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Journal Article

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

2013-09-24
2013-01-2362
The tire mechanics characteristics are essential for analysis, simulation and control of vehicle dynamics. This paper develops the UniTire model for tire forces and moments under combined slip conditions with anisotropic tire slip stiffness. The anisotropy of tire slip stiffness, which means the difference of tire longitudinal slip stiffness and cornering stiffness, will cause that the direction of tire resultant shear stress in adhesion region is different from that in sliding region. Eventually the tire forces and moments under combined slip conditions will be influenced obviously. The author has proposed a “direction factor” before to modify the direction of resultant force in the tire-road contact patch, which can describe tire forces at cornering/braking combination accurately. However, the aligning moments which are very complicated under combined slip conditions are not considered in previous analysis.
Technical Paper

UniTire Model for Tire Cornering Properties under Varying Traveling Velocities

2016-09-27
2016-01-8037
The tire mechanics characteristics are essential for analysis and control of vehicle dynamics. Basically, the effects of sideslip, longitudinal slip, camber angle and vertical load are able to be represented accurately by current existing tire models. However, the research of velocity effects for tire forces and moments are still insufficient. Some experiments have demonstrated that the tire properties actually vary with the traveling velocity especially when the force and moment are nearly saturated. This paper develops an enhanced brush tire model and the UniTire semi-physical model for tire forces and moments under different traveling velocities for raising need of advanced tire model. The primary effects of velocity on tire performances are the rubber friction distribution characteristics at the tire-road interface.
Technical Paper

Tire Roller Contact Model for Simulation of Vehicle Vibration Input

1993-11-01
932008
To improve the quantitative accuracy of vehicle vibration studies, a roller contact tire model with the geometric filtering concept and a method to determine the effective road input are proposed. Computer simulation with the 13 DOF vehicle model for a light truck, based on two different tire models, and relevant outdoor tests for measuring the vehicle accelerations of both sprung and unsprung masses are presented. Comparisons of test data and simulation results show that the roller contact tire model renders much better simulation accuracy than the single point contact tire model. It is concluded that the roller contact tire model is a powerful concept which acts as a geometric filter, giving a simple method to calculate the enveloping effects of tires and the effective road elevation input.
Journal Article

Tire Model for Turn Slip Properties

2013-09-24
2013-01-2371
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.
Technical Paper

Tire Carcass Camber and its Application for Overturning Moment Modeling

2013-04-08
2013-01-0746
The properties of contact patch are key factors for tire modeling. Researchers have paid more attention to the contact patch shape and vertical pressure distribution. Some innovative concepts, such as Local Carcass Camber, have been presented to explain special tire modeling phenomena. For a pragmatic tire model, a concise model structure and fewer parameters are considered as the primary tasks for the modeling. Many empirical tire models, such as the well-known Magic Formula model, would become more complex to achieve satisfactory modeling accuracy, due to increasing number of input variables, so the semi-empirical or semi-physical modeling method becomes more attractive. In this paper, the concept of Tire Carcass Camber is introduced first. Different from Local Carcass Camber, Tire Carcass Camber is an imaginary camber angle caused only by lateral force on the unloaded tire.
Technical Paper

Simulations of Tire Cornering Properties in Non-Steady State Conditions

1998-02-01
980254
Simulations of tire cornering properties with small-amplitude lateral inputs are carried out in non-steady state conditions. The simulation algorithm is derived and the discrete expressions are presented in detail. Based on the simulations, lateral force and aligning moment can be calculated numerically with time-varying yaw angle and lateral displacement as inputs in spatial domain. The flexibility of both tread and carcass along with tire width is taken into account effectively in the simulations, in which the flexibility of carcass includes translating, bending and twisting flexibility. The simulations in non-dimensional form are associated with four tire structure parameters only, which are non-dimensional parameters reflecting the characteristics of tire stiffness, tire width and contact length. Simulation results are validated by test data from step lateral inputs tests. Several typical simulation results are provided.
Technical Paper

Research on Tire Lateral Force Prediction under High-Load Condition

2015-04-14
2015-01-1524
The tire lateral force is essential to the vehicle handling and stability under cornering. However, it is difficult for engineers to get the tire lateral force under high loading condition due to the limitation of loading ability for most tire test machine in the world. The widely used semi-empirical tire lateral force models are obtained by curve-fitting experiments data and thus unable to predict the load dependent lateral force. The objective of this paper is to predict the tire lateral force under high-load condition based on the low-load tire data. The nonlinear characteristics of the tire cornering stiffness with the load are greatly affected by the tire carcass compliance. In this paper, a theoretical tire lateral model was built by considering carcass complex deformation. Combined with the relationship between the half-length of the tire contact patch and the load, the non-linear characteristics of the tire cornering stiffness with load were obtained.
Technical Paper

Research on Closed-Loop Comprehensive Evaluation Method of Vehicle Handling and Stability

