Estimation of the tyre–road maximum friction coefficient and slip slope based on a novel tyre model

In this article, a new approach to estimate the vehicle tyre forces, tyre–road maximum friction coefficient, and slip slope is presented. Contrary to the majority of the previous work on this subject, a new tyre model for the estimation of the tyre–road interface characterisation is proposed. First, the tyre model is built and compared with those of Pacejka, Dugoff, and one other tyre model. Then, based on a vehicle model that uses four degrees of freedom, an extended Kalman filter (EKF) method is designed to estimate the vehicle motion and tyre forces. The shortcomings of force estimation are discussed in this article. Based on the proposed tyre model and the improved force measurements, another EKF is implemented to estimate the tyre model parameters, including the maximum friction coefficient, slip slope, etc. The tyre forces are accurately obtained simultaneously. Finally, very promising results have been achieved for pure acceleration/braking for varying road conditions, both in pure steering and combined manoeuvre simulations.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

Tangential problem solution for non-elliptical contact areas with the FastSim algorithm

This article deals with the application of the FastSim algorithm to the solution of the tangential contact problem for non-elliptical contact areas. At first, the causes creating problems for the solution of non-hertzian contact areas with this algorithm shall be analyzed. Then, different currently existing methods shall be studied, analyzing their accuracy characteristics and computational cost to determine whether or not they are appropriate to use in dynamic simulations. Finally, a new strategy shall be proposed that, in the opinion of the authors, offers good characteristics of precision and computational cost.     

A vehicle ABS adaptive sliding-mode control algorithm based on the vehicle velocity estimation and tyre/road friction coefficient estimations

A sliding-mode observer is designed to estimate the vehicle velocity with the measured vehicle acceleration, the wheel speeds and the braking torques. Based on the Burckhardt tyre model, the extended Kalman filter is designed to estimate the parameters of the Burckhardt model with the estimated vehicle velocity, the measured wheel speeds and the vehicle acceleration. According to the estimated parameters of the Burckhardt tyre model, the tyre/road friction coefficients and the optimal slip ratios are calculated. A vehicle adaptive sliding-mode control (SMC) algorithm is presented with the estimated vehicle velocity, the tyre/road friction coefficients and the optimal slip ratios. And the adjustment method of the sliding-mode gain factors is discussed. Based on the adaptive SMC algorithm, a vehicle's antilock braking system (ABS) control system model is built with the Simulink Toolbox. Under the single-road condition as well as the different road conditions, the performance of the vehicle ABS system is simulated with the vehicle velocity observer, the tyre/road friction coefficient estimator and the adaptive SMC algorithm. The results indicate that the estimated errors of the vehicle velocity and the tyre/road friction coefficients are acceptable and the vehicle ABS adaptive SMC algorithm is effective. So the proposed adaptive SMC algorithm can be used to control the vehicle ABS without the information of the vehicle velocity and the road conditions.     

Estimation of maximum road friction coefficient based on Lyapunov method

With the real time and accurate information of motor torque and rotation speed of the four-in-wheel-motordrive electric vehicles, a slip based algorithm for estimating maximum road friction coefficient is designed using Lyapunov stability theory. Modified Burckhardt tire model is used to describe longitudinal slip property of the tire. By introducing a new state variable, a nonlinear estimator is proposed to estimate the longitudinal tire force and the maximum road friction coefficient simultaneously. With the appropriate selection of estimation gain, the convergence of the estimation error of the tire longitudinal force and maximum road friction coefficient is proved through Lyapunov stability analysis. In addition, the error is exponentially stable near the origin. Finally the method is validated with Carsim-Simulink co-simulation and real vehicle tests under multi working conditions in acceleration situation which demonstrate high computational efficiency and accuracy of this method.     

