Vertical Tire Stiffness Research Articles

Modeling and Experimental Validation of an Off-Road Truck’s (4 × 4) Lateral Dynamics Using a Multi-Body Simulation

In the automotive sector, the use of multi-body software for modeling of existing vehicles has become essential due to its advantages in understanding vehicle dynamics in different situations and improving vehicle performances. This paper aims to model an off-road truck (4 × 4) by using ADAMS software 2020. Several steps must be achieved, including experimentally identifying some truck characteristics such as the mass, center of gravity coordinates, and tire vertical stiffness. The truck features leaf springs in both the front and rear suspensions, which must be validated before their integration into the full model due to their modeling complexity. This validation is performed by comparing the force–displacement characteristics obtained experimentally with simulation results from ADAMS, showing a good agreement. Then, the full truck is modeled in ADAMS software and validated through an experimental test using a repeated double-lane change scenario with two tests for the validation of the truck’s lateral dynamics. The comparison between the results shows a good correlation, validating the multi-body truck model.

Racing bicycle tyres – Influence on mechanical characteristics of internal pressure, vertical force, speed and temperature

The paper describes how internal pressure, vertical force, speed and rolling surface temperature may affect the mechanical characteristics of a road racing bicycle tyre. The results were obtained from an experimental test campaign performed with VeTyT, a test-rig specifically designed for measuring the mechanical characteristics of bicycle tyres.The static deflection of tyre for different inflation pressures and vertical loads was measured to determine the static tyre vertical stiffness. Results for tyre rolling on flat track or on a drum were compared. Dynamic analyses were focused on evaluating the effect of inflation pressure and vertical load, for two rims featured by different lateral stiffness. Then, the respective effects of speed and of temperature of the rolling surface on the lateral force were considered.Stiffer rims can ensure higher values of cornering stiffness. In addition, higher inflation pressure is recommended only for heavy vertical loads. For low vertical loads, too inflated tyre results to be less performant, i.e. to show lower values of cornering stiffness. The speed can affect the mechanical characteristics of bicycle tyres mainly for slip angles less than 1.5°, while the temperature of the rolling surface is the most affecting parameter for slip angles larger than 3°.

State estimation of tire-road friction and suspension system coupling dynamic in braking process and change detection of road adhesive ability

During vehicle braking, when vehicles move on the road with unknown road roughness elevation and unknown tire/road friction coefficient, fewer sensors shall be used for vehicle braking closed-loop control and braking distance prediction to obtain the dynamic states of the vehicle suspension and tire systems. In this paper, a vehicle dynamic model is established in Carsim software. Modify lump LuGre friction model and road roughness elevation model of four tires are proposed based on matlab. When vehicles brake on the road with time-varying split-μ, a braking control algorithm established in this paper. The road roughness elevation and the braking force of each tire are supplied to the vehicle dynamic model in Carsim. A state estimate algorithm of suspension system is proposed. The scheme for minimum sensor of this estimator is determined. A state estimate algorithm of the tire/road friction using only tire angular velocity information is proposed. When vehicles brake on the road with different levels of roughness, the influence of the number of installation groups of the sensors, the tire vertical stiffness deviations, and the measurement noise on the estimation error of the estimator is analyzed. When the vehicle is driving on the road with unknown adhesive ability, based on the estimator of tire/road friction using only tire angular velocity information, the tire/road friction internal state, the changes of road adhesive ability, and the vehicle velocity are estimated well.

Modeling and analytical calculation of road damage coefficient considering tire pressure and damping of vehicles

The road damage coefficient [Formula: see text] is a significant indicator to estimate the degree of the road damage caused by vehicles. The existing calculation method of [Formula: see text] is not convenient for the engineering application. To effectively evaluate the damage degree and facilitate the engineering application, this paper studied the simple and reliable analytical calculation method of [Formula: see text]. Firstly, a dynamic model of the vehicle–road system was created. The tire pressure and the tire damping were considered in the model. Moreover, the relationship between the tire vertical stiffness and the tire pressure is approximated as a linear function. Secondly, based on the dynamic model, according to the definition of [Formula: see text], a concise analytical formula of [Formula: see text] was derived and verified by numerical simulations. The relative errors of the analytical calculation results are all less than 0.1%. Thirdly, the influences of the tire pressure [Formula: see text], the damping ratio [Formula: see text] of the suspension system, and the damping ratio [Formula: see text] of the wheel system on [Formula: see text] were analyzed. Moreover, based on the analytical formula of [Formula: see text], a mathematical model of the optimal damping matching for the suspension system was established and a case study was also given. The research results show that the larger the tire pressure [Formula: see text], the larger the value of [Formula: see text] is. For each [Formula: see text], there is an optimal damping ratio [Formula: see text]. If the tire damping is ignored, it will lead to the design error for [Formula: see text]. Finally, some important conclusions were drawn. The analytical formula of [Formula: see text] and the conclusions can provide valuable references for the analysis of the road damage and the initial design of vehicle suspensions.

