Brake System Model Research Articles

Prediction of automotive response using supervised machine learning in antilock braking systems and comparison with different models for improved vehicle safety

Abstract Previous research on predicting automotive response in antilock braking systems faced several common drawbacks. Limited availability of high-quality datasets and computational constraints hindered the models' ability to generalize and perform effectively in real-time. Additionally, integrating these models into existing vehicle systems is challenging, often requiring extensive calibration and testing to ensure reliability and safety. This study focuses on enhancing automotive safety through the integration of machine learning with advanced braking systems. An antilock braking system model is developed using MATLAB, accounting for key parameters such as speed, mass, wheel radius, and moment of inertia. Various probability ranges are simulated to evaluate the system's real-time response in dynamic environments. A supervised machine learning approach is applied, with lasso regression used for model validation. Braking response was evaluated at three speeds: 25 km/h, 45 km/h, and 65 km/h. To assess model accuracy, error analysis was conducted using metrics such as mean absolute percentage error (MAPE), mean absolute error (MAE), root mean squared error (RMSE), and mean squared error (MSE). Results showed a significant improvement in prediction accuracy, with MAPE reduced to 3.2%, MAE to 0.15 seconds, RMSE to 0.25 seconds, and MSE to 0.06 seconds.A comparative analysis is done using the Python Jupyter Framework, further validating the findings. The machine learning model successfully forecasts braking response times, and validates its prediction against random datasets.

Electronic brake system-based hierarchical motion control of commercial vehicle for autonomous obstacle avoidance

As a high-level autonomous driving technology, efficient and safe automatic obstacle avoidance on highway is one of the critical and ongoing topics that requires in-depth research for commercial vehicles. Electronic control air pressure brake system, owing to its fast response and active braking ability, is an effective active-chassis technology to function path tracking and stability control in such condition. Yaw motion stability control problem of autonomous driving commercial vehicle based on active braking control with electronic air brake system for automatic obstacle avoidance is investigated. First, a hierarchical yaw motion dynamics control architecture is introduced after vehicle and brake system modeling. The quintic polynomial curve-based trajectory planning method and a Model Predictive Control based trajectory tracking control strategy are formulated. Second, to evade the possible stability losing issue in this circumstance, Cubature Kalman Filter (CKF) is utilized to estimate the vehicle motion states, and a fuzzy PID control-based differential brake stability control strategy is designed for the electronic brake system composed of front-and-rear two sets of dual-channel pressure regulator and ABS solenoid valve. Finally, the proposed hierarchical yaw stability control strategy for a commercial vehicle in typical obstacle avoidance conditions is comparatively verified based on the joint simulation tools. After the yaw stability control, the peak value of the lateral displacement error of trajectory tracking can be reduced by 44.7%. The yaw stability control strategy based on fuzzy PID control can reduce the yaw rate by 46%–57% and the sideslip angle by 60%–73% under different conditions. The results show that the proposed control strategy can effectively improve the yaw stability of the vehicle while avoiding obstacles at high speed.

Design, Modeling, and Control of Electronic Mechanical Brake System: A Review

Design, Modeling, and Control of Electronic Mechanical Brake System: A Review

Freight train air brake modelling with emergency valves

The 120-type air brake system is unique around global rail industry and critical for Chinese freight train operation. Existing research about its simulations does not include detailed models for the emergency brake valves. This paper filled this research gap by developing a detailed fluid dynamic air brake system with a focus on the emergency brake valve. The working principle of the emergency brake vale was reviewed. The brake system model was based on gas flow governing equations (mass and momentum) and orifice flow equations. The model was validated by comparing with measured data from a 150-wagon train. Four braking scenarios were compared. The simulated maximum cylinder pressure was only 5 kPa out of the range of the measured data. The maximum difference regarding the time when cylinder pressure reaches maximum pressure was 4 s. The simulation results have also shown variable switch pressure points for the two-stage brake valve. This is agreed by the measured results and was not shown in previously published research.