Robust control for 4WS vehicles considering a varying tire-road friction coefficient

A µ-synthesis for four-wheel steering (4WS) problems is proposed. Applying this method, model uncertainties can be taken into consideration, and a µ-synthesis robust controller is designed with optimized weighting functions to attenuate the external disturbances. In addition, an optimal controller is designed using the well-known optimal control theory. Two different versions of control laws are considered here. In evaluations of vehicle performance with the robust controller, the proposed controller performs adequately with different maneuvers (i.e., J-turn and Fishhook) and on different road conditions (i.e., icy, wet, and dry). The numerical simulation shows that the designed µ-synthesis robust controller can improve the performance of a closed-loop 4WS vehicle, and this controller has good maneuverability, sufficiently robust stability, and good performance robustness against serious disturbances.     

双轮式横向力摩擦系数自动测试系统

路面抗滑能力是道路安全性能的重要指标。路面抗滑测试技术的发展趋势,将在先进的检测硬件设备的支撑下,实现快速连续的检测,且测试设备的制造及测试费用低。据此,文章评述了双轮式横向力摩擦系数自动测试系统的组成结构和工作原理,对其测试数值与我国现行试验规程的SFC值进行相关性研究以及SFC值修正。双轮式横向力摩擦系数自动测试系统的总体使用效果良好,具有明显可观的社会和经济效益。     

Comparative study of vehicle tyre–road friction coefficient estimation with a novel cost-effective method

This paper qualitatively and quantitatively reviews and compares three typical tyre–road friction coefficient estimation methods, which are the slip slope method, individual tyre force estimation method and extended Kalman filter method, and then presents a new cost-effective tyre–road friction coefficient estimation method. Based on the qualitative analysis and the numerical comparisons, it is found that all of the three typical methods can successfully estimate the tyre force and friction coefficient in most of the test conditions, but the estimation performance is compromised for some of the methods during different simulation scenarios. In addition, all of these three methods need global positioning system (GPS) to measure the absolute velocity of a vehicle. To overcome the above-mentioned problem, a novel cost-effective estimation method is proposed in this paper. This method requires only the inputs of wheel angular velocity, traction/brake torque and longitudinal acceleration, which are all easy to be measured using available sensors installed in passenger vehicles. By using this method, the vehicle absolute velocity and slip ratio can be estimated by an improved nonlinear observer without using GPS, and the friction force and tyre–road friction coefficient can be obtained from the estimated vehicle velocity and slip ratio. Simulations are used to validate the effectiveness of the proposed estimation method.     

Robust estimation of maximum tire-road friction coefficient considering road surface irregularity

An accurate estimation of the maximum tire-road friction coefficient may provide higher performance in a vehicle active safety control system. Unfortunately, real-time tire-road friction coefficient estimation is costly and necessitates additional sensors that must be installed and maintained at all times. This paper proposes an advanced longitudinal tire-road friction coefficient estimation method that is capable of considering irregular road surfaces. The proposed algorithm uses a stiffness based estimation method, however, unlike previous studies, improvements were made by suggesting a third order model to solve problems related to nonlinear mu-slip curve. To attain the tire-road friction coefficient, real-time normalized force is obtained from the force estimator as exerted from the tire in the low slip region using the recursive least squares method. The decisive aspect of using the suggested algorithm lies in its low cost and versatility. It can be used under irregular road conditions due to its capability of easily obtaining wheel speed and acceleration values from production cars. The newly improved algorithm has been verified to computer simulations as well as compact size cars on dry asphalt conditions.     

Estimation of vehicle sideslip angle and tire-road friction coefficient based on magnetometer with GPS

This paper presents a method that estimates the vehicle sideslip angle and a tire-road friction coefficient by combining measurements of a magnetometer, a global positioning system (GPS), and an inertial measurement unit (IMU). The estimation algorithm is based on a cascade structure consisting of a sensor fusing framework based on Kalman filters. Several signal conditioning techniques are used to mitigate issues related to different signal characteristics, such as latency and disturbances. The estimated sideslip angle information and a brush tire model are fused in a Kalman filter framework to estimate the tire-road friction coefficient. The performance and practical feasibility of the proposed approach were evaluated through several tests.     

