1. Introduction and Study Motivation
With the booming advancement of the new-energy automotive industry, the global fleet of electric vehicles has continued to expand at an exceptional pace. During this rapid transformation in mobility, higher demands have been placed on vehicle driving safety, especially within the braking system. The braking system directly determines vehicle safety performance. Traditional hydraulic braking systems widely used in current new energy electric cars often suffer from several critical drawbacks, including large space requirements, structural complexity, longer braking response times, and inherent response delays caused by hydraulic transmission. Such shortcomings may jeopardize the overall emergency braking performance, possibly causing longer braking distances and threatening driver safety.
Magnetorheological braking systems, as novel intelligent actuators, have drawn significant attention from researchers and automotive engineers. Magnetorheological fluid is a new kind of smart material. Under the application of an external magnetic field, it can transform within milliseconds from a Newtonian fluid into a Bingham fluid with solid-like characteristics. This transition is completely reversible; moreover, the shear stress can be continuously adjusted by changing the external magnetic field magnitude. Consequently, MR braking systems offer advantages like extremely fast response, low wear of braking components, excellent safety, and high durability. However, the traditional MR brakes are still hampered by limited achievable braking torque values. Moreover, conventional ABS control strategies currently used or proposed for electric cars, such as logic threshold or classical PID algorithms, still face issues involving slow response time, constrained control precision, and insufficient road adaptability.
The major motivation of this research is to solve the practical problems encountered when MR brakes are applied to electric cars. To achieve improved braking torque, shorten vehicle emergency braking time and braking distance, and ensure comprehensive driving safety, this work designs a three-coil comb-type disc magnetorheological brake and proposes a model predictive control strategy augmented by road recognition. By integrating temperature-dependent MR fluid properties, accurate braking torque mathematical modeling, finite element electromagnetic simulation, bench tests, and comparison with different ABS control methods, both simulation and experiments verified significant improvements in braking response and control stability.
2. Structural Design of the Three-Coil Comb-Type Disc Magnetorheological Brake
2.1 Operational Principle
The magnetorheological brake operates on the shear mode working principle of the MR fluid. Inside the brake, the MR fluid is located in the gaps between the rotating component and the stationary housing. In the absence of an exciting current, the MR fluid behaves approximately as a low-viscosity Newtonian fluid, generating negligible resistance so the wheel rotates freely. Once the excitation coil is activated, the magnetic field generated across the working gap causes the ferromagnetic particles inside the MR fluid to form chain-like structures along the magnetic flux direction. This microstructural evolution raises the fluid’s shear yield stress, producing retardation torque on the rotating disk. The magnitude of the braking torque can be continuously regulated by adjusting the coil current.
Table 2-1 Nomenclatures of brake structural dimensions
| No. | Component description | Symbol | Value (mm) |
|——|———————-|——–|————|
| 1 | Maximum radius of comb disc | R1 | 105 |
| 2 | Radius of comb tooth | R2 | 92 |
| 3 | Minimum radius of comb structure | R3 | 87 |
| 4 | Maximum radius of side coils | R4 | 77 |
| 5 | Radius of inner housing-rotor matching area | R5 | 28 |
| 6 | Thickness of rotor fixed part | L1 | 9 |
| 7 | Length of side coil | L2 | 25 |
| 8 | Thickness of magnetic isolation ring | L3 | 10 |
| 9 | Width of main coil | L4 | 15 |
| 10 | Thickness of external magnetic sleeve | L5 | 10 |
| 11 | Width of comb tooth | H1 | 8 |
| 12 | Thickness of outer housing | H2 | 15 |
| 13 | Thickness of crescent-shaped magnetic guide | H3 | 4 |
| 14 | Width of brake disc connecting section | H4 | 10 |
| 15 | Width of brake disc fixed part | H5 | 40 |
| 16 | Width of side coils | H6 | 20 |
| 17 | Width of outer-inner housing connection | H7 | 5 |
| 18 | MR fluid working gap width | D | 1 |
The newly designed three-coil comb-type disc MR brake shown above mainly consists of a comb-structured brake disk, external main coil, two side (auxiliary) coils, an external magnetically conductive sleeve, an inner housing, relatively rotating shaft arrangements, dust seals and tapered roller bearings. Compared with conventional single-disk MR brakes, the comb-shaped structure significantly enlarges the effective shearing area between rotor and stator while maintaining a compact radial envelope. Eight radial effective braking gaps are created. Moreover, the distal comb teeth provide a larger moment arm, generating greater braking torque for the same shear area. The structural arrangement with one primary external coil and two secondary side coils plays a critical role in the magnetic circuit. When the two side coils receive currents in the same direction, they work as one equivalent effective coil. The flux produced by the main coil is favorably constrained and guided by the auxiliary coil field. This results in increased magnetic induction intensity through the effective MR fluid working zones and mitigates flux leakage, further increasing achievable braking torque.
