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A unified non-steady non-linear tyre model under complex wheel motion inputs including extreme operating conditions
Abstract
This study is to describe the transient force and moment characteristics of tyres involving large lateral slip, longitudinal slip, turn-slip and camber, and to develop a dynamic tyre model applicable to vehicle dynamic simulation and control for extreme operating conditions. Based on the steady state USES tire model [4,6], the effective slip ratios and quasi-steady concept are introduced to represent the non-linear dynamic tire properties in large slip cases. A high-order non-steady tyre model is presented. Special attention has been paid on the relationship between turn-slip and camber. Various kinds of experiments are performed to verify the tire model.
... The modeling of the road load is crucial in the development of the model in order to take into account the different forces generated at the wheel-road contact, in this respect several models have been proposed e.g. Guo's model (Guo et al., 2001), Dugoff's model (Dugoff et al., 1970), Gim's model (Gim et al. 1990), Kiencke's model (Kiencke et al., 2005) and Pacejka's model (Bakker et al., 1987;Pacejka, 2012 This paper is organized as follows: Section 2 is devoted to modeling the association: inverter-In Wheel BLDC motorhalf EV in the longitudinal motion during acceleration and deceleration modes, thus, a global state-space representation of the system is given at the end of this section; in section 3, the developed model is tested in different driving conditions using a global cascade controller, and its behavior is illustrated by numerical simulations. A conclusion and reference list end the paper. ...
... The modeling of the road load is crucial in the development of the model in order to take into account the different forces generated at the wheel-road contact, in this respect several models have been proposed e.g. Guo's model (Guo et al., 2001), Dugoff's model (Dugoff et al., 1970), Gim's model (Gim et al. 1990), Kiencke's model (Kiencke et al., 2005) and Pacejka's model (Bakker et al., 1987;Pacejka, 2012). In the present work, Pacejka's model is retained since it describes more precisely the different forces generated at the wheel-road contact. ...
The problem of modeling the longitudinal motion of an Electric Vehicle (EV) or Hybrid Electric Vehicle (HEV) propelled by In-Wheel motor is considered. A complete non-linear model of the vehicle propelled by brushless DC (BLDC) in-wheel motor is presented. The model describes the association of the inverter, BLDC in-wheel motor and the chassis of the vehicle. It describes the behavior of the vehicle in the different driving phases, i.e. acceleration mode and deceleration mode. The relevant fundamental laws are used to model the chassis dynamics taking into account the different non-linear aspects such as aerodynamic effects, rolling resistance and road load. The Pacejka tire model is retained to describe the various phenomena generated at the wheel-road contact. It is shown that the proposed model describes correctly the longitudinal behavior of the vehicle in the acceleration and deceleration modes in different driving conditions.
... Tire relaxation effects are introduced in [34] for both lateral and longitudinal directions of the tire. The lateral relaxation length is given by the ratio of cornering stiffness of the tire ( ∝ ), and the translating stiffness of the carcass ( ) ...
... An analogy in the consideration of non-steady side slip processes can be observed between the approaches presented in [34] and [21]: compare Eq. (1) and (5). A relaxation effect on the longitudinal slip and the aligning moment in the tire patch (the latter is caused by the traction and lateral reactions in the tire patch) is given by the longitudinal relaxation length: ...
For military all-terrain vehicles, there is a need to radically increase tactical and operational mobility through new modalities by fundamentally improving vehicle terrain control. By characterizing the tire relaxation length and time constants for lateral and longitudinal dynamic changes, mobility control can be enhanced to accommodate agile tire dynamics.
This paper analyzes the transient period of the tire reaction force development process, which is characterized by the relaxation length, for the purpose of agile tire dynamics control as a pre-emptive, fast and exact response of a tire to dynamic changes of its interaction with terrain. In this regards, a comprehensive literature review was undertaken and the tire relaxation length was analyzed for different types of vehicles and their operational velocities. The time relaxation constants, which are derived from the relaxation length, are determined and analyzed based on the data gathered in technical literature. Based on the analysis, reference magnitudes of the time relaxation constants are proposed to be used in agile tire dynamics control algorithm and hardware developments of military all-terrain vehicles.
... Paper [5] derived a theoretical model of tire turn slip properties which could calculate tire force with large turn slip. And the effects of turn slip were also considered in various semi-empirical models [5,6,7,8]. ...
... The condition of pure turn slip, while the sideslip angle α and longitudinal slip ratio S x [6] remain at zero, is shown in Figure 1, where R is the radius of path curvature and Ω is the wheel speed of revolution. The turn slip ratio φ t is defined as the ratio of the wheel yaw rate and the updating speed V r of the contact path, and V r is defined as the product of the wheel speed of revolution Ω and the effective rolling radius R e . ...
