Combined Slip Conditions Research Articles

Coordinated Longitudinal and Lateral Motion Control for Distributed Drive Electric Vehicles With Mechanical Elastic Wheels

The distributed drive electric vehicle (DDEV) with active front wheel steering is an over-actuated system. For such a system, more optimization targets should be considered to make the system better in addition to meeting the driving command of drivers and keeping the vehicle stable. The slip energy generated by excessive tire slipping reduces the utilization of the output energy of the motor, resulting in a reduction of electric vehicle mileage. In order to improve the vehicle performance, a coordinated longitudinal and lateral controller is designed for DDEV with mechanical elastic wheels (MEWs). The motion control layer of the hierarchical controller adopts the integral sliding mode control (ISMC) to determine the desired longitudinal force, lateral force and yaw moment as virtual inputs of the vehicle. Then, a novel tire force distribution strategy is proposed to dynamically assign the virtual inputs among front wheels and four motors with the goal of optimizing the vehicle stability and longitudinal tire slip energy dissipation. To characterize tire slip energy more accurately, the brush model matching MEW is deduced in the combined slip conditions. The proposed controller is evaluated on the hardware-in-the-loop (HIL) test platform under different driving conditions. Simulation results demonstrate that this controller not only ensures the vehicle handling stability performance, but also improves the utilization of motor output energy and reduces tire wear.

Improvement of Traction Force Estimation in Cornering through Neural Network

<div>Accurate estimation of traction force is essential for the development of advanced control systems, particularly in the domain of autonomous driving. This study presents an innovative approach to enhance the estimation of tire–road interaction forces under combined slip conditions, employing a combination of empirical models and neural networks. Initially, the well-known Pacejka formula, or magic formula, was adopted to estimate tire–road interaction forces under pure longitudinal slip conditions. However, it was observed that this formula yielded unsatisfactory results under non-pure slip conditions, such as during curves. To address this challenge, a neural network architecture was developed to predict the estimation error associated with the Pacejka formula. Two distinct neural networks were developed. The first neural network employed, as inputs, both longitudinal slip ratios of the driving wheels and the slip angles of the driving wheels. The second network utilized longitudinal slip ratios of the driving wheels and longitudinal and lateral accelerations of the vehicle as inputs. The training of the neural networks was performed using data from straight-line accelerations, circuit maneuvers, and a sinus steering maneuver. Both neural networks were designed as multi-output networks capable of simultaneously estimating longitudinal force errors for both driving wheels. The estimator was tested by making two laps on the Hockenheim circuit in the opposite direction. The initial root mean square error (RMSE) was substantially reduced using corrective neural networks. These findings affirm the effectiveness of the neural network-based approach in improving traction force estimation under combined slip conditions, overcoming the limitations of the Pacejka formula in cases of non-pure slip, thereby paving new avenues for the implementation of more advanced and secure vehicle control systems.</div>

Tire Performance and Testing under Longitudinal and Combined Slip States: Induced vs Resultant Wheel-Related Slip

ABSTRACT Tires influence many overall vehicle characteristics, including safety, performance, comfort, and handling. Testing is needed to characterize tires for the selection of original equipment manufacturers submissions as well as for the development of other suspension and chassis components. The reality that tire responses are highly nonlinear and change significantly with temperature, wear, and surface pairing makes testing to adequately characterize tires for vehicle development difficult. Furthermore, achieving robust, repeatable braking and driving measurements is particularly challenging. Unlike cornering tests, the test rig input is directly opposed to the tire response vector. Moreover, using an estimated parameter (e.g., slip ratio) as a control value prohibits a clear distinction between the linear test rig input and the nonlinear tire response. In this paper, the influence of the wheel-related slip control on tire performance under longitudinal and combined slip conditions is investigated. Two different tire types are measured in a laboratory environment on an MTS Flat-Trac CT+ tire test rig. A variety of test procedures are used to consider the influence of slip and torque rates under different operating conditions (e.g., wheel loads). A recommendation is given for a low-wear and cost-efficient testing methodology for an improved assessment of tire longitudinal and combined slip characteristics by using a linear test rig input.