The material selection of the brake is as follows: 20# low-carbon steel is chosen for magnetically conducting parts, including the comb brake disk, external sleeve, and outer housing. 304 stainless steel is used for non-magnetic structures such as the coil isolation rings, inner housing, and bearing sleeves. The shaft is fabricated from 45# steel. The electromagnetic coils use 0.8 mm enameled copper wire. Skeleton oil seals are used for dynamic sealing.
2.2 Magnetic Circuit Modeling
Because the structural configuration is symmetric with respect to the central plane, only one half of the magnetic circuit is analyzed. Magnetic circuit simplification reduces the half-structure to thirty-four equivalent magnetic resistances. The primary coil flux path contains twenty-three magnetic resistances, while the secondary coil path contains twelve resistances, with both paths sharing the common resistance of the MR fluid effective region. The total reluctance for the main coil circuit and the auxiliary coil circuit is obtained by applying magnetic Ohm’s law to the simplified magnetic network.
Magnetic reluctance of each individual section is expressed as:
$$R_{mi} = \frac{l_i}{\mu_i S_{mi}}$$
where:
– \(R_{mi}\) = magnetic resistance of the i-th section (A/Wb)
– \(l_i\) = length of the i-th magnetic path (mm)
– \(\mu_i\) = magnetic permeability of the material (H/m)
– \(S_{mi}\) = cross-sectional area of the i-th flux path (mm²)
The total reluctance of the main and secondary coil circuits is calculated using the superposition principle of series-connected magnetic resistances. The relationship between the magnetic induction intensity \(B\) in the effective MR fluid gap and the excitation current \(I\) is obtained by Ampere’s circuital law:
$$B = \frac{N I}{R_m S_0}$$
where \(N\) denotes the coil turn number, \(R_m\) the total reluctance, and \(S_0\) the effective area of the magnetic circuit, calculated as \(S_0 = \pi(R_1^2 – R_3^2)\). Substituting all dimensions and material properties yields the current-to-field relationships:
$$B = 0.125I \qquad \text{(main coil energized alone)}$$
$$B = 0.13I \qquad \text{(main and secondary coils energized together)}$$
These linear relationships serve as the bridge between excitation current and output braking torque, laying the foundation for developing the control-oriented mathematical model used by the MPC algorithms.
3. Mathematical Modeling of Braking Torque
The total braking torque generated in an MR fluid brake consists of two contributions: the field-induced magnetorheological torque and the zero-field viscous torque. Since the zero-field viscous contribution is small relative to the controllable magnetorheological part, it is neglected in the theoretical derivation.