Measurement of the disc-pad friction coefficient for mechanical brakes using direct and indirect methods

It is necessary to guarantee the proper brake force to stop a train safely in a limited distance and o adjust its speed. Currently, most trains are run by electrical power and have a combined electrical and mechanical (friction) braking system. The mechanical brake force is determined by many parameters, such as the friction coefficient of the brake disc and pad, the pressure in the brake cylinder, the brake cylinder’s cross sectional area and the brake linkage ratio. In general, the friction coefficient data of the brake disc and pad have been taken through a dynamo-test in a laboratory, but these data might not be well matched with real data under operating conditions because of the difference in data acquisition conditions. The present study examined two methodologies that can measure the friction coefficient of the brake pad and disc based on a train’s real operating conditions. The first method was the direct method, which measured the brake force and clamping force applied on the mechanical brake by using strain gauges installed on the brake to calculate the friction coefficient. The second was an indirect method that obtained the friction coefficient by using the weight of the train and the equivalent brake force. Those variables were calculated from the longitudinal dynamic characteristics, such as resistance to motion, gradient resistance and curved resistance. These two methodologies were used to obtain the disc-pad friction coefficient for the mechanical brakes of a Korean high-speed train (HSR350x).     

Effect of arc surfaces friction coefficient on coupler stability in heavy haul locomotives: simulation and experiment

The heavy haul coupler/buffer system equipped with arc surfaces on the coupler tail and the follower is widely applied to connect the locomotives and wagons. As one of the most important parameters, arc surfaces friction coefficient plays a key role in coupler instability, which threatens the safety of trains. To investigate the effect of arc surfaces friction coefficient on coupler stability, a simulation model adopting the latest modelling methods is established and field tests employing the locomotives equipped with different friction coefficients are conducted. The results show that the friction coefficient of arc surfaces can affect the coupler yaw angle remarkably. Increasing the friction coefficient can improve the coupler stability. However, under severe compressive force condition, the increased friction coefficient can be reduced quickly, which calls for further attention.     

Multi-state control strategy of starting for a wet friction clutch via a fuzzy logic algorithm

Wet multi-plate friction clutches are used in automotive drivelines to transfer torque, change gears, and prevent motion by locking-up components in the transmission. The control strategy of starting is a crucial technology for the application of a wet multi-plate friction clutch in the automotive industry. In this paper, a multi-state fuzzy control strategy for starting is presented and applied to a continuously variably transmission (CVT) powertrain for the validation of this strategy. The operation of the clutch was divided into four states: parking, starting, riding and emergency. The starting state was investigated in detail. A fuzzy algorithm was employed to control the pressure of the hydraulic cylinder acting on the clutch. A distinguishing feature is that the pressure does not increase but decreases to implement smooth starting during the initial period of starting. The rapid-control prototype (RCP) of the wet friction clutch was developed to validate the new control strategy onboard a test vehicle. Based on the experimental results, the multi-state control strategy for a wet friction clutch is a viable candidate for engineering applications.     

摩擦离合器与制动器的摩擦材料分析

从摩擦学的角度出发，对摩擦离合器与制动器的摩擦材料的性能，特点及失效的原因进行了分析，最后又对摩擦系数稳度这一概念进行了描述。     

Novel coordinated algorithm for Traction Control System on split friction and slope road

A Traction Control System (TCS) is used to avoid excessive wheel-slip via adjusting active brake pressure and engine torque when vehicle starts fiercely. The split friction and slope of the road are complicated conditions for TCS. Once operated under these conditions, the traction control performance of the vehicle might be deteriorated and the vehicle might lack drive capability or lose lateral stability, if the regulated active brake pressure and engine torque can’t match up promptly and effectively. In order to solve this problem, a novel coordinated algorithm for TCS is brought forward. Firstly, two brake controllers, including a basic controller based on the friction difference between the two drive wheels for compensating this difference and a fuzzy logic controller for assisting the engine torque controller to adjust wheel-slip, are presented for brake control together. And then two engine torque controllers, containing a basic PID controller for wheel-slip control and a fuzzy logic controller for compensating torque needed by the road slope, are built for engine torque control together. Due to the simultaneous and accurate coordination of the two regulated variables the controlled vehicle can start smoothly. The vehicle test and simulation results on various road conditions have testified that the proposed method is effective and robust.     

