Tire Model Research Articles

Numerical simulation of mechanical response analysis of asphalt pavement under dynamic loads with non-uniform tire-pavement contact stresses

The selection of accurate input design parameters is important for understanding the dynamic response of an asphalt pavement structure. The transverse and longitudinal shear stresses that affect the dynamic response of asphalt pavement are not considered in traditional asphalt pavement design. To this end, this study utilizes the finite element method (FEM) to analyze the mechanical response of asphalt pavement under dynamic loads with non-uniform tire-pavement contact stresses. For this purpose, firstly a three-dimensional (3D) finite element (FE) model of a rubber tire is developed. Secondly, the predicted and laboratory measured stresses are compared to develop a 3D FE model of the contact stresses. Finally, a 3D FE model of the tire–pavement contact is analyzed to investigate the influence of shear stresses on the response of the asphalt pavement and the superposition effect of the mechanical response. The results show that the distribution and magnitude of the vertical contact pressure under the free-rolling state are the same as those under the static state, and the traction and braking conditions could change the symmetry of tire-pavement interactions. In addition, the shear stress at the tire-pavement interface affects the peak response of the surface layer, indicating that shear stress plays a considerable role in controlling the development of rutting and longitudinal cracks. Considering the viscoelasticity of the asphalt material, it is observed that the superposition effect of the mechanical response is a comprehensive result of the space–time domains. In conclusion, this study analyzes the influence of tire-pavement contact on the mechanical response of asphalt pavement and proposes input design parameters for improving the design of asphalt pavement.

A Dynamics Coordinated Control System for 4WD-4WS Electric Vehicles

With the aggravation of the energy crisis and environmental problems, the new energy electric vehicle industry has ushered in vigorous development. However, with the continuous increase in car ownership, traffic accidents and other issues have gradually attracted widespread attention. Some existing stability coordination control systems often have problems, such as single stability judgment method and strong coupling between different subsystems. Therefore, based on previous research, it is necessary to further optimize the method of judging the vehicle’s stability state, establish clear coordination rules, and reasonably solve the coupling problem between subsystems. This is of great significance for promoting the further development of the electric vehicle industry. Due to four-wheel-distributed driving and four-wheel-distributed steering electric vehicles having the characteristics of integrated driving, flexible steering, and easy fault-tolerant control, it has unique advantages in improving vehicle stability and is a good carrier for designing and constructing the stability coordination control system. In this paper, four-wheel-distributed driving and four-wheel-distributed steering (4WD-4WS) electric vehicles are taken as the research object, and a coordinated control strategy of four-wheel steering and four-wheel drive is proposed. Firstly, in order to realize the accurate judgment of vehicle stability, based on the vehicle two-degree-of-freedom two-track model and magic tire model, this paper uses the phase plane law to divide the phase plane stability region of the vehicle and introduces the stability quantification index PPS-region for the evaluation of vehicle stability. Secondly, a fuzzy variable parameter active rear-wheel steering controller and a compensated yaw moment controller are designed. Then, for the coupling problem between the two controllers, a coordination rule is proposed based on the stability index PPS-region of the phase plane stability region. Finally, a hardware-in-the-loop testbed is built to verify the feasibility of the coordination control strategy proposed in this paper. Experimental results show that: When the vehicle is in different stable states, according to the divided steady state, the control strategy can be correctly switched to the corresponding control strategy, and the work of each subsystem can be reasonably coordinated. Under the continuous gain sine condition, the control algorithm can reduce the maximum amplitude of the yaw rate error response curve by 73% and the side slip angle error response curve by 85%. Compared with a single stability control system, the coordinated stability control algorithm can improve the control effect of yaw rate and side slip angle by 20% and 62.5%. In the case of double lane-change, the control algorithm can reduce the maximum amplitude of the yaw rate error response curve by 68.5% and the side slip angle error response curve by 57.4%. Compared with a single stability control system, the coordinated stability control algorithm can improve the control effect of yaw rate and side slip angle by 40.6% and 44.7%.

