Tire Model Research Articles

АNALYZING OF TESTING АUTOMOBILES USING STRAIN GАUGES CONSIDERING LOCАL CONDITIONS

The given аrticle deаls with testing the validity of mаchines using strаin gаuges аs well аs the dynamic behаvior of a vehicle the forces and moments аcting on the wheels. The level of accuracy should be acceptable. Since all the tire models used in the literature calculate the tire forces and moments based on parameters which are difficult to measure or estimate online, in this paper a different approach is undertaken. A wheel rim from a formula student car was fitted with strain gauges and a study was conducted with respect to the feasibility to estimate the static load applied to it. The results of this research highlight the differences encountered and discuss possible solutions.

NMPC-Based Path Tracking Control Strategy for Autonomous Vehicles With Stable Limit Handling

A novel nonlinear model predictive control (NMPC) strategy for path tracking of autonomous vehicles with stable limit handling is proposed in this article. To improve the path tracking performance under complex driving maneuvers, a tire lateral force model, which treats road adhesion coefficient and vertical load as variable parameters, is discussed first. It has the advantage that the dynamics model can be applied under different driving conditions. In addition, the stability properties of the dynamics system with the front tire lateral force as the virtual control input are analyzed. The global asymptotical stability with zero input and local input-to-state stability with nonzero input of the dynamics system are proved respectively. To perform path tracking within the handling limits, both constraints of front tire lateral force and rear tire slip angle are included in the NMPC controller. The constraint of front tire lateral force is considered as peak limits related to load transfer and adhesion coefficient. And for the rear tire slip angle, a combining constraint scheme is proposed, where the indirect constraint is implemented by a penalty term that predicts the saturation of rear tire lateral force, while the direct constraint is implemented by a dead-zone exponential penalty function. The Continuation/Generalized Minimum Residual (C/GMRES) algorithm is applied to improve the computation efficiency of the NMPC. The performance of the controller is evaluated in simulations and hardware-in-the-loop (HIL) tests, and the results show that the controller is able to track the reference path with high precision in real-time.

Model Construction and Numerical Simulation for Hydroplaning of Complex Tread Tires

Euler-Lagrange coupling method is used to establish the fluid-structure interaction model for tires with different tread patterns by obtaining the grounding mark and normal contact force between tire and the road surface during tire rolling. The altering of load force, tire pressure, and water film thickness in relation to the effect on tire-road force during both constant speed and critical hydroplaning speed was analyzed. Results show that the critical hydroplaning speed and normal contact force between tire and the road surface are positively correlated with vehicle load and tire pressure and negatively correlated with water film thickness. Python language is used to develop the pre-processing plug-ins to achieve parametric modeling and rapid creation of Finite Element Analysis (FEA) model to reduce time costs, and the effectiveness of the plug-ins is verified through comparative tests.

The Improvement of a Traction Model for Agricultural Tire–Soil Interaction

The goodness-of-fit analysis performed over the results provided by a model presented in a previous paper proved that the theoretical data were very well correlated with the experimental data with regard to the traction force (with Pearson coefficient r2 over 0.9); however, the model was less accurate in predicting traction efficiency, with r2 = 0.203. In order improve the model and obtain a better fit between the theoretical and experimental data (especially for the traction efficiency), the model was updated and modified by taking into account the geometry of the tire cross section, which was considered to be a deformable ellipse. Due to the deformable cross section, the minor axis of the tire–ground contact super ellipse decreased compared with the previous model (from 0.367 m to 0.222 m), while the major axis increased (from 0.530 m to 0.534 m). As a result, different data for the traction force and traction efficiency were obtained. The effect of the wheel travel reduction (wheel slip) over the tire–soil shear area was also investigated, and the hypothesis of a constant shear area (independent of wheel slip) provided the most accurate results. The goodness-of-fit analysis performed using the data predicted by the modified model showed that the Pearson coefficient increased significantly with regard to the traction efficiency (from 0.203 to 0.838), while it decreased by only 2.7% with regard to the data for the traction force, still preserving a high value (r2 = 0.896).