Simplifying the electronic wedge brake system model through model order reduction techniques

The electronic wedge brake (EWB) uses self-reinforcement principles to optimise stopping power, but its mathematical model has various actuation angles and system dynamics making controller design complex and computationally burdensome. Therefore, the model order reduction (MOR) is made based on three factors that may have a negligible influence on the EWB system: the motor inductance, lead screw axial damping, and wedge mass. Six reduced order model (ROM) types were proposed when one, two, or all factors were ignored. The ROM accuracy was analysed using the frequency and time domain. The percentage of root means square error (RMSE) response value between the EWB benchmark model, and the predicted response based on the ROM was found to be less than 2%, with ROM size reduced from 5 to 2 orders. It guarantees that the new ROM series will be useful for simpler EWB controller design. The proposed ROM simplifies the original model drastically while retaining accuracy at an adequate level. Even though the simplest EWB model is a 2nd order linear system, the best ROM vary depending on EWB design parameters.

Design and manufacturing of an active brake system model using Lidar sensor

Design and manufacturing of an active brake system model using Lidar sensor

Electro-hydraulic composite stability control for regenerative braking failure of in-wheel motors drive electric vehicle

The in-wheel motor simplifies the structure of drive system and improves dynamic performance of vehicle. However, the regenerative braking failure of unilateral motor could greatly reduce braking strength and cause the instability of vehicle. The existing control methods are difficult to guarantee the braking performance and driving stability at the same time. To resolve this fail-safe problem, an electro-hydraulic composite stability control method is proposed and verified. Firstly, the vehicle model, the in-wheel motor model, and the hydraulic braking system model are built. Secondly, the electro-hydraulic composite stability control method is proposed and a stability controller based on model predictive control algorithm is designed to solve the problems of model uncertainty and external interference in the control process. Thirdly, the control effect of proposed method is compared with torque truncation control, hydraulic compensation control, and yaw stability control. Finally, the electro-hydraulic composite stability control method proposed in this paper is verified and tested on the real vehicle. The results show that the combination of the torque truncation control, the hydraulic compensation control, and yaw stability control could improve the driving stability of vehicle and meet the demand of braking intensity.

Hopf-curve-based torque distribution strategy for avoiding limit cycle vibration in hybrid braking system model

Limit cycle vibration affects ride comfort and safety of electric vehicle. In the present study, a Hopf curve was proposed for development of brake torque distribution strategy to circumvent limit cycle vibration. The stability and bifurcation conditions were evaluated based on brake-driveline coupling model of the hybrid braking system. The limit cycle vibration was predicted through the boundary between stable and unstable equilibrium regions. The findings showed that the limit cycle vibration was circumvented by tuning the hydraulic braking force based on the Hopf curve. The insufficient braking torque caused by the decrease in hydraulic braking force was compensated by the driven motor. The findings of the present study provide information on the passive suppression of limit cycle vibration in hybrid braking system to improve the comfort of electric vehicles.

Evaluation of the dynamic behaviors of a train braking system considering disc–block interface characteristics

Disc–block interface properties have prominent influence on the dynamic behaviors of train braking systems. In this study, the tribological characteristics of small-scale train friction blocks with different perforation diameters at the centre of the block surface were investigated using a disc–block test rig. And the Stribeck model parameters of the disc–block friction interface were identified to intuitively characterize the evolution law of stick–slip characteristics with the variation of block perforation diameters. Then, a trailer bogie braking system model of a high-speed train considering the coupling effects between the essential brake unit, wheelset and bogie frame was established. And the identified Stribeck parameters were introduced into the proposed braking system dynamics model to establish a relationship between the friction characteristics of the disc–block interface and the dynamic behaviors of the train braking system. Based on this, the cross-scale analysis was performed to evaluate the dynamic performance of a train braking system affected by the perforated friction block via classical stability theory and numerical simulation. The results show that the friction block with a perforation diameter of 3 mm can effectively suppress the stick–slip vibration of the disc–block friction interface, then reducing the oscillation of system components and enhancing the stability of the entire trailer bogie system.