2000-03-06
2000-01-0694
A closed-loop comprehensive evaluation and a test method for vehicle handling and stability have been studied by using development driving simulator. Simulator test scheme has been designed and carried out with 14 vehicle configurations, and subjective evaluation has been made for easy handling of vehicle by drivers. A closed-loop comprehensive evaluation index has been put forward considering the factors affecting vehicle handling and stability. The reliability of the index has been validated by driver's subjective evaluation. A driver/vehicle/ road closed-loop system model has been established, and the theoretical predictive evaluation has been carried out with 14 vehicle configurations. Simulation showed that similar result for both theoretical predictive evaluation and subjective evaluation.
Journal Article

Modeling Combined Braking and Cornering Forces Based on Pure Slip Measurements

2012-09-24
2012-01-1924
A novel predictable tire model has been proposed for combined braking and cornering forces, which is based on only a few pure baking and pure cornering tests. It avoids elaborate testing of all kinds of combinations of braking and side forces, which are always expensive and time consuming. It is especially important for truck or other large size tires due to the capability constraints of tire testing facilities for combined shear forces tests. In this paper, the predictive model is based on the concept of slip circle and state stiffness method. The slip circle concept has been used in the COMBINATOR model to obtain the magnitude of the resultant force under combined slip conditions; however the direction assumption used in the COMBINATOR is not suitable for anisotropic tire slip stiffness.
Technical Paper

Key Items in Tire Non-Steady State Test

2002-07-09
2002-01-2231
In the paper, the Flat Plank Tire Tester of Changchun Automobile Institute is introduced. This paper, according to practical experiences, generalizes some issues in the tire's non-steady state test. In the non-steady state test, it must be assured that the footprint centerline of tire coincides with that of slid platform, which guarantees no sliding motion between tire and slid platform during the movement. Due to tire taper effect and inhomogeneous tire material, when its side slip angle is zero, side force and aligning torque are not zeros, but have initial values. Here two approaches are discussed to eliminate the side force and aligning torque. Besides, other factors in the test are put forward for discussion. Eliminating the interference can obviously improve the test accuracy. This paper also provides test curves of both pure side slip angle input and pure yaw angle input.
Technical Paper

Influences of Non-Steady State Tire Cornering Properties on Automobile Shimmy

1999-11-15
1999-01-3757
One of the most essential factors causing automobile and aircraft shimmy is energy import from road to tires due to tire hysteresis characteristic. The magnitudes and direction of the energy import are close to frequency responses of tire cornering properties (TCP), which can be calculated directly according to the presented non-steady state TCP theoretical model. Selfexcited shimmy is the main type of wheel shimmy and behaves as negative equivalent damping characteristic of the tire-road vibration subsystem. The values of energy import or equivalent damping determine the tendency of wheel shimmy. Tire structural parameters have certain effects on frequency response of TCP and thereby result in influences on wheel shimmy. Based on the tire model, some valid ways to decrease shimmy tendency are concluded through proper variations of carcass stiffness, tire-width, kingpin caster, tire pneumatic trail, tire cornering stiffness and so on.
Technical Paper

Incorporating Inflation Pressure into UniTire Model for Pure Cornering

2016-09-27
2016-01-8028
This paper focuses on the modeling process of incorporating inflation pressure into the UniTire model for pure cornering. Via observing and manipulating the tire experimental data, the effects of inflation pressure on the tire cornering property are analyzed in detail, including the impacts on cornering stiffness, the peak friction coefficient, the curvature of transition region and the pneumatic trail. And the brief mechanism explanations are also given for some of these impacts. The results show that some effects of inflation pressure are similar to that of vertical load on the non-dimensional tire cornering property, and there are strong interactive effects between the two operating conditions. Therefore, in order to obtain concise expressions, the inflation pressure is incorporated into the UniTire tire model by analogy with the expressions for vertical load, and the interactive effects are also taken into account.
Technical Paper

Development of Leaf Spring Kinematical Model and Its Applications in Improvement of Truck Braking and Steering Analysis

1991-11-01
912566
This paper presents a general kinematical model for all variety of leaf springs, including traditional laminated, asymmetrical, and tapered leaf springs, to calculate the longitudinal and winding deformations of axles during bouncing, braking and traction, which may introduce additional steering effects or variations of roll-steer property of a vehicle. Some experiments were introduced to verify the model. Accordingly, braking performance of a light truck has been improved.
Technical Paper

Analysis of Non-Steady State Tire Cornering Properties Based on String-Concept Deformation and Geometric Relationship of Contact Patch