Robust Optimization of Road Vehicle Suspension Considering the Variation of Tire Vertical Stiffness

Tire vertical stiffness is influenced by many factors. The inflation pressure, tire dimension, and usage of run-flat tire are considered in this paper. Robust multi-objective optimization technique is used to optimize the suspension performance considering the variation of the tire vertical stiffness. Three objective functions, discomfort, road holding, and working space are used to evaluate the dynamic behavior of the suspension considering a two-degree-of-freedom quarter-car model excited by a random road profile. The Pareto-optimal solutions in terms of suspension spring stiffness and damping coefficient are obtained and compared with the one computed by means of a deterministic approach. Solutions obtained by means of the robust optimization method are proven to be less sensitive to the possible variations of the tire vertical stiffness without influencing significantly the expected performance.

Feasibility Study for the Identification of FTire Model Parameters Using FE Simulations

ABSTRACT Normally, FTire model parameters are determined by experimental tests. However, because of the high cost of experiment equipment and limitations in rig design and operating conditions, it is hard to obtain all the required data by experimental tests, especially for some large tires, such as the running wheel tires of straddle-type monorail vehicles. To solve this problem, a method based on finite element (FE) simulations is put forward. To achieve the goal, a three-dimensional FE model of a 345/85R16 radial tire is developed using ABAQUS software. In addition, a modified exponential decay friction model, derived from tire tread rubber friction tests, is put forward and applied in the following FE simulations using the ABAQUS user subroutine FRIC. To verify the accuracy of the present model, tire vertical stiffness test, lateral stiffness test, and tire contour geometry measurement are designed. Through the comparison of measurements and FE simulations, it turns out that the model is capable of predicting tire properties accurately. Tire static, steady-state, modal, and dynamic cleat tests are modeled. Finally, data such as vertical stiffness, cornering stiffness, and natural frequencies are derived from FE simulations. Based on the data derived from FE simulations, the FTire model parameters are identified and then validated by comparing the force responses of the FTire simulation in the ADAMS/Tire test rig and FE simulations. The results show that there is an acceptable agreement between them, reflecting that the method is feasible.

Geometric-based tyre vertical force estimation and stiffness parameterisation for automotive and unmanned vehicle applications

ABSTRACTAdvanced empirical, and physical-based tyre models have proven to be accurate for simulating tyre dynamics; however, these tyre models typically require expensive and intensive tyre parameterisation. Recent research into wheeled unmanned ground vehicles requiring vertical force analysis has shown good results using a simple linear spring model for the tyre which demonstrate the continued use for simple tyre models; however, parameterisation of the tyre still remains a challenge when load test equipment is not available. This paper presents a cost-effective tyre vertical stiffness parameterisation procedure using only measured tyre geometry and air pressure for applications where high-fidelity tyre models are unnecessary. Vertical forces calculated through an air volume optimisation approach are used to estimate tyre vertical stiffness. Nine tyres from the literature are compared to evaluate the performance of the vertical force estimation and stiffness parameterisation algorithms. Experimental results on a pair of ATV tyres are also presented.

Investigation on cornering brake stability of a heavy-duty vehicle based on a nonlinear three-directional coupled model

A nonlinear three-directional coupled lumped parameters (TCLP) model is proposed for a heavy-duty vehicle to investigate the longitudinal, lateral and vertical dynamics of vehicles simultaneously. The nonlinear property of suspension damping is described by a fitted exponent model from experimental data. The nonlinear tire forces in different directions are modeled by the nonlinear Gim model and the vertical single dot contact model with square nonlinearity. The system responses are calculated by numerical integration and compared with the Functional Virtual Prototyping (FVP) model and the test data, so as to verify the validity of this new vehicle model. With Lateral-Load Transfer Ratio (LTR) and yaw rate as evaluation indexes, the influences of system parameters on cornering brake stability are analyzed. The critical vehicle speed table is also obtained. The study shows that high vehicle running speed, large front wheel steering angle, large tire cornering stiffness or small braking moment is harmful to yaw stability and roll stability. Road surface frictional coefficient mainly influences yaw stability, and vertical tire stiffness and road surface roughness mainly influence roll stability.