Effect of inflation pressure on tyre forces under combined-slip conditions based on the UniTire model

Effect of inflation pressure on tyre forces under combined-slip conditions based on the UniTire model

Effect of inflation pressure on tyre forces under combined-slip conditions based on the UniTire model

Effect of inflation pressure on tyre forces under combined-slip conditions based on the UniTire model

Data-Driven Tire Capacity Estimation With Experimental Verification

Tire states and capacity monitoring is critical for vehicle and wheel stabilization controls in automated driving and active safety systems. Tire capacity, which represents the performance margin of tire forces from its limits, determines the operational range for vehicle control systems and their actuation through steering or torques at each tire to maintain stability while performing trajectory following. This paper presents a generic tire capacity identification framework that can handle different normal loads, road surface friction, and combined-slip driving scenarios, which are challenging for stabilization and tracking control programs in automated driving systems. A novel measuring method for generating force-training data is designed by combining the indoor tire test procedure and tread rubber friction test rig, in order to obtain adequate and high-quality benchmark datasets. The results from large data sets from road experimenting and indoor tire test facilities, including pure- and combined-slip conditions, confirm effectiveness of the developed learning-based tire capacity estimation which utilizes notions from the model description with bounded uncertainty. More importantly, the proposed method can provide reliable tire properties ranging from the linear to the sliding regions. Further validation is performed on a real test car with on-board sensory measurements, and the results confirm accuracy of the proposed method for various free rolling and hard launch/brake scenarios.

Theoretical Tire Model for Wear Progress of Tires with Tread Pattern Considering Two-Dimensional Contact Patch

ABSTRACT A new theoretical tire model for the wear progress of tires with tread block pattern is developed considering a two-dimensional contact patch. In the model, the wear energy is calculated from the shear force and pressure distribution in a two-dimensional contact patch that are changed with not only shear forces in a contact patch but also with the wear and irregular wear of tires. The fore–aft shear force in a contact patch consists of six mechanisms related to slip ratio, camber, contact between a tire and a road, barrel deformation of a loaded block, rolling resistance, and a rolling tire with rounded crown shape, whereas the lateral shear force consists of three mechanisms related to slip angle/camber, contact of a tire with rounded crown shape, and barrel deformation of a loaded block. The heel and toe irregular wear and the progress of irregular wear under pure slip condition qualitatively agree with the conventional knowledge of tire engineers. The expected wear energy is introduced to predict the wear progress under combined slip condition in the wear course. Using the vehicle dynamics to predict the tire force history, a histogram of external forces is obtained by transforming from it. Calculating wear energies by changing slip angle and slip ratio, the relation between external forces and the wear energy is expressed as the response surface. Multiplying the wear energy by the histogram, the expected wear energy distribution in a block is calculated. Assuming that the worn depth is proportional to the expected wear energy, the wear progress is predicted.

Analysis of the Effect of Inflation Pressure on Vehicle Handling and Stability under Combined Slip Conditions Based on the UniTire Model

Analysis of the Effect of Inflation Pressure on Vehicle Handling and Stability under Combined Slip Conditions Based on the UniTire Model

New Integrated Vehicle Stability Control of Active Front Steering and Electronic Stability Control Considering Tire Force Reserve Capability

To address the problem of the mutual interference and control distribution in the integrated stability control of active front steering (AFS) and electronic stability control (ESC), this study proposes a new integrated stability controller of AFS and ESC based on holistic control framework. A distribution rule of longitudinal and lateral tire force based on equal reserve capacity of tire force is designed to distribute the control right of steering and braking. A UniTire model with combined slip condition is also designed for the integrated control of steering and braking. Model predictive control (MPC) is adopted to address the constrained multi-objective control problem. To reduce the complexity of the system and improve the real-time performance of the system, a linear time-varying MPC controller is designed by linearizing the nonlinear system, and then the constrained MPC control problem is transformed into a quadratic programming problem for solving. Finally, the proposed method is validated on the basis of Matlab/Simulink and CarSim co-simulation platform. Results show that the proposed method has obvious effects on solving the mutual interference and control right distribution of steering and braking and improving vehicle stability.