A Model Predictive Control Approach for Electro-Hydraulic Braking by Wire

In this article, based on a novel electro-hydraulic braking system for full self-driving vehicles, a model predictive control approach is designed for precisely tracking of braking pressure. Concerning electric motor, reduction mechanism, and hydraulic system, a new braking system model is formulated. Due to the nonlinear hydraulic characteristic of the master cylinder piston, a quadratic polynomial is utilized to fit a relationship between piston position and cylinder pressure, by which a desired pressure of master cylinder is transformed into a desired position of the piston. A recursive least square with forgetting factor is developed to find the optimal parameters of pressure–position relationship. A system friction model is established to calculate the equivalent friction torque, which is regarded as the compensation of the desired torque. A vehicle test bench of full self-driving is established to validate the designed approach. According to the accurate tracking and the quick response of braking pressure from experimental results, it can be concluded that the model predictive control approach is a good candidate for the pressure demand control of electro-hydraulic braking by wire.

Cascaded fast terminal sliding mode control for UAV electric braking system

The anti-skid braking system of unmanned aerial vehicle has the characteristics of high-order nonlinearity, strong coupling, and time-varying parameters, which will seriously affect the taxiing performance of the unmanned aerial vehicle. This paper proposed a cascaded fast terminal sliding mode control method for unmanned aerial vehicle electric braking system, which can accurately track the optimal slip rate and ensure the stability of the braking system. First, the electric braking system model of unmanned aerial vehicle is established, which gets rid of the reliance on the ground binding coefficient fitting formulas. Second, combined with the concept of the inversion control, the cascaded fast terminal sliding mode controller is designed to achieve the accurate tracking of the slip rate and the reference braking force. The stability of the controller is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed control strategy is verified by simulation results.

Torsional oscillation suppression-oriented torque compensate control for regenerative braking of electric powertrain based on mixed logic dynamic model

This paper presents a novel torsional oscillation suppression-oriented torque compensate control for regenerative braking (TS-RTC) of electric powertrain, which is based on the gear-pair backlash and half-shaft flexibility-considered dynamic model of regenerative braking in electric powertrain (REP). According to the characteristics of transition from driving mode to regenerative braking mode (DM-to-RM), the dynamic models under different stages are transmitted into an equivalent mixed-logical dynamical (MLD) hybrid model. MLD-based hybrid braking system model and hybrid model predictive control are adopted to design the TS-RTC strategy, in which the torsional oscillation suppression-oriented cost function proved efficient in improving the regenerative braking performance during DM-to-RM process. Simulations and REP hardware in the loop test show that the fluctuation of half shaft torque are efficiently suppressed and the vehicle drivability is improved.

Robust Adaptive Autonomous Braking Control for Intelligent Electric Vehicles*

This paper presents a two-stage autonomous braking control for electric vehicles with preview information acquired by intelligent transportation systems (ITS) or connected and autonomous vehicle (CAV) technologies. The goal of the control method is firstly to plan a speed profile to comply with a target speed and a target residual distance to an upcoming deceleration event and then to track the planned speed profile by generating tracking-driven braking control torques, which maximally employ regenerative braking. Once deceleration circumstances are perceived, the intelligent reference speed planner computes a smooth speed profile by using a current vehicle speed, a target speed, and a target residual distance. For the braking control to robustly track the planned speed profile, a chattering-free sliding mode controller is designed on the interconnected vehicle and braking system model with braking system uncertainties and external disturbances, and a sufficient condition for the sliding mode gain is introduced. Also, adaptive update laws to compensate for the braking system uncertainties provide feed-forward control efforts for the tracking control inputs. To verify the effectiveness of the proposed control approach, the control methods are applied to a real commercial vehicle and the consecutive driving experiments with various deceleration circumstances illustrate a successful tracking-driven cooperative braking performance.