The shear stress of the MR fluid under an applied field is given by the Bingham constitutive model:
$$\tau = \tau_y(B) + \eta \dot{\gamma}$$
where:
– \(\tau\) = total shear stress (kPa)
– \(\tau_y\) = field-dependent yield stress (kPa)
– \(\eta\) = zero-field viscosity (Pa·s)
– \(\dot{\gamma}\) = shear strain rate (1/s)
The shear strain rate is determined by the angular velocity \(\omega\), the radial position \(r\) and the working gap thickness \(\delta\):
$$\dot{\gamma} = \frac{\omega r}{\delta}$$
Since the MR brake consist of multiple disk surfaces with shear gaps, element integration is applied over the effective working radii. For the comb-type rotor structure with \(n\) working surfaces:
$$T_{side} = \int_{R_{min}}^{R_{max}} r \cdot \tau \cdot 2\pi r \, dr$$
This formulation yields the relation between total braking torque and shear yield stress. Substituting the design parameters from Table 2-1, the simplified numerical expression is:
$$T = 1.113 \times 10^{-2} \tau_y$$
3.1 Temperature-Dependent Shear Yield Stress
MR fluid properties depend on temperature to a significant degree. To precisely describe the shear yield stress under different thermal conditions, a series of rheological tests were conducted using an MCR302 rheometer over the working temperature range of 5–70 °C. Four different magnetic field strengths (0.2 T, 0.3 T, 0.4 T and 0.5 T) were applied while shear rates gradually rose from zero to 1000 s⁻¹. The experimental results clearly showed that the shear yield stress of the MR fluid decreased with increasing temperature for all tested magnetic field values. Notably, the higher the magnetic induction intensity, the more pronounced the decreasing trend appears. This behavior mainly originates from the decrease in magnetic permeability of MR fluid as temperature rises, weakening the magneto-induced interaction among ferromagnetic particles.
By using the Boltzmann thermodynamic equation to fit each measured curve, four formulas were obtained. The high accuracy of those fits is confirmed by R-squared values exceeding 0.99. Based on those curve-fitting results, a two-variable mathematical expression is established by least-squares regression to comprehensively characterize the shear yield stress as a function of both magnetic induction intensity and temperature:
$$\tau_y = 0.0102Q^2 + 111.5818B + 32.9942 – 0.5652QB$$
where \(Q\) is the temperature in degrees Celsius and \(B\) is the magnetic induction intensity in Tesla.
Table 3-1 Physical parameters of MRF-J25T MR fluid
| Technical parameter | Value |
|——————–|——-|
| Density | 2.65 g/cm³ |
| Zero-field viscosity | 1 Pa·s |
| Shear stress | 45 kPa |
| Operating temperature | -35 to 140 ℃ |
Combining the relationship between the shear yield stress and the braking torque derived previously:
$$T = 226.1B + 764.6B^2 + 3.87BQ – 7 \times 10^{-5}Q$$
The substitution of the magnetic-field-to-current expression into the above equation produces temperature and current-dependent torque formulas.
When the main coil alone is energized:
$$T = 3.53I^2 + 95.6I + 0.48Q – 7\times10^{-5}IQ$$
When main and secondary coils are energized together:
$$T = 3.83I^2 + 99.4I + 0.5Q – 7\times10^{-5}IQ$$
These equations form the control-oriented mathematical model for designing ABS control algorithms and are used both in simulation and bench validation.
4. Finite Element Electromagnetic Field Simulation
The finite element method is valuable for predicting the magnetic flux distribution of the designed MR brake. A simplified two-dimensional axial symmetric model of the three-coil comb-type disc brake was established in Maxwell software. In the model, different colors represent the material zones: the magnetic flux path ring, MR fluid domain, non-magnetic separators, and coil windings.
When the main coil is energized alone, the predicted magnetic field distribution reveals that the flux lines tend to distribute through the radial MR working zones around the comb teeth. However, a certain amount of flux leakage is detected near the shaft region since only the magnetic and non-magnetic material arrangement constrains the flux path. The effective MR working zone reaches magnetic induction values near 0.5 T.
When both the main coil and the two side coils are excited simultaneously, flux leakage is significantly mitigated. The auxiliary coil produces additional magnetic flux that effectively pushes the main flux into the desired active shear zones. As a result, the magnetic induction within the radial MR fluid working gaps increases. The simulation validates the proposed magnetic circuit layout and confirms the functional role of the additional coils in intensifying the magnetic field in the working zone.