Research on Tire–Road Parameters Estimation Algorithm for Skid-Steered Wheeled Unmanned Ground Vehicle

Skid-steered wheeled vehicles can be applied in military, agricultural, and other fields because of their flexible layout structure and strong passability. The research and application of vehicles are developing towards the direction of “intelligent” and “unmanned”. As essential parts of unmanned vehicles, the motion planning and control systems are increasingly demanding for model and road parameters. In this paper, an estimation method for tire and road parameters is proposed by combining offline and online identification. Firstly, a 3-DOF nonlinear dynamic model is established, and the interaction between tire and road is described by the Brush nonlinear tire model. Then, the horizontal and longitudinal stiffness of the tire is identified offline using the particle swarm optimization (PSO) algorithm with adaptive inertia weight. Referring to the Burckhardt adhesion coefficient formula, the extended forgetting factor recursive least-squares (EFRLS) method is applied to identify the road adhesion coefficient online. Finally, the validity of the proposed identification algorithm is verified by TruckSim simulation and real vehicle tests. Results show that the relative error of the proposed algorithm can be well controlled within 5%.

A complex rollover dynamics model with active stabilizer bar controlled by the fuzzy algorithm

The active stabilizer bar is used to improve the vehicle's safety when steering at high speeds. In this paper, the spatial dynamics model and nonlinear double-track dynamics model are used to simulate vehicle oscillations. Besides, the nonlinear tire model is also used. This is a completely novel and complex model. Besides, the fuzzy control algorithm is used to control the active stabilizer bar. This algorithm uses two input signals, which are obtained from the simulation. The membership function and fuzzy rules are designed optimally based on the results of many previous simulations and calculations. The simulation process is performed by MATLAB-Simulink software with three specific cases. The results of the paper show that the roll angle of the vehicle body and the change in vertical force at the wheel are significantly reduced when the vehicle uses the active stabilizer bar controlled by the fuzzy algorithm. The rollover phenomenon has been significantly improved in all the investigated cases, corresponding to three specific speeds. The stability and responsiveness of the controller are very high. The fuzzy algorithm can be combined with some other algorithms to improve system efficiency.

Trajectory Tracking Control of Intelligent X-by-Wire Vehicles

Vehicle intelligence is an effective way to improve driving safety and comfort and reduce traffic accidents. The trajectory tracking control of unmanned vehicles is the core module of intelligent vehicles. As a redundant system, the X-by-wire electric vehicle has the advantage that the turning angles and driving torque of the four wheels can be precisely controlled and it has a higher degree of controllability and flexibility. In this paper, a trajectory tracking control algorithm based on a hierarchical control architecture is designed based on x-by-wire vehicles. The hierarchical control algorithm architecture includes the trajectory tracking layer, tire force distribution layer, and actuator control layer. The trajectory tracking layer uses the longitudinal force, lateral force, and yaw moment as the control variables; the model predictive control algorithm controls the vehicle to follow the desired trajectory. The tire force distribution layer is solved by transforming the tire force distribution problem into a quadratic programming problem with constraints. Based on the expected resultant force and resultant moment, the longitudinal force and lateral force of each tire in the vehicle coordinate system are obtained. The actuator control layer converts the coordinate system to obtain the longitudinal force and lateral force in the tire coordinate system, which uses the arctangent function tire model to solve the desired tire slip angle, and then obtains the vehicle steer angle and driving torque. To verify the effectiveness of the trajectory tracking control algorithm of the hierarchical control architecture, the proposed trajectory tracking control algorithm is simulated and verified through the variable speed double line change condition and the low road friction coefficient double line change condition. The simulation results show that the control algorithm proposed in this paper has the accuracy to follow the desired trajectory.Definition:

Real-Time Predictive Control of Path Following to Stabilize Autonomous Electric Vehicles Under Extreme Drive Conditions