Study of Brake Disc Friction Characteristics Effect on Low Frequency Brake Induced Vibration of Aircraft Landing Gear

During aircraft braking, the change of ground adhesion forces can cause forward and backward vibration of the landing gear, and the performance of the brake disc may exacerbate this vibration. In order to solve this problem, a rigid–flexible coupling dynamic model of a two-wheel strut landing gear considering the friction characters of brake discs with different materials and a hydraulic brake system model is established in this paper. The brake disc friction characteristics effect on the low-frequency brake-induced vibration of the landing gear given different brake disc materials and ambient temperatures is studied. It is shown that the C/SiC brake disc has a “negative slope” phenomenon between the friction coefficient of the brake disc and the wheel speed, and this variable friction characteristic has a great effect on the low-frequency braking-induced vibration of the landing gear. In addition, the variable friction characteristics of the C/SiC brake disc are easily affected by ambient temperature, while the friction coefficient of the C/C brake disc changes stably.

Contribution Analysis of Assembled Brake System to Reduce Squealing

Brake noise is a problem that is still being studied owing to continuous issues in the vehicle industry, and many countermeasures have been suggested using experimental and simulation approaches. The assembled brake system comprises several subparts, and a contribution analysis is an efficient solution for selecting the subpart with the most influence on squealing. In this study, a finite-element model of the assembled brake system was verified with modal test results for each part. Then, a forced response analysis of the assembled brake system model was conducted to obtain the spectral response vector of the subparts under white-noise excitation. A contribution analysis was formulated by calculating the similarity between the total and partial response vectors of each part and deriving the contribution index of all subparts of interest. The brake pad was selected as the target of design modification, and the feasibility was validated using an experimental chassis dynamometer test.

Research on a novel electro-hydraulic brake system and pedal feel control strategy

The existing electro-hydraulic brake system does not consider the adverse effect of the failure of the brake pedal feel simulator on the function of the braking system and the driving safety of the vehicle. To solve the above problems, a novel electro-hydraulic brake system is proposed. Firstly, the structural scheme and the working modes of the system are analyzed, and the electro-hydraulic brake system model is established, and a control strategy for the controlling of the wheel cylinder pressure is put forward. Then, the pedal feel control strategy is studied, which can simulate arbitrary pedal characteristics by controlling the output torque of the motor. Moreover, for the failure of the pedal travel sensor, a pedal displacement estimation method is proposed based on the pressure sensor information of the front chamber of the master cylinder. And for the failure of the pedal feel simulation motor, the pressure of the front chamber of the master cylinder is controlled by adjusting the opening of the pedal feel simulation valve to realize the simulation of the pedal feel. The simulation results based on CarSim/AMESim/Simulink show that the proposed electro-hydraulic brake system has fast pressure response speed and quick pressure tracking accuracy. The pedal characteristics are essentially unchanged before and after the failure of the pedal feel simulation motor or the pedal travel sensor.

Research on Modeling and Load Simulation Algorithm of Tracked Vehicle Braking System on Mu-Split Road Surfaces

The efficient work of the braking system ensures the safety of the driver’s life and property during the driving process. For tracked vehicles, a reliable braking system is the guarantee of completing the job or the task. This paper studies a high-speed electric-driven tracked vehicle’s driving state on different mu-split road surfaces and establishes the braking system model and the longitudinal dynamics model of the vehicle and driving wheels. Steering stability analysis was carried out and a relative motion between the two-sided braking systems resulting in a transfer torque was found. A load simulation test system has been built and the improved forward speed tracking algorithm has been used to adjust the inertia by combining the flywheel and the loading motor to simulate the load of the driving wheel. The results of the motor load simulation test show that the load simulation algorithm in this paper can effectively simulate the load on the driving wheel and restore working conditions of the real tracked vehicle. This paper also conducts the combined braking test of the two-sided system which gives the torque situation on both sides of the vehicle and obtains the transfer torque by applying the load simulation algorithm.