5. Bench Testing of Braking Torque and Energy Efficiency
5.1 Experimental Platform Description
To test the actual torque output of the MR brake, a comprehensive disc-type MR brake performance test platform was employed. The platform is equipped with a frequency converter to set the motor speed, a digital DC power supply providing adjustable voltage and current, a torque transducer measuring instantaneous torque, and a multi-channel temperature measuring instrument to monitor the operating temperature of the MR fluid. Tests were carried out under eight initial speeds ranging from 10 km/h to 80 km/h, because the A00-class electric car platform has a maximum speed of 80 km/h. The supply voltage was fixed at 60 V. The working temperature was maintained at approximately 40 °C to minimize temperature-induced deviations when validating the torque-current relation.
5.2 Braking Torque Experimental Results
For the main coil energized alone, the measured output braking torque increases with current amplitude. Under 4 A current, the maximum output torque reaches around 340 N·m. The torque-current curves maintain the same trend at different initial speeds, although minor discrepancies are observed that originate from the temperature sensitivity of the MR fluid and the finite response time of its rheological transition.
When the secondary coil is energized alone, because the wire diameter is 0.6 mm and the allowable current is 2 A, its maximum torque contribution is about 23 N·m. This modest level is expected, because primary function of the side coils is field shaping rather than direct torque generation.
Tests were also performed when both main and auxiliary coils were simultaneously activated. The auxiliary coil current was set to a constant 2 A. The maximum braking torque increased from roughly 360 N·m to 380 N·m under saturation conditions, corresponding to approximately a 6% enhancement when compared to the main-coil-only operation.
Table 5-1 Comparison of torque generation capability at different modes
| Working mode | Maximum torque (N·m) | Improvement |
|———–|——————–|————-|
| Main coil alone | 340 | Baseline |
| Main coil with 2 A secondary coil | 360 | +6% |
| Theoretical maximum (both coils) | 380 | +11% |
To further quantify the field-shaping effect of the side coils, an additional experiment was carried out at 60 km/h, holding the main coil at 3 A. Raising the auxiliary coil current from 0 to 2 A increased the output torque by 4.1%. This indicates that the secondary coil successfully reduces flux leakage and focuses a stronger magnetic field inside the MR fluid working regions.
5.3 Validation of the Mathematical Model
The torque-current relationship obtained from bench testing matches well with the model prediction within the low-to-medium current range. For currents below approximately 3.2 A, experimental torque values are slightly higher than those of the model. This can be explained by the zero-field viscous resistance of the MR fluid contributing to an approximately 15 N·m additional baseline torque. For currents above 3.2 A, the measured torque becomes slightly lower than the theoretical prediction, because magnetic flux saturation occurs in the ferromagnetic materials and MR fluid. The maximum difference remains modest, confirming the proposed mathematical model is sufficiently accurate for the design of control algorithms.
5.4 Energy Efficiency Ratio Analysis
The energy efficiency ratio (EER) of the MR brake was evaluated to compare the economic performance of different coil configurations. The ratio is defined as:
$$EER = \frac{T}{W}$$
where T is output braking torque (N·m) and W is consumed electrical power (W). At a given speed, input power increases with excitation current. Experiments were carried out to record both torque output and total electrical power consumption.
When the main coil alone was energized, EER decreases continuously with rising current. The viscous resistance contributes relatively more to torque output at smaller field intensities resulting in higher EER values in the low-current regime. Once the current surpasses a moderate level, the magnetic contribution dominates and the EER curve follows the expected descending trend.
Table 5-2 Energy efficiency ratio comparison
| Operating mode | EER trend at 4 A | Difference |
|————–|——————|————|
| Main coil alone | Higher EER | Baseline |
| Main coil plus side coils | Lower EER | -5.3% relative |
When auxiliary coils are energized, the total power draw increases faster than the additional torque provided. Under high main coil current, the two-mode efficiency gap narrows. At the maximum tested current, feeding both main and side coils lowers the EER by about 5.3%.
Taking these results together, for normal driving demands, power-saving operation would favor main coil excitation alone. However, if maximum emergency braking torque is necessary to activate ABS and secure driving safety, simultaneously energizing the main and auxiliary coils provides a 6% higher braking torque. Considering that ABS activation directly relates to driving safety in potentially critical scenarios, the consequent efficiency drop is acceptable. Therefore, in the ABS control strategies studied in this work, both main and secondary coils are simultaneously powered.