A novel real-time predictive control strategy is proposed for path following (PF) and vehicle stability of autonomous electric vehicles under extreme drive conditions. The investigated vehicle configuration is a distributed drive electric vehicle, which allows to independently control the torques of each in-wheel motor (IWM) for superior stability, but bringing control complexities. The control-oriented model is established by the Magic Formula tire function and the single-track vehicle model. For PF and direct yaw moment control, the nonlinear model predictive control (NMPC) strategy is developed to minimize PF tracking error and stabilize vehicle, outputting front tires’ lateral force and external yaw moment. To mitigate the calculation burdens, the continuation/general minimal residual algorithm is proposed for real-time optimization in NMPC. The relaxation function method is adopted to handle the inequality constraints. To prevent vehicle instability and improve steering capacity, the lateral velocity differential of the vehicle is considered in phase plane analysis, and the novel stable bounds of lateral forces are developed and online applied in the proposed NMPC controller. Additionally, the Lyapunov-based constraint is proposed to guarantee the closed-loop stability for the PF issue, and sufficient conditions regarding recursive feasibility and closed-loop stability are provided analytically. The target lateral force is transformed as front steering angle command by the inversive tire model, and the external yaw moment and total traction torque are distributed as the torque commands of IWMs by optimization. The validations prove the effectiveness of the proposed strategy in improved steering capacity, desirable PF effects, vehicle stabilization, and real-time applicability.

Static-Parking Tyre Modelling

Siemens has developed a semi-empirical tyre model for realistic parking manoeuvre scenarios that can aid the virtual development of steering systems

Experimental Estimation of the Camber Reduction Factor of Tyres

One of the most used tyre models is the so-called Magic Formula, which provides the contact forces and moments as a function of the tyre slips and normal load. Among the slip inputs, there is the spin–slip, which is defined as the combination of a camber component and a path-curvature component. The two components are related to each other by the camber reduction factor, for which only a few data have been reported in the literature. In addition, these data are often obtained from indirect measurements. In this work, an experimental procedure for the direct measurement of the camber reduction factor was devised, and applied to six specimens of motorcycle tyres (three front and three rear). The approach employs a rotating-disk machine, where the tyre is intrinsically subjected to path curvature. A specific aligning procedure to mitigate sideslip disturbances is introduced and employed during testing. The three specimens of the rear tyres tested showed a camber reduction factor that was close to zero, which is the typical result suggested by the literature. On the contrary, the three specimens of front tyres showed slightly negative values, i.e., the camber component increased with respect to the curvature component. The results suggest that the classic assumption of a zero camber reduction factor does not hold valid for all motorcycle tyres.

NMPC-based controller for vehicle longitudinal and lateral stability enhancement under extreme driving conditions

This paper proposes a real-time NMPC-based controller for four-wheel independent motor-drive electric vehicles to improve vehicle longitudinal and lateral stability under extreme driving conditions. First, considering the interactive and highly coupled longitudinal–lateral vehicle dynamics, a combined-slip tire model is applied to develop the stability controller on low friction coefficient surfaces. Second, the wheel slip ratios and slip angles are selected as the virtual control inputs of the NMPC controller to concurrently achieve three main control objectives: Slip control, lateral stability control, and handling performance improvement. Simultaneously, multiple safety constraints are contained. Then, based on the dynamic relationships between the longitudinal tire force and virtual control inputs, the wheel slip ratios and slip angles obtained from the NMPC controller are converted into additional torques acting directly on each wheel. Finally, the control performance is investigated by co-simulation with MATLAB/Simulink and CarSim, and a hardware-in-the-loop simulation system. The effect of uncertainties on control performance is also verified. The results show that the proposed controller can rapidly solve the optimization problem, and vehicle overall stability are efficiently enhanced under extreme conditions. The robustness of the controller is proved with uncertainties on the road adhesion coefficient and vehicle mass.

Nonlinear dynamics analysis in pneumatic tire modeling

Nonlinear dynamics analysis in pneumatic tire modeling

Development of Collision Avoidance System in Slippery Road Conditions

This paper presents an autonomous vehicle’s path planning and tracking system optimized for collision avoidance on slippery roads. During path planning, a path that can induce the maximum possible lateral acceleration is generated through the fifth-order spline in consideration of the tire-road friction. The generated path is tracked based on the model predictive control (MPC), and the nonlinearity generated by the tire and low friction surface is reflected through the extended bicycle model and the combined brushed tire model. Inside the controller, a new type of yaw rate constraint considering side-slip angles is utilized to prevent the vehicle from becoming unstable on slippery roads and maximize lateral maneuver of the vehicle at the same time. The proposed system is verified by the vehicle dynamics software CarSim, and the simulation results show that it significantly increases the possibility of collision avoidance in slippery road conditions.