Handling and Stability Control of Four-wheel Drive Electric Vehicle under Combined Slip Conditions

Handling and Stability Control of Four-wheel Drive Electric Vehicle under Combined Slip Conditions

UniTire Model under Combined Slip Conditions with the Coupling Effect of Inflation Pressure and Vertical Load

UniTire Model under Combined Slip Conditions with the Coupling Effect of Inflation Pressure and Vertical Load

An Analytical Tire Model with Flexible Carcass for Combined Slips

The tire mechanical characteristics under combined cornering and braking/driving situations have significant effects on vehicle directional controls. The objective of this paper is to present an analytical tire model with flexible carcass for combined slip situations, which can describe tire behavior well and can also be used for studying vehicle dynamics. The tire forces and moments come mainly from the shear stress and sliding friction at the tread-road interface. In order to describe complicated tire characteristics and tire-road friction, some key factors are considered in this model: arbitrary pressure distribution; translational, bending, and twisting compliance of the carcass; dynamic friction coefficient; anisotropic stiffness properties. The analytical tire model can describe tire forces and moments accurately under combined slip conditions. Some important properties induced by flexible carcass can also be reflected. The structural parameters of a tire can be identified from tire measurements and the computational results using the analytical model show good agreement with test data.

UniTire Model for Tire Forces and Moments under Combined Slip Conditions with Anisotropic Tire Slip Stiffness

UniTire Model for Tire Forces and Moments under Combined Slip Conditions with Anisotropic Tire Slip Stiffness

A novel semi-empirical tyre model for combined slips

A new tyre-force model for simultaneous braking and cornering is presented, which is based on combining existing empirical models for pure braking and cornering with brush-model tyre mechanics. The aim is to offer an easy-to-use, accurate model for vehicle-handling simulations. On a working tyre the contact patch between the tyre and the road is, in general, divided into an adhesion region where the rubber is gripping the road and a sliding region where the rubber slides on the road surface. The total force generated by the tyre is then composed of components from these two regions. The brush model describes this in a mechanical framework. The proposed model is based on a new method to extract adhesion and sliding forces from empirical pure-slip tyre models. These forces are then scaled to account for the combined-slip condition. The combined-slip self-aligning torque is also described. A particular feature of the model is the inclusion of velocity dependence, even if this is not explicitly present in the empirical pure-slip model. The approach is quite different from most previous combined-slip models, in that it is based on a rather detailed mechanical model in combination with empirical pure-slip models. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model and in this work the Magic Formula is used in examples. Results show good correspondence with experimental data.

An experimental study on the longitudinal and lateral adhesive coefficients between the tyre and the road for a light motorcycle

The paper presents an analytical approach for estimating the longitudinal and the lateral adhesive coefficients between the tyre and the road surface through the Pacejka ‘magic formula’ tyre model for both pure-slip and combined-slip conditions. The Pacejka ‘magic formula’ tyre model describes the relationship between the normal force and the adhesive force. The relationship between the vehicle velocity and the parameters of the Pacejka ‘magic formula’ tyre model is discussed in the study. One may analyse the adhesive coefficient through genetic algorithm identification to search for the parameters of the Pacejka ‘magic formula’ tyre model from experimental data. A test stand is set up for adhesive force experiments. Only brake slip is studied in the experiments.