6. Vehicle Dynamics and ABS Control Strategies
6.1 Single-Wheel Vehicle Model
A quarter-car single wheel model is adopted to describe longitudinal braking behavior of electric cars. The governing differential equations are derived from force analysis.
Vehicle translational motion:
$$m\dot{v} = -F_x$$
Wheel rotational motion:
$$J\dot{\omega} = F_x R_r – T_b$$
where the braking force due to the road-tire interface is:
$$F_x = \mu F_N = \mu m g$$
Combining the equations yields:
$$\dot{v} = -\mu g$$
$$J\dot{\omega} = \mu m g R_r – T_b$$
Table 6-1 Main parameters of the target A00-class electric car
| Parameter | Symbol | Value | Unit |
|———–|——–|——-|——|
| Full vehicle mass | Ga | 1020 | kg |
| Wheelbase | L | 1.94 | m |
| Distance from CG to front axle | la | 0.92 | m |
| Distance from CG to rear axle | lb | 1.02 | m |
| CG height | hg | 0.50 | m |
| Wheel rolling radius | r | 0.25 | m |
| Quarter vehicle mass | Ga/4 | 254 | kg |
| Wheel moment of inertia | Jwheels | 0.98 | kg·m² |
6.2 Slip Ratio Definition
Slip ratio S is the most important state variable for ABS control because it defines the relationship between vehicle speed and wheel speed:
$$S = \frac{v – \omega R_r}{v} \times 100\%$$
Maintaining the slip ratio around its optimal value (approximately 0.2 on most road conditions) provides both high longitudinal friction and sufficient lateral stability.
6.3 Tire-Road Model – Magic Formula
The tire-road friction coefficient is described by Pacejka’s magic formula:
$$\mu = D \sin\{C \arctan[B S – E(B S – \arctan(B S))]\}$$
The empirical coefficients B, C, D and E characterize the stiffness, shape, peak, and curvature factors, respectively. Three different road surfaces are simulated to represent typical driving conditions for electric cars.
Table 6-2 Magic formula parameters for three road conditions
| Road adhesion level | B | C | D | E |
|———————|—–|—–|——-|—–|
| High (dry asphalt) | 5.00 | 2.00 | 0.75 | 0.90 |
| Medium (wet soil) | 5.50 | 2.00 | 0.40 | 0.90 |
| Low (icy/snowy) | 6.50 | 2.00 | 0.15 | 0.90 |
The peak friction coefficient on high-adhesion road is 0.75, medium-adhesion 0.4, and low-adhesion road 0.15. The optimal slip rate stays near 0.2 across these conditions.
6.4 Road Recognition Algorithm
Traditional road recognition approaches use extensive calculation with limited real-time performance, or rely on estimating the friction coefficient and are vulnerable to disturbances. To overcome these constraints, a Convolutional Neural Network (CNN) based road image recognition method is proposed to determine the current road surface in real time. The CNN architecture consists of an input layer, convolutional layers, pooling layers, fully connected layers, and an output layer. Images representing three different road categories were collected: 30 low adhesion road images, 30 medium adhesion road images, and 30 high adhesion road images.
The training was conducted using 20 images from each category as the training set, five per category as validation set, and the remaining 15 images as the test set. The trained CNN achieved 100% classification accuracy on the test set. This road recognition approach can rapidly pre-identify the road adhesion condition, greatly reducing the computation burden of the model predictive controller. It supplies important prior information that enables MPC to impose the appropriate constraints and target slip rate.
6.5 Magnetorheological Brake Control-Oriented Model
The actual MR brake has non-negligible electromechanical dynamics and rheological response delays. To make the control design tractable, the torque-current characteristic shown by the experimental curves is linearized over the operating region where magnetic saturation has not yet occurred. The experimental curve closely follows linear behavior up to current values of 3.5 A, which drives output torque to about 340 N·m. Within this region, the static gain is fitted as \(k_H = 100\). The dynamic behavior caused by the finite response of magnetization and rheological transition is captured by a first-order lag element with a time constant. Based on the dynamic response tests of MR actuators, the time constant is selected as 0.01 s.