Integrated Longitudinal and Lateral Vehicle Stability Control for Extreme Conditions With Safety Dynamic Requirements Analysis

Under extreme conditions, vehicle states change rapidly between stable and unstable, resulting in dynamic requirements for the vehicle’s overall safety stability. Simultaneously, the coupled nonlinear characteristics of vehicle dynamics cannot be ignored in controller design. To address the above problems and improve vehicle longitudinal and lateral stability integrally, an envelope-based model predictive control (MPC) strategy with dynamic objectives is proposed for four-wheel independent motor-drive electric vehicles (4WIMD EVs). First, according to the current driving behavior and the collected road information, the envelope control regions concerning vehicle side-slip angle and yaw rate are obtained online, and divided into stable, critically stable, and instable regions with different safety requirements. Then, the safety dynamic requirements are constructed in the designed MPC-based control structure. A nonlinear vehicle dynamics model with a combined-slip tire model, which integrates the longitudinal and lateral dynamics, is utilized to predict vehicle states. The switching of requirements is reflected in the variation of weighting factors and constraint values. Finally, CarSim and Matlab/Simulink co-simulation, and hardware-in-the-loop simulation test results show better satisfactory performance in improving overall vehicle stability under extreme driving conditions.

Clinical efficacy of occlusive splints manufactured by computer modeling and volumetric printing in patients with bruxism: research results and a clinical case

BACKGROUND: Among dental diseases, various types of musculoskeletal dysfunctions occupy a special place. The myogenic theory of temporomandibular joint dysfunction is interesting, where the fundamental role is assigned to the parafunctional state of the masticatory muscles. Analysis of the results of electromyographic studies has shown that patients with TMJ disorders complicated by muscle hypertension have significant functional disorders of the masticatory muscles. Also, the causes of TMJ dysfunction include bruxism, which can occur against the background of parafunctions of the masticatory muscles. To date, there are a large number of methods for the treatment of TMJ dysfunction: splint therapy, occlusive and immobilizing splints. CAD/CAM computer technologies have also become widespread, which are used for the manufacture of these structures. But there are no uniform treatment standards, therefore, studies and comparisons of different techniques are relevant.
 AIM: the effectiveness of treatment of patients with bruxism by developing a clinical protocol for the use of an occlusive splint made by volumetric printing.
 MATERIAL AND METHODS: To evaluate the effectiveness of occlusive splints manufactured by computer milling and 3D printing in patients with bruxism. All study participants at the stage of formation of clinical groups underwent a comprehensive dental examination, which included a clinical and instrumental examination, surface electromyography of the masticatory muscles, computer monitoring of occlusion, cone-beam computed tomography of the TMJ. To exclude the somatoform component from the pathogenesis of bruxism, an electroencephalogram (EEG) was performed in all patients at the stage of formation of clinical groups. At the first stage of treatment, all patients underwent selective grinding of centric and eccentric interferences under the control of a T-scan computer occlusion monitoring device, after which the therapeutic position of the mandible was determined, stabilizing nocturnal occlusal splints made by volumetric printing were manufactured and fixed. Monitoring of treatment results included clinical and instrumental examination and surface electromyography of the masticatory muscles, carried out 3.6 and 12 months after the start of treatment. Upon completion of treatment, an assessment of the integrity of occlusal splints was carried out.
 RESULTS: According to the results of the performed myography, at the time of the start of treatment, the PU coefficient was 74%, after 3 months, it significantly decreased by 6%, after 6 months, its decrease was recorded by 11%, and after 12 months by 16%. The assessment of the integrity of the occlusal splint was carried out at the end of treatment after 12 months, by combining virtual tire models in a computer program before and after the start of treatment obtained by laboratory scanning. When analyzing the comparison of virtual tire models, their almost complete identity was revealed, with the exception of one area on the occlusal surface, which is 0.044 mm, which is not critical in the general treatment concept.
 CONCLUSION: Taking into account the positive result of clinical testing of the proposed technology, it is advisable to conduct a randomized study to evaluate the effectiveness of the use of occlusive splints made by computer modeling and volumetric printing from domestic material in the treatment of patients with musculoskeletal dysfunction complicated by bruxism.

