Estimation Of Friction Coefficient Research Articles

Tyre–road friction coefficient estimation based on the discrete-time extended Kalman filter

This paper presents a new algorithm for estimation of the instantaneous value and the maximum value of the tyre–road friction coefficient (the adhesion coefficient) depending on the quality of the road surface. The algorithm applies the discrete-time extended Kalman filter for state estimation. The underlying discrete-time non-linear state-space model was based on a two-wheel longitudinal vehicle dynamics model extended to include the scale factor parameter of the ‘magic formula’ for the longitudinal tyre force introduced by Pacejka. To verify the Kalman-filter-based algorithm, a validated real-time hardware-in-the-loop simulation environment was utilized, and the results were in agreement with the expectations.

Comprehensive tire–road friction coefficient estimation based on signal fusion method under complex maneuvering operations

The accurate estimation of the tire–road friction coefficient plays a significant role in the vehicle dynamics control. The estimation method should be timely and reliable for the controlling requirements, which means the contact friction characteristics between the tire and the road should be recognized before the interference to ensure the safety of the driver and passengers from drifting and losing control. In addition, the estimation method should be stable and feasible for complex maneuvering operations to guarantee the control performance as well. A signal fusion method combining the available signals to estimate the road friction is suggested in this paper on the basis of the estimated ones of braking, driving and steering conditions individually. Through the input characteristics and the states of the vehicle and tires from sensors the maneuvering condition may be recognized, by which the certainty factors of the friction of the three conditions mentioned above may be obtained correspondingly, and then the comprehensive road friction may be calculated. Experimental vehicle tests validate the effectiveness of the proposed method through complex maneuvering operations; the estimated road friction coefficient based on the signal fusion method is relatively timely and accurate to satisfy the control demands.

Comparison of Feedback Control Techniques for Torque-Vectoring Control of Fully Electric Vehicles

Fully electric vehicles (FEVs) with individually controlled powertrains can significantly enhance vehicle response to steering-wheel inputs in both steady-state and transient conditions, thereby improving vehicle handling and, thus, active safety and the fun-to-drive element. This paper presents a comparison between different torque-vectoring control structures for the yaw moment control of FEVs. Two second-order sliding-mode controllers are evaluated against a feedforward controller combined with either a conventional or an adaptive proportional-integral-derivative (PID) controller. Furthermore, the potential performance and robustness benefits arising from the integration of a body sideslip controller with the yaw rate feedback control system are assessed. The results show that all the evaluated controllers are able to significantly change the understeer behavior with respect to the baseline vehicle. The PID-based controllers achieve very good vehicle performance in steady-state and transient conditions, whereas the controllers based on the sliding-mode approach demonstrate a high level of robustness against variations in the vehicle parameters. The integrated sideslip controller effectively maintains the sideslip angle within acceptable limits in the case of an erroneous estimation of the tire-road friction coefficient.

A study on the road friction coefficient estimation and motor torque control for an in-wheel electric vehicle

In this study, a motor torque control algorithm for improving the stability of an in-wheel electric vehicle is proposed. The longitudinal and normal forces acting on the tyre were estimated with the wheel speed, the vehicle acceleration and the motor torque, and a road friction coefficient estimation method based on these factors is suggested. Furthermore, a method for determining the control normal force of each wheel and for limiting the in-wheel motor torque is proposed by introducing the concept of virtual movement of the centre of gravity by the slip ratio. The performance of the proposed in-wheel motor torque control algorithm was validated through MATLAB/Simulink and CarSim co-simulation and real-vehicle tests. The simulations and experimental results show that the in-wheel motor torque control algorithm braked the vehicle with no spin on a slippery road.

Estimating Friction Coefficient and Fraction of Sliding in Friction Stir Welding

The heat generation, contact state, material flow and friction coefficient are all intertwined during friction stir welding (FSW) because of the fully thermomechanical coupling nature of FSW. The value of friction coefficient and the fraction of sliding will dominate heat generation which is the driving force to make the FSW process successful. This work detailedly clarified how to roughly estimate the fraction of sliding and friction coefficient at the tool/workpiece interface. Results showed that friction coefficients in FSW of various materials were in a range of 0.2-0.56. The fraction of sliding was significantly affected by friction coefficient. The fraction of sliding was in a range of about 73-88% for FSW of Al1100-H14 alloy and about 38-65% for FSW of Al7050-T7451 alloy. Moreover, the fraction of sliding increased with decreasing heat input.