The UniTire model: a nonlinear and non-steady-state tyre model for vehicle dynamics simulation

The UniTire model is a nonlinear and non-steady-state tyre model for vehicle dynamics simulation and control under complex wheel motion inputs involving large lateral slip, longitudinal slip, turn slip and camber. The model is now installed in the driving simulator in the Automobile Dynamic Simulation Laboratory at Jilin University for studying vehicle dynamics and their control systems. Firstly, the nonlinear semiphysical steady-state tyre model, which complies with analytical boundary conditions up to the third order of the simplified physical model, is presented. Special attention has been paid to the expression for the dynamic friction coefficient between the tyre and the road surface and to the modification of the direction of the resultant force under combined-slip conditions. Based on the analytical non-steady-state tyre model, the effective slip ratios and quasi-steady-state concept are introduced to represent the non-steady-state nonlinear dynamic tyre properties in transient and large-slip-ratio cases. Non-steady-state tyre models of first-order approximation and of high-order approximation are developed on the basis of contact stress propagation processes. The UniTire model has been verified by different pure and combined test data and its simulation covered various complex wheel motion inputs, such as large lateral slip, longitudinal slip, turn slip and camber.

A semi-empirical tyre model for combined slips including the effects of cambering

This article presents the addition of camber to a previously published semi-empirical tyre model by the same authors. The model combines empirical models for pure braking, cornering and cambering with a model for simultaneous braking, cornering and cambering. It is based on brush-model tyre mechanics and aims to offer an easy-to-use accurate model for vehicle-handling simulations. The proposed model is a method to extract and rescale the adhesion and sliding forces from empirical pure-slip tyre models to account for the combined-slip condition. The combined-slip self-aligning torque is described likewise. Cambering affects the natural path of the tyre carcass on the road surface and deforms the threads to produce an additional force in the lateral direction. Thereby, the proportions of the sliding and adhesive forces changes. The model is computationally sound and efficient and does not rely on any additional parameters that depend on combined-slip data for calibration. It can be used in combination with virtually any empirical pure-slip model.

The Local Contact Between Tyre and Road Under Steady State Combined Slip Conditions

Summary Tyre handling behaviour has long been the subject of many studies. Originally aimed at deriving the tyre performance characteristics, motivation has now moved to more environmentally related tyre properties. Reduction of tyre wear, noise emission, rolling resistance as well as improvement of tyre braking properties require a good understanding of local contact behaviour, which is very much depending on the interaction of vehicle and suspension behaviour with the tyre in relationship with local friction phenomena and road conditions. These local phenomena are poorly understood up to now. Clearly, one could try to find a realistic quantitative description of such phenomena with a detailed tyre model, i.e. including a highly discretised patch model in combination with some physical belt model. But what is the use of such approach if, at least in a qualitative sense, we do not even understand local contact phenomena based on basic analytical models? This paper deals with a theoretical tyre model in which both the belt and the treads are accounted for using a combination of a stretched string and brush elements. Bare stretched string tyre models (i.e. without treads) have been applied extensively as stand-alone model in case of pure slip (mainly out-of-plane) under steady and transient conditions (as for example related to shimmy). Combined braking and cornering has been studied only for the bare tyre model. So far, the extension with tread elements is limited to lateral slip under restrictive conditions. In this paper, the combined brush-string model is treated for an arbitrary combination of combined slip and tyre properties such as carcass stiffness, tread stiffness and relaxation length. The solution of the steady state contact problem is derived using the so-called singular integral approach where the local tyre deflections are described in terms of integrals of shear stress over the contact area using certain kernel functions. It is discussed how this approach can be generalised to any tyre model including FEM, making it a potentially very powerful tool to analyse local contact phenomena. The steady state solution is discussed for various combinations of tyre properties, with emphasis on the impact on local shearforces, local sliding velocities and (belt and tread) deflections in the contact area.

A THEORETICAL OBSERVATION ON EMPIRICAL EXPRESSION OF TIRE SHEAR FORCES

SUMMARY Theoretically a unified tire model with non-isotropy of friction is presented as a foundation for studying the key features of a reasonable expression of tire shear force and alignment torque under combined slip conditions. The effects of longitudinal force and pressure distributionon tire cornering stiffness are analyzed. A unified semi-empirical tire model with high accuracy and convenience in vehicle dynamics simulation is proposed. Some experimental validations are shown.