Numerical investigation of load-induced fatigue cracking in curved ramp bridge deck pavement considering tire-bridge interaction

Load-induced fatigue cracking is one of the main distresses of bridge deck pavement; however, due to the complexity of curved ramp bridge structures, it is difficult to effectively consider this damage behavior in the deck pavement design procedure. To deal with this problem, a three-dimensional (3D) tire-bridge interaction finite element (FE) model was developed in the present study to investigate the load-induced fatigue damage behavior within the curved ramp bridge deck pavement. In this FE model, an inflated tire model was developed to simulate the rolling tire load, and the Yeoh model was used to define the constitutive relationship of the hyperelastic material. In addition, the extended finite element method (XFEM) was utilized to describe the crack initiation and evolution, and a direct cycle algorithm was used to calculate the fatigue crack propagation law of deck pavement under different structural design parameters. The results indicated that the developed tire-bridge interaction FE model furnishes an in-depth insight into the fatigue crack propagation within curved ramp bridge deck pavement. The consideration of the tire-bridge interaction and structural design parameters has a significant influence on the accurate prediction of the fatigue crack evolution law within different deck pavement locations. Because the developed full-scale FE model is capable of simultaneously considering multiple factors, including the curvature radius, transverse and longitudinal slope, traffic speeds and tire-bridge interaction loads, it can be expected to be a mechanistic tool to facilitate and enhance fatigue damage analysis of curved ramp bridge deck pavement.

Identification of the tire model and road adhesion coefficient based on vehicle dynamic response data and the BP neural network algorithm

The longitudinal and lateral dynamic responses of a vehicle are essentially determined by the forces resulting from the contact between the tire and road surface. Therefore, identifying the tire model and road adhesion coefficient plays an important role in vehicle dynamics control. At present, the identification of a nonlinear tire model essentially assumes that slip ratio-longitudinal force data or wheel side slip angle-lateral force data are known and that nonlinear fitting is performed, and the road adhesion coefficient based on the dynamic response is also identified on the premise of a known tire model. In this paper, the characteristic of approximating arbitrary nonlinear mapping relationships by a BP neural network is taken advantage of, and an off-line identification method of the Dugoff tire model based on onboard sensors and vehicle dynamics response is proposed. On this basis, an online identification method for the road adhesion coefficient is subsequently proposed. Finally, vehicle experiments on steering and braking are performed to verify the accuracy of the method in the Simulink-CarSim joint simulation environment.

A Novel Numerical Method for Theoretical Tire Model Simulation

Theoretical tire models are often used in tire dynamics analysis and tire design. In the past, scholars have carried out a lot of research on theoretical model modeling; however, little progress has been made on its solution. This paper focuses on the numerical solution of the theoretical model. New force and moment calculation matrix equations are constructed, and different iterative methods are compared. The results show that the modified Richardson iteration method proposed in this paper has the best convergence-stability in the steady and unsteady state calculation, which mathematically solves the problem of nonconvergence of discrete theoretical models in the published reference. A novel discrete method for solving the total deformation of tires is established based on the Euler method. The unsteady characteristics of tire models are only related to the path frequency without changing its parameters, so the unsteady state ability of the tire model can be judged based on this condition. It shows that the method in the references have significant differences at different speeds with the same path frequency under turn slip or load variations input, but the method proposed in this paper has good results.

An adapted Burckhardt tire model for off-road vehicle applications

Off-road vehicle mobility is a real challenge in many areas such as agriculture, military, or construction machinery. The introduction of autonomous vehicles in these fields requires more advanced control algorithms. Furthermore, the deformable nature of the terrain has a significant impact on vehicle behavior. In this context, a lot of research has been conducted to describe the wheel-ground interaction phenomena. Among the most significant factors, traction force, lateral force, and wheel sinkage are crucial aspects in the study of vehicle mobility. One of the most used approaches is based on the Bekker-Wong description. However, due to the mathematical complexity of this model, this approach is rather intended for vehicle simulation. Since the design of control laws requires less complex models, this paper proposes a method based on a road tire model structure adapted to deformable surfaces. This modification is based on the original Burckhardt tire model with a modified structure and estimated parameters. Furthermore, the parameter identification is performed by simulating a realistic virtual test bench allowing the data collection for the parameter estimation process. Finally, the obtained results show the applicability of the proposed method through a new tire model called the Adapted Burchardt Tire Model (ABTM).