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.

Higher‐order sliding mode observer for estimation of tyre friction in ground vehicles

The estimation of friction coefficient for a vehicle when it traverses on different surfaces has been an important issue. In this work, the longitudinal vehicle dynamics, the torsional tyre dynamics and the non-linear LuGre friction dynamics are integrated to model the quarter vehicle dynamics. The road adhesion coefficient in the vehicle dynamics is unknown and varies with the contact surface. To address this issue, the authors consider a class of non-linear uncertain systems that covers the vehicle dynamics and develop a higher-order sliding mode observer based on supertwisting algorithm for state and unknown input estimations. Under Lipschitz conditions for the non-linear functions, the convergence of the estimation error is established. By estimating the road adhesion coefficient, the coefficient of friction can be estimated. Simulation results demonstrate the effectiveness of the proposed observer for state and unknown input estimation.

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.

PIV experiments in rough-wall, laminar-to-turbulent, oscillatory boundary-layer flows

Exploratory measurements of oscillatory boundary layers were conducted over a smooth and two different rough beds spanning the laminar, transitional and turbulent flow regimes using a multi-camera 2D-PIV system in a small oscillatory-flow tunnel (Admiraal et al. in J Hydraul Res 44(4):437–450, 2006). Results show how the phase lag between bed shear stress and free-stream velocity is better defined when the integral of the momentum equation is used to estimate the bed shear stress. Observed differences in bed shear stress and phase lag between bed shear stress and free-stream velocity are highly sensitive to the definition of the bed position (y = b). The underestimation of turbulent stresses close to the wall is found to explain such differences when using the addition of Reynolds and viscous stresses to define both the bed shear stress and the phase lag. Regardless of the flow regime, in all experiments, boundary-layer thickness reached its maximum value at a phase near the flow reversal at the wall. Friction factors in smooth walls are better estimated using a theoretical equation first proposed by Batchelor (An introduction to fluid dynamics. Cambridge University Press, Cambridge, 1967) while the more recent empirical predictor of Pedocchi and Garcia (J Hydraul Res 47(4):438–444, 2009a) was found to be appropriate for estimating friction coefficients in the laminar-to-turbulent transition regime.

Tyre–road friction coefficient estimation based on tyre sensors and lateral tyre deflection: modelling, simulations and experiments

The estimation of the tyre–road friction coefficient is fundamental for vehicle control systems. Tyre sensors enable the friction coefficient estimation based on signals extracted directly from tyres. This paper presents a tyre–road friction coefficient estimation algorithm based on tyre lateral deflection obtained from lateral acceleration. The lateral acceleration is measured by wireless three-dimensional accelerometers embedded inside the tyres. The proposed algorithm first determines the contact patch using a radial acceleration profile. Then, the portion of the lateral acceleration profile, only inside the tyre–road contact patch, is used to estimate the friction coefficient through a tyre brush model and a simple tyre model. The proposed strategy accounts for orientation-variation of accelerometer body frame during tyre rotation. The effectiveness and performance of the algorithm are demonstrated through finite element model simulations and experimental tests with small tyre slip angles on different road surface conditions.

Estimation of Friction Coefficient in Sediment Contained Flow through Rockfill

An increase in the flow velocity in flow through large porous media and deflection of flow regime from Darcy law causes a nonlinear relationship between hydraulic gradient and pore velocity of media. One of the most important subjects in flow through large porous media is relationship between friction coefficient and flow characteristics which was previously focused by some investigators but it is needed to extract general and more accurate relationships for all of their data series. Also, in most of previous studies the friction coefficient was presented in Darcy-Weisbac h form which is not so common in the open channel flow between hydraulic engineers like Manning coefficient. In this study, the required data were collected from four different sources. Three series of them were operated in the sediment contained flowthrough mode and another one was operated in sediment free flowthrough mode. Using some basic equations about pore velocity and frictional coefficient, the new relationships were developed and calibrated for estimation of manning coefficient in open channel fow through porous media. It was found that modified Wilkins equation had a better estimation for manning coefficient in both sediment free and sediment contained flow rather than Ergun and Sedghi’s one. Also, it was found that general trend of Moody diagram for pipe flow is established in flow through large porous media such that by increase in the media Reynolds number, the Manning coefficient limits to a constant value and become dependent to the media characteristics.