The transfer function is therefore formulated as:
$$H(s) = \frac{100}{0.01s+1} U(s)$$
This simplified linear dynamic model is used for all subsequent ABS controller designs and simulation studies.
7. Controller Design and Simulation Results
Three types of ABS control strategies were designed in Simulink for the magnetorheological brake and evaluated on low, medium, and high adhesion road surfaces. The controlled output is braking torque, converted into the coil current command through the inverse relation of the torque-current model. The control objective is to regulate the wheel slip ratio to a target value, minimizing braking distance and time.
7.1 Simple Negative Feedback Strategy
The simplest ABS algorithm compares the measured slip ratio against the target threshold of 0.2. If S ≥ 0.2, the current is reduced to lower braking torque, allowing wheel acceleration. If S < 0.2, the current increases to augment braking torque. This bang-bang style control logic is easy to implement but inherently produces continuous high-amplitude oscillations around the setpoint.
The simulation results demonstrate that on low-adhesion surface, the vehicle stops after 3.899 s and travels 47.72 m. On the medium surface, stopping time is 2.918 s and distance 36.81 m. On the high-adhesion road, stopping time is 2.146 s and distance 28.5 m. Slip rate oscillations remain significant throughout the whole braking event, implying weaker stability.
7.2 Conventional PID Strategy
The PID strategy computes the current command according to the error between actual slip ratio and target slip ratio. The control signal follows:
$$u(t) = K_p e(t) + K_i \int_{0}^{t} e(\tau) \, d\tau + K_d \frac{de(t)}{dt}$$
The parameters \(K_P\), \(K_I\), \(K_D\) were tuned based on the medium-adhesion road condition. Simulation results show relatively good performance on medium surfaces, where the stopping time reaches 2.513 s and braking distance 30.47 m. However, because PID gains remain constant across different road types, low-adhesion conditions give overshoot and unstable transient behavior, while high-adhesion conditions cause slower response. Low-adhesion stopping time is 3.478 s and distance is 41.17 m. High-adhesion simulation gives 1.768 s and distance 22.23 m. The slip variation is narrower than simple negative feedback.
7.3 Proposed MPC Strategy Aided by Road Recognition
Model predictive control was designed using the linearized first-order dynamic model of the MR brake as the internal prediction model. The MPC formulation solves a constrained finite horizon optimal control problem at every sampling instant. The cost function penalizes predicted deviation of slip ratio from its desired optimum and the control effort:
$$J(k) = \sum_{j=1}^{N_p} \left\| S(k+j|k) – S_{ref}(k+j) \right\|_Q^2 + \sum_{j=1}^{N_c} \left\| \Delta I(k+j|k) \right\|_R^2$$
subject to constraints on the current amplitude and its increment:
$$0 \le I \le I_{max}$$
$$|\Delta I| \le \Delta I_{max}$$
Because the road recognition CNN pre-identifies the road adhesion level, the model predictive controller uses the proper friction curve and target slip ratio immediately after the braking starts. This feature shortens response time relative to other methods, reduces online parameter estimation complexity, and provides more robust tracking under changing conditions. The simulation results demonstrate the following performance on three different road surfaces:
Table 7-1 Simulation results comparison among three ABS control strategies
| Adhesion level | Strategy | Braking time (s) | Braking distance (m) |
|—————-|———-|——————|———————-|
| Low | Negative feedback | 3.899 | 47.72 |
| Low | PID | 3.478 | 41.17 |
| Low | MPC with recognition | 3.319 | 37.70 |
| Medium | Negative feedback | 2.918 | 36.81 |
| Medium | PID | 2.513 | 30.47 |
| Medium | MPC with recognition | 2.349 | 26.89 |
| High | Negative feedback | 2.146 | 28.50 |
| High | PID | 1.768 | 22.23 |
| High | MPC with recognition | 1.593 | 18.48 |
The quantitative improvement of MPC with road recognition over classical PID control is summarized as follows:
| Adhesion level | Braking time improvement | Braking distance improvement |
|—————-|————————–|——————————-|
| Low | 4.57% | 8.36% |
| Medium | 6.53% | 11.75% |
| High | 9.90% | 16.87% |
Across all three simulated road conditions, MPC with road recognition provided the fastest braking response, shortest stopping distance, and tightest slip ratio tracking around the optimum value. The simulation further indicates that MPC’s response time is 30% faster than PID control. The acceleration curves show MPC can reach maximum deceleration faster and maintain it stably to complete the stop earlier.