In this paper a tire model for describing tire turn slip properties is derived. The tread of the contact patch is divided into many massless elastic elements in both the length and width direction. Carcass deformation is expressed by the translation, bending and twisting function. A turn slip tire model is derived by analyzing the geometric relationships among the deformation of contact patch, tread and carcass. The model is validated by experimental results of parking maneuver. The model seems capable of generating transient and steady state forces and moments for turn slip, and showing varied trend of tire force according to different turn slip velocity. It could not only describe the tread deformation, but also analyze how the tread deformation affects the tire force and moment properties.
... In this paper, UniTire model, developed by Prof. Konghui Guo of Jilin University, is used to model the lateral force [1,2]. The outline of the UniTire model for lateral slip combined with camber properties includes the following equations: ...
... Considering camber effect on cornering stiffness and friction coefficient, the new version of UniTire-UniTire 2.0 is presented [1,2]. The comparisons between model results and test data are shown in figures 3-6. ...
Vehicle behaviors under extreme cornering are complex events that might result in rollover accidents. Simulations have been extensively used in the auto industry to protect vehicles from such accidents. Predictive capability of simulation relies on how accurate the math-based model represents the vehicle and its operating condition. Camber effects of tire are studied in this paper to promote the accuracy of simulation. First, a tire model with simplified camber effect is introduced, and the comparison between the model results and test data is shown. Then, a more precise model that includes camber effects on cornering stiffness are friction coefficient is presented. The comparison between these model results and test data is also given. In addition, the camber effects on tire overturning moment and loaded radius are studied. Finally, vehicle fishhook simulation with different tire models is conducted to further investigate the effect of tire camber on vehicle dynamics.
... For a cambered tire, overturning moment is generated due to the contact pressure distribution tends to the direction of the wheel cambered. With the effect of lateral force and overturning moment, an additional camber angle will be added to the tire, forming the effective carcass camber e (shown in figure 4) known as the 'effect of effective carcass camber' [13]. This will lead to the actual camber smaller than the nominal value. ...
... The relationships between the longitudinal force and the slip ratio, the lateral force and the slip angle, and the aligning torque and the slip angle were established, as shown in Figure 8. The slip angle is defined as the angle between tire rolling direction and tire plane direction, and the slip ratio is calculated using Equation 5 (34). ...
Water film on a pavement surface greatly increases vehicle accident rates on rainy days. The simple use of a lower friction coefficient to evaluate the vehicle braking performance oversimplifies the contact mechanism between the tire and the pavement, and the use of a pure single tire model simulating hydroplaning was not able to reflect actual vehicle braking-cornering behaviors. This paper proposes an integrated tire-vehicle model to evaluate vehicle braking performance based on Persson’s friction theory, a tire hydroplaning finite element model, and a vehicle dynamic analysis. The friction coefficients between the tire and the pavement were calculated theoretically from the pavement surface morphology and the tire rubber properties; the tire hydrodynamic forces were obtained mechanistically from the hydroplaning model with different water film thicknesses and were used as inputs for calculating the braking distances in a vehicle model. The calculated friction coefficients and braking distances were verified using the field test results. A case study was conducted to illustrate the approach and evaluate the vehicle braking performance on straight and curved road sections. The results show that both longitudinal braking distances and lateral slip distances should be considered in the evaluation of vehicle braking performance.
... Expanding the E-function expressions in a Taylor series, and neglecting the higher-order terms ofs. equation (38) can be simplified as [18][19][20][22][23][24] E{s)^as. AEy{s)^as. ...
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.
... Expanding the E-function expressions to Taylor's series, and neglecting the higher-order terms of s, equation (44) can be simplified as [9][10][11]: ...
UniTire is a unified non-linear and non-steady tire model for vehicle dynamic simulation and control under complex wheel motion inputs, involving large lateral slip, longitudinal slip, turn-slip, and camber. The model is now installed in an ADSL driving simulator at Jilin University for studying vehicle dynamics and their control systems. In this paper, first, a brief history of UniTire development is introduced; then the application scope of UniTire and available interfaces to MBS software are presented; thirdly, a more detailed description of UniTire is given; fourthly, a tool aiming at parameterization of UniTire is also demonstrated; and finally, some comments on TMPT are made.
Skid steering is different from the traditional Ackermann steering. Skid steering vehicles don't turn by swinging the wheel, but by changing the wheels' rotational speed of the either side. Skid steering has been applied to various intelligent vehicles because it has advantages in mobility and general layout. To study the steering performance of skid-steered wheeled vehicles, a three degree of freedom skid steering dynamic model is established. The load transfer and the effects of vehicle parameters on steering performance are considered in simulation. The result shows that the stability is influenced by the type of steering input, turning radius and vehicle forward speed.
