)
Coefficient of thermal expansion (calculated values) Unit volume
per ?C
0–50 (?C) 5.5e?4
50–100 (?C) 6.6e?4
100–150 (?C) 6.7e?4
Specific heat at 25 (?C) 800 (J/kg K)
Thermal conductivity at 25 (?C) 0.25–1.06 (W/m K)
Flash point ?150 (?C)
Viscosity (slope between 800 and 500 Hz at 40 ?C) 0.09(?0.02) Pa s
k 0.269 (Pa m/A)
β 1


Full-size table
View Within Article

Full-size image (19K)
Fig. 7. Shear stress versus magnetic field intensity for MRF-132DG?.
View Within Article
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 Multiphysics?.
The following governing magnetostatic equations [14] are used by the
COMSOL electromagnet module

(13)×H=J

(14)?B=0where H is the magnetic field intensity, B is the magnetic
flux density and J is the electric current density. By solving these
equations 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