Staying within the nullcline boundary for vehicle envelope control using a sliding surface

Envelope control has been implemented successfully in aircraft for over a decade to assist pilots in stabilising their planes. With current advances in sideslip angle and friction coefficient estimation, envelope control can now be applied to the automotive industry as well. Using full state estimation of yaw rate and sideslip angle, stability controllers can assist the driver by keeping the vehicle within a safe region of the planar state space. This paper discusses the physical phenomena that must be taken into account when choosing an envelope and details a specific choice of envelope comprised of the yaw acceleration nullcline and the maximum rear slip angle limits. The vehicle is kept within the envelope using a computationally simple sliding surface control scheme. Experimental data show the success of the controller, which is implemented on a vehicle through the use of steer-by-wire.

Novel estimation of tyre-road friction coefficient and slip ratio using electrical parameters of traction motor for electric vehicles

The estimation of the friction coeffi cient and the slip ratio is crucial for advanced traction control or anti-brake control of electric vehicles. In this paper, dynamic behaviours of electrical parameters of the traction motor under road change are modelled and analysed. Novel estimation only using the measurements of the armature voltage and the current is proposed. The proposed method is much quicker than traditional methods, contributing to adjust the vehicle’s motion state more quickly and precisely. Further, it can eliminate the speed measuring devices of the wheel speed and the vehicle speed. Simulations verify the effectiveness.

Estimation of Bottom Friction Coefficients Based on an Isopycnic-Coordinate Internal Tidal Model with Adjoint Method

Based on an isopycnic-coordinate internal tidal model with the adjoint method, three groups of ideal experiments are carried out in order to investigate the estimation of spatially varying bottom friction coefficients (BFCs). In group 1, five values of distance between independent points (DIP) are used to invert the BFCs with the distribution of conical surface. Results show that the BFCs can be inverted successfully with independent point scheme and the strategy with a DIP of 50′ can yield the best results. In group 2, five values of interpolation radius (IR) are used to invert the BFCs with the distribution of conical surface. Results show that the strategy with an IR of 1.9 times of DIP can yield the best results. Based on the results of the first two groups, group 3 adopts the optimal DIP and IR to estimate 4 kinds of spatially varying BFCs. The results indicate that the isopycnic-coordinate internal tidal model with the adjoint method has a good ability to estimate the spatially varying BFCs; the inversion results of the BFCs with the distribution of revolution paraboloid are better than those with the distribution of conical surface.

S112034 転がり・すべり接触面の接線力とピッチング発生限界の関係([S112-03]伝動装置の基礎と応用(3))

The design for pitting (rolling fatigue) of rolling-sliding contact surface under mixed lubrication condition is based on the combination of maximum contact pressure (Hertzian stress) and lubrication condition (ratio of surface roughness value and oil film thickness value). But there is indirect relationship in the combination of contact pressure and lubrication condition to the pitting phenomena. The origins of rolling fatigue pit are the micro cracks in contact surface due to tangential force. In this paper, the pitting test results are re-examined from a standpoint of influence of the tangential force on pitting. The new parameter f(p_H/H_B)^2 based on the friction coefficient estimation formula by Matsumoto for pitting design is introduced. And it is cleared that the new parameter has same value to every different contact pressure and lubrication condition. In conclusion, it is necessary to reconsider the pitting design method for power transmission gears excepted tangential force from consideration.

Slip-Slope Estimation of Mutative Road Friction Coefficient Based on Unscented Particle Filter

The accurate information of road friction coefficient allows the control algorithm in vehicle activity system to adapt to external driving conditions. This paper developed a slip-slope friction coefficient estimation method based on Unscented Particle Filter. A 7-DOF non-linear vehicle dynamic model was established. The normal force of tire was approximately calculated from the vehicle dynamic model; the slip and longitudinal force of tire were estimated through a combination of tire mechanical model and UPF(Unscented Particle Filter) method. Finally slip-slopes of different adhesion level roads was obtained. Through virtual test environment in ADAMS/Car, the estimation method proposed was verified to be effective and reliable under various road condition. From the method the relationships between the slip-slope and road friction coefficient are achieved.