8. Experimental Validation on an ABS Test Bench
8.1 Hardware-in-the-Loop Test Bench
In order to experimentally validate the simulation findings, a magnetorheological brake ABS test bench was constructed. This bench uses a magnetic powder clutch as a torque controller to emulate different road adhesion conditions. The fundamental principle of this device is the slip transmission between the driving and driven rotors through magnetized powder chains. By controlling the input current to the magnetic powder clutch, road friction conditions can be adjusted and reproduced.
The measurement system monitors both the input shaft speed (wheel speed) and output shaft speed related to the vehicle longitudinal speed. The slip ratio during braking can then be computed from these speed signals according to the slip ratio definition. The test bench enables direct evaluation of stopping time and braking distance under different control strategies, and recorded results were subsequently compared with the predicted values from simulations.
8.2 Braking Tests Without ABS Function
Tests without anti-lock braking were conducted first to establish a baseline. The MR brake was energized with a constant 4 A current and 60 V voltage so it delivered its maximum output braking torque.
On the low-adhesion surface, the wheel locks up about 0.2 s after brake initiation. The slip ratio stays almost at 100% until the vehicle comes to a stop at 3.72 s, covering a total braking distance of 47.61 m.
On the medium-adhesion surface, the wheel locks at about 0.3 s, with minor slip oscillation before complete locking. The vehicle stops after 2.98 s and the braking distance equals 38.85 m.
On the high-adhesion surface, wheel locking occurs within 0.2 s, but more pronounced slip fluctuations appear as the wheel transiently releases and relocks due to the strong tire-road friction. The stopping time is 2.36 s and the distance equals 29.69 m.
Table 8-1 Experimental results without ABS function
| Road surface | Braking time (s) | Braking distance (m) |
|————–|——————|———————-|
| Low adhesion | 3.72 | 47.61 |
| Medium adhesion | 2.98 | 38.85 |
| High adhesion | 2.36 | 29.69 |
8.3 ABS Testing under Conventional PID Control
Because the simple negative feedback strategy performed poorly in simulations, only PID and MPC strategies were experimentally tested. For the PID-controlled ABS tests, the slip ratio rises quickly from zero to about 20% at the onset regardless of the road surface.
On the low-adhesion road, the vehicle took 3.61 s to stop with a braking distance of 45.39 m. Compared with the no-ABS case, time and distance are reduced by 3.1% and 4.7%, respectively.
On medium-adhesion, the stopping time reaches 2.73 s, while braking distance equals 35.16 m. Reduction compared with no-ABS is 8.4% in time and 9.5% in distance.
On high-adhesion, the stopping time equals 2.11 s with a distance of 26.71 m. Reductions are 10.6% and 10.1%.
The measured PID slip ratio data show some degree of oscillation around 0.2, with the most significant fluctuation amplitude observed on high-adhesion surfaces. Nevertheless, ABS operation shortens both stopping distance and stopping time in all tested circumstances.
Table 8-2 Experimental results under PID control
| Road surface | Braking time (s) | Braking distance (m) | Time reduction | Distance reduction |
|————–|——————|———————-|—————-|——————–|
| Low adhesion | 3.61 | 45.39 | 3.1% | 4.7% |
| Medium adhesion | 2.73 | 35.16 | 8.4% | 9.5% |
| High adhesion | 2.11 | 26.71 | 10.6% | 10.1% |
8.4 ABS Testing under Model Predictive Control with Road Recognition
The model predictive control strategy with the proposed road image recognition method was subsequently tested on the same bench. With road recognition identifying the surface condition in advance, MPC immediately selects the target slip ratio and constraints corresponding to the actual road type. This leads to a shorter initial transient and improved slip ratio regulation throughout the braking process.