Friction Prediction and Application to Lateral or Longitudinal Slip Force Prediction

The empirical or semi-empirical model is widely used for vehicle simulation because of its high accuracy but relies on massive experimental data of tire force and moment. Therefore, tire mechanical prediction is of great significance to improve tire modeling efficiency and to reduce costs. Typical prediction methods or models based on normalization presented by Pacejka and Radt assume that different loads could be close to one normalized curve, but it is not always accurate enough to predict tire force under pure slip conditions and there is no mention of friction prediction methods. In the paper, a theoretical model considering the deformation of belt/carcass is established, which lays the foundation for a normalization model. A method for separation of friction from test data and the proportional assumption of longitudinal and lateral peak friction coefficient between target tire and reference tire are proposed, and the experimental results show that this assumption is acceptable. Finally, according to the separation of friction method and assumption, a new prediction method for tire force under pure slip conditions is presented and validated by comparison with the experimental data. It shows that the proposed method has good prediction capability with satisfactory accuracy.

A new preprocessment method for road peak adhesion coefficient fusion estimation

Accurate estimation of road peak adhesion coefficient is of great significance in vehicle active safety systems. In order to prevent the vehicle from running out of control in actual driving process, the estimation algorithm should be able to adapt to various working conditions, and transmit estimated information of road peak adhesion coefficient to Electronic Control Unit (ECU) of the vehicle timely and accurately. Therefore, a new preprocessment method for the fusion estimation algorithm of road adhesion coefficient is proposed. The core of this method is the equal ratio relationship between the longitudinal, lateral peak adhesion coefficients and the utilization adhesion coefficient under adjacent typical roads. According to this relationship, this method accomplishes normalization of the tyre model in the form of introducing parameters from the outside, so that the tyre model can be combined with the filtering algorithm to be applied to estimation, which solves the problem that the precise tyre model cannot be used for road adhesion coefficient estimation due to its complex construction. This method can adapt to most of tyre models in the field of vehicle dynamics. In addition, the existing estimation algorithms need sufficient excitation (when the comprehensive slip ratio is 0.15–0.20) to estimate the accurate road peak adhesion coefficient. This method can greatly reduce the system error caused by insufficient road excitation, and can also obtain accurate estimation results when the excitation is insufficient. Finally, in order to verify the preprocessment method, the magic formula tyre model is used to describe the tyre characteristics. After processing by the preprocessment method, the road peak adhesion coefficient is estimated in combination with Unscented Kalman Filter (UKF). The high accuracy and timeliness of the estimated results in simulation and real vehicle tests verify the effectiveness of the preprocessment method.

Nonlinear analysis of the delayed tyre model with control-based continuation

In this study, the numerical bifurcation analysis of a shimmying wheel is performed with a non-smooth, time-delayed model of the tyre-ground contact. This model is capable of reproducing the bistable behaviour often observed in experiments: a stable equilibrium and a stable periodic orbit coexisting for the same set of system parameters, that the simpler quasi-steady tyre models fail to capture. In the bistable parameter domain, there also exists an unstable periodic orbit within the separatrix between the domains of attractions of the two stable steady-state solutions. Although this solution never appears in a real-life system, one may still gain valuable information from tracing it as it gives an indication about the level of perturbation that would drive the system from one stable solution to the other. However, the complexity of the laws governing partial sticking and sliding in the tyre-ground contact makes the numerical bifurcation analysis with the traditional, collocation-based techniques infeasible. Instead, this study is based on numerical simulations and the technique of control-based continuation (CBC) to track the stable and unstable periodic solutions of the system allowing for the assessment of the accuracy of the non-smooth, delayed tyre model in replicating the dynamics observed in experiments. In the meantime, the physics-based model provides an insight into the relationship between the sticking and sliding regions appearing in the tyre-ground contact and the global dynamics of the system.