Algorithms for Real-Time Estimation of Individual Wheel Tire-Road Friction Coefficients

It is well recognized in the automotive research community that knowledge of the real-time tire-road friction coefficient can be extremely valuable for active safety applications, including traction control, yaw stability control and rollover prevention. Previous research results in literature have focused on the estimation of average tire-road friction coefficient for the entire vehicle. This paper explores the development of algorithms for reliable estimation of independent friction coefficients at each individual wheel of the vehicle. Three different observers are developed for the estimation of slip ratios and longitudinal tire forces, based on the types of sensors available. After estimation of slip ratio and tire force, the friction coefficient is identified using a recursive least-squares parameter identification formulation. The observers include one that utilizes engine torque, brake torque, and GPS measurements, one that utilizes torque measurements and an accelerometer and one that utilizes GPS measurements and an accelerometer. The developed algorithms are first evaluated in simulation and then evaluated experimentally on a Volvo XC90 sport utility vehicle. Experimental results demonstrate the feasibility of estimating friction coefficients at the individual wheels reliably and quickly. The sensitivities of the observers to changes in vehicle parameters are evaluated and comparisons of robustness of the observers are provided.

Tire–road friction coefficient and tire cornering stiffness estimation based on longitudinal tire force difference generation

A sequential tire cornering stiffness coefficient and tire–road friction coefficient (TRFC) estimation method is proposed for some advanced vehicle architectures, such as the four-wheel independently-actuated (FWIA) electric vehicles, where longitudinal tire force difference between the left and right sides of the vehicle can be easily generated. Such a tire force difference can affect the vehicle yaw motion, and can be utilized to estimate the tire cornering stiffness coefficient and TRFC. The proposed tire cornering stiffness coefficient and TRFC identification method has the potential of estimating these parameters without affecting the vehicle desired motion control and trajectory tracking objectives. Simulation and experimental results with a FWIA electric vehicle show the effectiveness of the proposed estimation method.

Enhancement of Collision Mitigation Braking System Performance Through Real-Time Estimation of Tire-road Friction Coefficient by Means of Smart Tires

In the case of modern day vehicle control systems employing a feedback control structure, a real-time estimate of the tire-road contact parameters is invaluable for enhancing the performance of the chassis control systems such as anti-lock braking systems (ABS) and electronic stability control (ESC) systems. However, at present, the commercially available tire monitoring systems are not equipped to sense and transmit high speed dynamic variables used for real-time active safety control systems. Consequently, under the circumstances of sudden changes to the road conditions, the driver's ability to maintain control of the vehicle maybe at risk. In many cases, this requires intervention from the chassis control systems onboard the vehicle. Although these systems perform well in a variety of situations, their performance can be improved if a real-time estimate of the tire-road friction coefficient is available. Existing tire-road friction estimation approaches often require certain levels of vehicle longitudinal and/or lateral motion to satisfy the persistence of excitation condition for reliable estimations. Such excitations may undesirably interfere with vehicle motion controls. This paper presents a novel development and implementation of a real-time tire-road contact parameter estimation methodology using acceleration signals from a smart/intelligent tire. The proposed method characterizes the terrain using the measured frequency response of the tire vibrations and provides the capability to estimate the tire road friction coefficient under extremely lower levels of force utilization. Under higher levels of force excitation (high slip conditions), the increased vibration levels due to the stick/slip phenomenon linked to the tread block vibration modes make the proposed tire vibrations based method unsuitable. Therefore for high slip conditions, a tire-road friction model-based parameter estimation approach is proposed. Hence an integrated approach using the smart/intelligent tire based friction estimator and the model based estimator gives us the capability to reliably estimate friction for a wider range of excitations. Considering the strong interdependence between the operating road surface condition and the instantaneous forces and moments generated; this real time estimate of the tire-road friction coefficient is expected to play a pivotal role in improving the performance of a number of vehicle control systems. In particular, this paper focuses on the possibility of enhancing the performance of collision mitigation braking systems. Language: en

Nonlinear homogenization approach to the friction coefficient of a quartz‐clay fault gouge

SUMMARYThis study aims at building a theoretical framework allowing for estimation of the macroscopic friction coefficient of a mixed quartz/clay fault gouge from the description of the microstructure and from relevant properties at the lower scale. The effect of clay content is particularly highlighted through two opposite morphology cases. The first one corresponds to a grain framework‐supported microstructure with a predominant content of quartz grains forming a connected structure and some clay filling the intergranular space. The second considered morphology corresponds to a clay matrix‐supported microstructure in which quartz grains are embedded. The friction coefficient of the gouge is derived with respect to the clay content for both morphologies because of theoretical homogenization techniques. The models prove to be in good agreement with experimental results from the literature. Copyright © 2012 John Wiley & Sons, Ltd.