Improvement of steady-state PAC2002 under the sideslip and turn slip inputs based on the discrete theoretical tire model

Semi-empirical tire model considering turn slip input is of great significance for the force feedback of vehicle at low speed or small turning radius conditions. In this paper a refined discrete model considering contact patch and the deformation of the belt/carcass which are from the finite element model is established. New force and moment calculation matrix equations are constructed and different iterative methods are compared and Richardson iteration has been chosen because of its best iteration speed. The tire dynamics characteristics under sideslip and turn slip inputs are analyzed based on the discrete model simulation results. It shows the PAC2002 influence coefficients of turn slip on peak value of side force and cornering stiffness can not be well expressed under different loads. And at small loads, the peak value and stiffness of aligning moment relative to turn slip under different sideslip angles can not well be expressed. According to above problems, the PAC2002 model is improved. After improvement, the average error of lateral force relative to sideslip angle under different turn slip is reduced from 3.7% to 1.4%, the average error of lateral force relative to turn slip under different sideslip angle is reduced from 9.9% to 3.6%. And the error of aligning moment relative to sideslip angle under different turn slip is reduced from 8.5% to 5.1% and the error of aligning moment relative to turn slip under different sideslip angle is reduced from 8.9% to 3.2% at small loads. The improvement proposed in this paper have a good result.

PSO-Based Variable Parameter Linear Quadratic Regulator for Articulated Vehicles Snaking Oscillation Yaw Motion Control

In this paper, the seven degrees of freedom (DOF) nonlinear system model of articulated vehicles, including the vehicle dynamics model, tire and hydraulic steering system model, and the linearized ideal reference model, is constructed. A layered stability controller for the articulated vehicle is built. The particle swarm optimization (PSO)-based variable parameter linear quadratic regulator (LQR) for the upper-level yaw torque controller and the lower-level torque distributor based on the principle of the minimum tire utilization are established. The effectiveness of the LQR upper-level yaw torque controller for an articulated vehicle at different speeds and control references are compared and analyzed through feedforward and feedback control. We optimize the parameters in the LQR controller using PSO and verify the improvement in the controller’s performance with optimized parameters. Overall, the effect of front and rear-integrated control is best, followed by rear-based and front-based control. The PSO algorithm to optimize the LQR controller parameters for snaking oscillation control is effective.

Research on tyre mechanics model for multi-axle coordinated steering of heavy vehicles

Compared with passenger cars, heavy vehicles have larger loads, longer bodies, more steering modes, and are more likely to cause improper steering angle relationships among the wheels, resulting in uncoordinated steering. This uncoordinated steering makes the tyres roll and drag, which results in abnormal lateral and longitudinal slips, changing the lateral and longitudinal mechanical characteristics of tyres and leading to low path tracking accuracy and poor steering performance of vehicles. Therefore, a tyre model containing lateral and longitudinal mechanical characteristics under heavy load is the key to solving the problem of uncoordinated steering in heavy vehicles. Firstly, with the physical tyre model, the lateral and longitudinal slip is described as carcass deflections. With the carcass deflections and contact pressure distribution of heavy load, the tyre forces under uncoordinated steering conditions are derived. Then, the tyre imprint parameters are obtained with a test bench, and a two-dimensional contact pressure distribution model is established to reproduce the contact pressure distribution of tyre under heavy loads and dynamic slips. The comparison results with Magic Formula (MF) and Trucksim are generally consistent, proving the effectiveness of the model. Finally, a lateral and longitudinal tyre force distribution control of vehicles is carried out based on the established model. The results of the Trucksim-Simulink co-simulation show that the path tracking accuracy of vehicles is significantly improved, which demonstrates that the tyre model incorporating lateral and longitudinal mechanical characteristics under heavy loads can provide a theoretical basis for solving the problem of uncoordinated steering in heavy vehicles.

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.