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

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Abstract

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.
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... e accuracy of the tire model has a great influence on vehicle performance. A lot of work has been done to establish the tire model, the Fila tire model [19], UA tire model [20], Gim tire model [21], Dugoff tire model [22], HRSI tire model [23], UniTire model [24], and Magic Formula tire model (MF tire) [25] are widely used in the vehicle dynamic model. In this case, two tire models are used: linear tire and MF tire. ...
... When the tire sideslip angle exceeds the range of ±5°, the gap of the lateral force of the tire gets non-negligible. e comparison of the lateral force acquired from the linear tire model and MF tire model of the front and the rear tire is shown in Figures 3 and 4. According to equation (24) and the variation of sideslip angle and tire cornering stiffness during the steering process, the needed torque can be calculated. In Figure 5, the dash lines represent the torque based on the linear tire, and the solid lines mean the tire cornering stiffness is nonlinear during the process. ...
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The EV (electric vehicle) with a wheel hub motor has the advantage of independent driving torque distribution for each wheel, which allows the vehicle performance to be improved. Therefore, a lot of work has been done to investigate the torque allocation algorithm for the mechanical and differential torque integration steering system. To investigate the differential steering process, the 2 DOF (degree of freedom) dual-track reference models with linear and nonlinear tire models are established, and based on the steering process analysis and yaw rate gain calculation, a BP-NN (backpropagation neural network) model is initiated to maintain the accuracy of the calculated yaw rate gain. The limitation of DTSS (differential torque steering system) and the difference of reference models with linear and nonlinear tires are drawn. In addition, an anti-windup variable PID (proportion integration differentiation) controller is designed for the torque distribution. Based on the built 8 DOF model, the vehicle performance indicators are calculated and compared, the gap between the models with linear and nonlinear tires is non-negligible, and a reference model with a nonlinear tire model is recommended for the relevant research. The anti-windup variable PID controller has a better performance than the normal PID controller except for the stability phase plane indicator.
... Therefore, the nonlinear tire model is essential in this system to describe the force condition at each tire. The UniTire tire model can express tire forces more accurately not only in single working conditions but also in complex working conditions [26], which means it is ideally suited to the part of the vehicle drifting motion. If the UniTire tire model is applied directly to the narrow tilting vehicle drifting controller, there will be a large amount of computation in the controller design. ...
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The narrow tilting vehicle receives extensive public attention because of traffic congestion and environmental pollution, and the active rolling motion control is a traffic safety precaution that reduces the rollover risk caused by the structure size of the narrow vehicle. The drifting motion control reflects the relatively updated attentive research of the regular-size vehicle, which can take full advantage of the vehicle’s dynamic performance and improve driving safety, especially when tires reach their limits. The narrow tilting vehicle drifting control is worthy of research to improve the driving safety of the narrow tilting vehicle, especially when tires reach the limit. The nonlinear narrow tilting vehicle dynamic model is established with the UniTire model to describe the vehicle motion characteristics and is simplified to reduce the computation of the drifting controller design. The narrow tilting vehicle drifting controller is designed based on the robust theory with uncertain external disturbances. The controller has a wide application, validity, and robustness and whose performance is verified by realizing different drifting motions with different initial driving motions. The narrow tilting vehicle drifting robust control has some practical and theoretical significance for more research.
... Afterwards, the authors performed another analytical study to overcome the shortcoming of the previous approach [12,13]. For the purpose of describing the complicated nonlinearity characteristics of a modern tire, several improved approaches of tire models with new conceptual parameters are still being developed and enhanced [14][15][16][17]. ...
... After nearly 30 years of development, the UniTire model has gradually developed and matured. It has a good expression ability for various working conditions and a simple model with outstanding prediction and extrapolation ability [9]. ...
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Tires are the only link between vehicles and roads and provide all forces for vehicle movement, including driving, steering, and braking. Therefore, the tire model is fundamental for vehicle dynamics, and an efficient tire model is necessary for further technology development of vehicle dynamics and control. In this article, a simplified physical tire model featuring tire hysteresis properties is presented. Firstly, an elastic hysteresis system is introduced to the tire physical model. Then, combining with resistor–capacitor operator, force–deformation characteristics of the elastic hysteresis system are established. Correspondingly, the force–deformation characteristics are applied to describe tire nonlinear dynamics, and a unified expression of HysTire, i.e., a semi-empirical tire model featuring hysteresis characteristics, is established. Finally, the nonlinear dynamics of two tires are modeled to verify the effectiveness and superiority of HysTire. Comparison results with the magic formula model (MF) show that the HysTire provides accuracy like that of the MF, while it is much better in the profiles of predictive and extrapolative capabilities.
... For tire and vehicle dynamics simulations and analyses, different types of tire models have been developed and categorized as empirical and theoretical models [1,2]. The empirical model, or combined theoretical and empirical model, is used for vehicle dynamics, and its model parameters are obtained by fitting measurements [2], including the MF/PAC2002 [2][3][4][5], TMeasy [6][7][8], UniTire [9,10], Hankook-Tire [11], TameTire [12,13], MF-Swift [14,15], FTire [16,17], CDTire [18,19] and RMOD-K [20,21] models, etc. ...
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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.
... Researchers have proposed various theoretical tire models, including but not limited to the Magic Formula [17,18], Kamm circle [19], Nicolas-Comstock [20], average lumped LuGre [21,22], UniTire [23], and Dugoff [24]. Meanwhile, finite element (FE) tire-pavement interaction models were also created to study the tire mechanics. ...
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Chapter
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This research has been divided into four parts for the purpose of serial publication in the International Journal of Vehicle Design. For the sake of completeness the abstracts for all four parts are given here. Part 1: Review of theories of rubber friction. Previous theoretical work on the dynamic properties of tyres is reviewed. Extensions of a theory relating tyre cornering properties to conditions of braking and traction are considered, along with factors relevant to a further extension to the dynamic properties of an actual pneumatic tyre. A theoretical derivation of the six components of force and moment generated in a tyre is given which involves integrating the vertical and friction forces acting on a rubber block and the resultant moments over the area of contact. Part 2: Experimental investigations of rubber friction and deformation of a tyre. Experiments designed to determine the basic properties of a tyre needed for the calculation of the six components of force and moment are described. Similar consideration is then given to experiments aimed at determining the frictional properties needed for the calculation of the six components. Part 3: Calculation of the six components of force and moment of a tyre. The method of calculating the six components of force and moment generated in a tyre is presented, and then applied. Partial results of the calculation are presented. Part 4: Influence of running conditions on the calculations and experiments. The results of calculations performed in previous sections of the paper are applied to the study of the influence of running conditions on the six components of force and moment in the case of real tyres. An experiment to determine the six components is described, and the experimental values compared with the calculated values.