The problem of controlling the longitudinal motion of front-wheels electric vehicle (EV) is considered making the focus on the case where a single dc motor is used for both front wheels. Chassis dynamics are modelled applying relevant fundamental laws taking into account the aerodynamic effects and the road slope variation. The longitudinal slip, resulting from tire deformation, is captured through Kiencke's model. Despite its highly nonlinear nature the complete model proves to be utilizable in longitudinal control design. The control objective is to achieve a satisfactory vehicle speed regulation in acceleration/deceleration stages, despite wind speed and other parameters uncertainty. An adaptive controller is developed using the backstepping design technique. The obtained adaptive controller is shown to meet its objectives in presence of the changing aerodynamics efforts and road slope.
This paper examines the feasibility of proposed control for independent four-wheel drive electric vehicle. According to vehicle longitudinal velocity and the tire-road condition, a new method to determine the target value, i.e., vehicle yaw rate and side slip angle, is presented. The effectiveness of the designed controller based on sliding mode control is investigated by simulations using a seven-degree-of-freedom dynamic model with a unified non-linear and non-steady tire model. The simulation results indicate a satisfactory handling performance through an external yaw moment which is achieved by sliding mode control strategy.
Since the autonomous vehicle is intended to simulate a human driver's behaviour, it is very helpful to introduce a driver model to the design of the autonomous vehicle controller. The intention of this paper is to exhibit the approaches of building a longitudinally and laterally integrated driver model and the methods of applying the model in autonomous vehicle control. A series of simulations is undertaken in typical driving conditions such as double lane change, speed or position following in straight line, braking-in-turn, high-speed U turn, etc. During the entire course of the simulations, the driver model has demonstrated the great accuracy in terms of following both the path and the vehicle speeds. It can be concluded that this particular type of driver model is highly applicable in autonomous vehicle control.
A direct yaw moment control (DYC) method based on optimal predictive method is proposed to achieve an external yaw moment which is as low as possible. This control method calculates the necessary moment according the vehicle condition, and then optimizes the distribution of drive/brake torque to achieve the necessary yaw moment considering the constraints of actuators. The effectiveness of the designed controller is investigated by simulations. The simulation results indicate that a satisfactory handling performance can be achieved when the proposed controller is applied.
this paper investigates the braking stability from the viewpoint of dynamic simulation. Braking stability refers to the abilities of the vehicle to keep straight or the controllability combined with steering wheel during braking. Suspension extra steer/toe angle caused by forces and moments could change the actual wheel angle directly as well as the tire slip angle, since there is a relationship between tire slip angle and lateral force, braking stability will be changed by the change of lateral force. The orientation of kingpin axis will change during braking, and Wheel alignment and the Position and Angle of the Kingpin Axis (PAKA) have a heavy influence on braking stability during emergence braking and braking on �� -split road. This paper analyzes the importance parameters of wheel alignment and PAKA in suspension K&C during braking stability for asymmetry chassis, and point out that ride-steer and Fx-toe are the key factors that affect braking stability. Vehicle dynamic model is built to analyze braking stability, which include precise description of suspension K&C characteristics, steering system model that can reflect the self-adaptive steering capacity of left and the right wheels, and non-linear UniTire model. Braking stability has been validated well using this vehicle model on the asymmetry chassis.
A direct yaw moment control (DYC) method based on optimal and predictive control is proposed in this paper. The 8-degree-of-freedom model of electric vehicle and the non-linear Unitire model have been developed. The simulation results verified the validity of control strategy. The control method of electric vehicle put forward in this paper can reduce the control energy in case of satisfying the control requirement.
A theoretical model of nonsteady state tyre cornering properties (NSSTCP) with small lateral inputs and its experimental validation are presented. The flexibility of carcass composed of translating, bending and twisting parts is considered. Tyre structure parameters in the model can be simplified as four nondimensional factors which associate with stiffness of tread and carcass, tyre width, length of contact patch respectively The tests of NSSTCP including pure yaw motion and pure lateral motion are designed and realized by step lateral inputs. Then the structure parameters are identified according to the expressions of the analytical model and frequency response data resulting from the test data in spatial domain. The derived model is validated by experiment results.
The tyre force and moment generating properties connected with the vehicle's horizontal motions are considered. Knowledge of tyre properties is necessary to properly design vehicle components and advanced control systems. For this purpose, mathematical models of the tyre are being used in vehicle simulation models. The steady-state empirical ‘Magic Formula tyre model’ is discussed. The aligning torque description is based on the concepts of pneumatic trail and residual torque. This facilitates its combined slip description. Following Michelin, weighting functions have been introduced to model the combined slip force generation. A full set of equations of the steady-state part of the model of the new version ‘Delft Tyre 97’ is presented. The non-steady state behaviour of the tyre is of importance in rapid transient maneuvres, when cornering on uneven roads and for the analysis of oscillatory braking and steering properties. A relatively simple model for longitudinal and lateral transient responses restricted to relatively low time and path frequencies is introduced.
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.
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