Co-simulation model coupling of flexible rope hoisting system and hydraulic braking system for a mine hoist

The hoist is an important equipment in the mine pit. Since the containers are lifted or lowered with flexible steel wire ropes, there are shocks and vibrations during operation, especially in the emergency braking stage, the shocks and vibration will be more severe. Mine hoist is a complex system; therefore, it is difficult to obtain all its dynamics information only by investigating the flexible hoisting subsystem or hydraulic brake subsystem. Therefore, it is very necessary to establish an accurate model to predict these characteristics of the hoist, this will provide useful tools for hoist design and maintenance. Therefore, a joint modeling methodology is proposed and implemented in this paper. A hoisting system model considering the non-linear factors such as contact characteristics and flexibility was established in RecurDyn. The hydraulic braking system model and control system model were established in AMESim, and the co-simulation model was constructed by the interface module. In this co-simulation model, not only the flexible hoisting subsystem and hydraulic brake subsystem are included, but also the coupling effect of subsystems is considered. Finally, taking the lifting condition as an example, execute emergency braking research on the hoisting system under experiment, mathematical model, and co-simulation model, respectively. Comparing the co-simulation model with the mathematical dynamics model, and the experimental test results, research indicates that the joint simulation model of coupled hoisting system and hydraulic braking system can effectively reflect the dynamic characteristics of the actual hoisting system. It provides an effective tool for hoist design, optimization, performance analysis, and operating condition simulation. In addition, the methods and techniques used in the co-simulation modeling procedure are portable. Therefore, the paper is of significance for the mine hoist.

Investigation into the braking performance of high-speed trains in the complex braking environment of the Sichuan-Tibet Railway

The Sichuan-Tibet Railway is an east-west rapid plateau railway under construction from Chengdu to Lhasa. One of its most remarkable features is the high altitude and notable altitude fluctuations. High altitudes will result in low atmospheric pressures and temperatures. The freezing caused by low temperatures will lead to low wheel-rail adhesions. Altitude fluctuations will generate complex spatial railway tracks. To investigate the braking performance of a train in such a complex braking environment, a train spatial dynamics model, a model of a direct pneumatic brake system and a model of a braking control strategy are constructed. A comprehensive analysis model for investigating the braking performance of high-speed trains in a complex braking environment is proposed based on the constructed train spatial dynamics model, direct pneumatic brake system model and braking control strategy model. A simulation computation platform for train braking performance analysis on the Sichuan-Tibet Railway is established based on SIMPACK, AMESim, Simulink and their interfaces. The braking performance under the different altitudes, different spatial railway tracks and low adhesions are analysed in detail and summarized. Computation time are compared in different altitudes and track conditions. Computational efficiencies of the dynamic model with multi-thread parallel computation are discussed. The results indicate that an increasing altitude and the alteration of railway track conditions have a remarkable influence on the braking distance, brake cylinder pressure, instantaneous deceleration, maximum wheel-load reduction rates and maximum longitudinal impact forces of high-speed trains. The track conditions in the dynamic model have a greater impact on the computation speed. Compared to single-thread parallel computation, the computational efficiency using 2-thread parallel computation can be promoted by 22.97%. These results will provide a reference for the Sichuan-Tibet Railway design and the optimization of train braking systems.

Modeling and Simulation of an Electromechanical Brake System

The effect of brake pad wear on the electromechanical disc brake system response using MATLAB/Simulink software was investigated in this paper. The analysis of the pad wear involves building thermal model and electromechanical brake model, and calculating the required braking force at a constant and variable coefficient of friction between the pad and disc. A comparison between the electromechanical brake responses without wear and during wear at a constant and variable coefficient of friction was carried out. The results show that the coefficient of friction has a major role in calculating the required braking force, and cumulated wear during breaking. The required braking force starts higher in the case of using a variable coefficient of friction by about 0.06%. The variable coefficient of friction presents higher wear than the constant coefficient of friction by about 30%.