Development of a new limited slip differential

A new limited slip differential was developed by Fuji Univance Corp. in co-operation with Automotive Products plc, which has a simple structure and applied special cams.The limited slip differential has a constant torque bias ratio regardless of the input torque. This paper presents its structure, principle of operation, analysis results of design parameters on the torque bias ratio characteristic, and experimental results.     

Active noise control in a duct system based on a frequency-estimation algorithm and the FX-LMS algorithm

In this paper, an indirect feedback active noise control (ANC) scheme, based on the fundamental frequency-estimation method, is proposed for systems with multiple tonal noises. The engine noise consists of the harmonic components of the rotation of the crankshaft in the engine. When it is difficult to obtain reference signals, which are necessary for a feedforward ANC, conventional ANC algorithms do not work. In this paper, a new method is proposed to generate reference signals with estimated frequencies. The proposed algorithm consists of two parts: the frequency-estimation (FE) algorithm for the estimation of the fundamental frequency of the rotating machinery and then the conventional filtered-x LMS (FX-LMS) algorithm. In the second algorithm, the reference signal is generated using the fundamental frequency as estimated in the first algorithm. The FE algorithm uses a second-order adaptive notch filter, which is insensitive to impulse noise. In addition, the FE algorithm has good tracking capability and a lower variance of frequency-estimation error for a constant sinusoid signal and chirp signal. The performance of the proposed ANC method is verified through simulations and an experiment using a DSP board (DS-1104) inside a short duct.     

Development of a slip control anti-lock braking system model

This paper describes the initial phase of work carried out as part of an on going study investigating the interaction between the tyre, suspension system and an antilock braking system (ABS). The modelling, analysis simulations and integration of results have been performed using an industry standard Multibody Systems Analysis (MBS) program. A quarter vehicle model has been used together with an individual front suspension system represented by interconnected rigid bodies. The tyre model used can be integrated into vehicle handling simulations but only the theory associated with the generation of longitudinal braking forces is described here. An ABS model based on slip control has been used to formulate the braking forces described in this paper. The simulations, which have been performed braking on wet and dry road surfaces, compare the performance of two different tyres.     

Modelling the effects of friction modifiers on rail corrugation in cornering

A proposed solution to the problem of rail corrugation on curves of urban lines is the use of friction modifiers. Recent experimental research indicates this approach can be effective. This paper makes use of two theoretical models to study the effects of friction modifiers on corrugation in cornering. The first one is a nonlinear time-domain model that predicts corrugation growth from a series of simulated passes of a bogie. The second one is a frequency domain model of wheel–rail interaction, linearised about a steady cornering state, estimated from the nonlinear model. Both models predict reduction of growth of corrugation due to the use of friction modifiers. Friction modifiers can alter the steady cornering state to one with somewhat lower creeps and much lower tractions. Major reductions in corrugation growth rate have been shown to occur if a wheel can be prevented from reaching a state of full sliding when subject to oscillating creeps caused by existing rail corrugation.     

Development of a hydraulic limited slip differential system using a pressure generator

The limited slip differential (LSD) is a device that enables the driving force to be transmitted from one slipping wheel to the other by temporarily restraining the differential function when unwanted slipping occurs on muddy or icy roads. Many types of LSD have been developed, such as mechanical lock, disk clutch, viscous coupling, torsen and multiple clutch. This study designed a new type of hydraulic LSD using a pressure generator base on a trochoid gear pump and evaluated the performance of the new design.