2007-04-16
2007-01-1514
Vehicle handling and stability performances are greatly determined by non-steady state (NSS) tire cornering properties. Analytical derivation of NSS tire cornering models are presented in this paper based on Pacejka's string-concept assumption, in which carcass is assumed to be a stretched string with lateral deformation and lateral relaxation. The lateral inputs of the models are either displacement-based (lateral displacement and yaw angle) or slip-based (slip angle and turn slip). The transient deformations in spatial domain in both longitudinal and lateral directions are obtained directly from geometric relationship of contact patch. The additional self-aligning moment due to longitudinal deformation of contact patch after effect of tire width is considered is also achieved according to geometric relationship of contact patch in longitudinal direction and two transient geometric conditions of contact point.
Technical Paper

Analysis of Automotive Handling Based on Tire Cornering Properties in Non-Steady State Conditions

1999-11-15
1999-01-3758
Non-steady state (NSS) tire cornering properties show obvious differences from steady state (SS) tire cornering properties. A two-DOF automobile model with steer angle as an input is established based on the known NSS tire model considering complex carcass deformation. The tire model can certainly be applied to modelling of a multi-DOF automobile system. The frequency responses of lateral acceleration and yaw rate are then derived. An evaluation index, amplitude-frequency characteristic of relative error (AFCRE), is used to analyze the influences of NSS front wheels (FW) and/or rear wheels (RW) on automotive handling. The influences of NSS FW are much greater than those of NSS RW only on automotive handling. The established automobile model can also be applied to other similar studies of vehicle dynamics.
Technical Paper

An Empirical Tire Model for Non-Steady State Side Slip Properties

2003-11-10
2003-01-3414
In this paper, on the basis of the extant semi-empirical tire models of non-steady state with pure yaw angle input and pure side slip angle input, two empirical tire models of non-steady state side slip properties are established, one is pure yaw angle input, the other is pure side slip angle input, and both of them have been verified by test data. These two models can be used to approximately express tire force within low frequency. They have their own advantages, and make up for the disadvantages of existing tire models. They provide more choice for the simulation of vehicle dynamics.
Technical Paper

An Efficient Assistance Tool for Evaluating the Effect of Tire Characteristics on Vehicle Pull Problem

2020-04-14
2020-01-1237
The vehicle pull problem is very important to driving safety. Major factors that may cause the pull problem related to tire include variations of geometric dimension (eg.RPK) and stiffness (eg. cornering stiffness, Aligning stiffness), Plysteer and Conicity effect. In the previous research, the influencing mechanism of these factors were well studied.But in fact, vehicle pull problem caused by tire is probabilistic. When we assemble four tires onto the car, there would be 384 kinds of assembly arrangements. If we want to evaluate the pull performance of all these arrangements by real test, it will take a very long time, almost 24 working days, and along with a high test cost. Therefore, it is very needed to develop an assistant simulation tool that can evaluate the effect of tire characteristics on vehicle pull problem quickly.
Technical Paper

A Unified Semi-Empirical Tire Model with HigherAccuracy and Less Parameters

1999-03-01
1999-01-0785
A unified tire model with non-isotropy of friction and arbitrary contact pressure distribution is presented as a foundation to study the key features of a reasonable expression of tire shear force and alignment torque under combined slip conditions. The effects of contact pressure distribution on tire mechanical characteristics are analyzed. A unified semi-empirical tire model with convenience in dynamics simulation is recommended. For determining the model parameters, a series of simple expressions that satisfy the boundary conditions are proposed and a new global fitting method for tire data processing is employed. Based on the improved semi empirical model, the USPA software is developed. This software reduces the modeling time from the tire data to a practical tire model and allows various tire characteristics analyses. Some experimental validations are shown.
Technical Paper

A Theoretical Model of Non-Steady State Tire Cornering Properties and its Experimental Validation

1997-11-17
973192
Based on the tire cornering properties in steady state condition, a theoretical model of non-steady state tire cornering properties (NSSTCP) with small lateral inputs is presented. The outputs of the model are lateral force and aligning moment, while the inputs are yaw angle and lateral displacement (or turn slip and slip angle). The deformation characteristics of contact patch are analyzed in non-steady state condition. The flexibility of tread and that of carcass are both taken into account. The deformation of carcass is assumed to compose of translating part, bending part and twisting part. The tests of NSSTCP including pure yaw motion and pure lateral motion are realized with step inputs of yaw angle and slip angle respectively and test data is then transformed into frequency domain. The model is validated through comparing the computational results with test frequency response.
Technical Paper

A Study of Tire Lag Property

2001-03-05
2001-01-0751
Tire lag property is a basic property of tire dynamics, and it has significant influence on the performance of vehicle dynamics. In distance domain, the side force and moments produced by a massless tire are basically displacement or path frequency dependent, rather than time dependent. In the paper, on the basis of the stretched-string model, the first-order filtering of deflection for the front point of the contact print and the first-order filtering of side force have been introduced. Tire system can be regarded as a first-order linear system under small slip angle. The force response of tire has the characteristics of the responses of first-order linear system under small angle. The relaxation length is an important parameter in studying tire lag property. It decreases with increasing slip angle. It plays an important role in the study of tire transient properties.
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