On the low-adhesion road, MPC-based ABS made the vehicle stop in 3.42 s, and the braking distance came to 40.56 m. In comparison to PID, time reduction equals 5.3%, while distance saving reaches 10.6%.
On the medium-adhesion surface, the vehicle stop time is 2.43 s, and braking distance equals 30.82 m. These results correspond to reductions of 10.9% and 12.3%, respectively, relative to the PID test.
On the high-adhesion surface, the stop time equals 1.97 s and the distance measured is 24.47 m, translating to 6.6% shorter time and 8.4% shorter distance compared to PID.
Table 8-3 Experimental results of MPC control with road recognition
| Road surface | Braking time (s) | Braking distance (m) | Time reduction vs PID | Distance reduction vs PID |
|————–|——————|———————-|————————|—————————|
| Low adhesion | 3.42 | 40.56 | 5.3% | 10.6% |
| Medium adhesion | 2.43 | 30.82 | 10.9% | 12.3% |
| High adhesion | 1.97 | 24.47 | 6.6% | 8.4% |
Throughout the MPC-based experiments, slip ratio reaches approximately 20% from the very beginning of braking faster than PID, and the subsequent oscillation range is smaller. Better stability, reduced stopping time and shorter braking distance are together achieved. These experimental findings agree closely with earlier simulation results, indicating that the designed model predictive control strategy is valid and reliable for magnetorheological brake ABS systems applied in electric cars.
9. Conclusions and Future Directions
This research presented an extensive study on the design, modeling, simulation, and experimental evaluation of a three-coil comb-type disc magnetorheological brake specifically developed for new energy electric cars. The main conclusions can be drawn as follows:
First, the newly proposed three-coil comb-type disc MR brake effectively increases the effective shear area and magnetic flux utilization. When both main coil and auxiliary side coils work together, the maximum braking torque reaches roughly 360 N·m in experiments. This exceeds the minimum braking requirement of the A00-class electric car platform under investigation. The side coils provide a field-shaping function, reducing flux leakage and intensifying the magnetic field in the working shear gaps. Nevertheless, because the additional side coils consume electrical energy that increases faster than the additional generated torque, the overall energy efficiency ratio decreases by approximately 5.3%. Since ABS activation directly protects passengers during emergency braking, sacrificing a small amount of braking energy efficiency to obtain a 6% higher torque is considered an acceptable and reasonable trade-off for electric cars.
Second, the temperature-dependent mathematical model of braking torque was developed based on rheometer tests of magnetorheological fluid. The braking torque decreases as the fluid temperature rises, with the decline rate slowing above 70 °C. The experimental bench tests conducted at a controlled temperature close to 40 °C validated the accuracy of the theoretical torque-current relationship. This model provides a dependable platform for developing model-based ABS strategies.
Third, simulation studies compared three control strategies: simple negative feedback control, conventional PID control, and model predictive control combined with CNN road recognition. The MPC-based strategy consistently achieves the shortest stopping time and braking distance on high, medium, and low adhesion road conditions. Compared with conventional PID, the maximum improvement reaches 9.9% in braking time and 16.87% in braking distance, with response time shortened by 30%.
Fourth, experimental ABS tests on a dedicated test bench verify the conclusions of the simulation. Compared with a no-ABS brake system, conventional PID control can reduce braking time by up to 10.6% and distance by up to 10.1%. The proposed MPC strategy outperforms PID experimentally, achieving up to 10.9% shorter braking time and 12.3% shorter braking distance. In addition, the MR brake under MPC consistently offers reduced slip ratio fluctuations and better directional stability during braking.
Future work could extend the current single-wheel model to a full four-wheel vehicle dynamic model that includes load transfer and lateral dynamics to more accurately predict vehicle handling during braking maneuvers for electric cars. Additionally, in-vehicle implementation and real road tests could be carried out to validate the performance of both the magnetorheological brake hardware and the MPC road recognition strategy under real driving environments. The study demonstrates that a properly designed magnetorheological braking system, coupled with advanced model predictive control and road recognition, is a very promising solution for improving braking safety and response capability in the new generation of electric cars.