Optimizing Tire Vertical Stiffness Based on Ride, Handling, Performance, and Fuel Consumption Criteria

Researchers mostly focus on the role of suspension system characteristics on vehicle dynamics. However tire characteristics are also influential on the vehicle dynamics behavior. In this paper, the effects of tire vertical stiffness on the ride, handling, accelerating/braking performance, and fuel consumption of a vehicle are analytically investigated. Furthermore, a method for determining the optimum vertical stiffness of tires is presented. For these purposes, first an appropriate mathematical criterion for the ride, handling, accelerating/braking performance, and fuel consumption is developed. Next, to achieve the optimum tire characteristic, a performance index, which contains all of the above-mentioned criteria, is defined and optimized. In the proposed performance index, the tire vertical stiffness is a design variable and its optimization provides a compromise among ride, handling, accelerating/braking performance, and fuel consumption of the vehicle. Last, the analytical optimization results are confirmed by performing precise numerical simulations.

Analysis of vehicle rollover dynamics using a high-fidelity model

Recent data show that 35% of fatal crashes in sport utility vehicles included vehicle rollover. At the same time, experimental testing to improve safety is expensive and dangerous. Therefore, multi-body simulation is used in this research to improve the understanding of rollover dynamics. The majority of previous work uses low-fidelity models. Here, a complex and highly nonlinear multi-body model with 165 degrees of freedom is correlated to vehicle kinematic and compliance (K&C) measurements. The Magic Formula tyre model is employed. Design of experiment methodology is used to identify tyre properties affecting vehicle rollover. A novel, statistical approach is used to link suspension K&C characteristics with rollover propensity. Research so far reveals that the tyre properties that have the greatest influence on vehicle rollover are friction coefficient, friction variation with load, camber stiffness and tyre vertical stiffness. Key K&C characteristics affecting rollover propensity are front and rear suspension rate, front roll stiffness, front camber gain, front and rear camber compliance and rear jacking force.

Research of Automobile Tire Vertical Stiffness Optimization Method on the Basis of ADAMS/Car

Because Tire not only impact on the handling stability of vehicle but also impact on the ride comfort, it is more practical significant that tire vertical stiffness parameters on handling stability and ride of vehicle impact is considered synthetically than considering handling stability and ride singly. In this paper, full vehicle model was built on the basis of ADAMS/Car. The vertical stiffness of tire was only changed and other parameters remain unchanged, then full vehicle analysis was carried out to get the simulation curves. The impact of the vertical stiffness of tires on the handling and stability and ride comfort was obtained from the curves of simulation. The tires of optimized vertical stiffness can be obtained from the comparison of simulation results. Analytical results can be conductive to designing and producing the tire.

Investigation of Tire-Soil Interaction with Analytical and Finite Element Method#

This article is devoted to the modeling of tire–soil interaction with the analytical and finite element method (FEM). Different from the traditional tire–soil interaction models in which the contact between tires and soils is described by nonlinear springs in the normal direction, the new analytical model added dampers accounting for the soil damping effects. A nonlinear three-dimensional tire–soil interaction model with the FEM, which takes into consideration the tire treads and belt/carcass layers, was validated by measuring tire vertical stiffness and contact stress. The conversion of the Modified Drucker-Prager/Cap soil model to the analytical soil model was demonstrated as well. The simulations for investigating the dynamic behavior of a bias tire running on the soft soil were performed. Good agreement was observed based on the simulation results obtained from these two tire–soil interaction models. However, experimental validation is necessary before the models can be further applied in the prediction of off-road vehicle dynamics.

The Influence of Road Surface Properties on Vehicle Suspension Parameters Optimized for Ride - Design Trends for Global Markets

Suspension design is influenced by many factors, especially by vehicle dynamics performance in ride, handling and durability. In the global automotive industry it is common to customize or tune suspension parameters so that a vehicle is more acceptable to a different customer base and in a different driving environment. This paper seeks to objectively quantify certain aspects of tuning via ride optimization, taking account of market differences in road surface spectral properties and loading conditions. A computationally efficient methodology for suspension optimization is developed using stochastic techniques. A small (B-class) vehicle is chosen for the study and the following main suspension parameters are selected for optimization-spring stiffness, damping rate and vertical tire stiffness. The road is characterized as a stationary random process, using scaling and shaping filters representative of comparable roads in India and the USA. A standard quadratic function is used, including terms for vertical body acceleration, tire load variations and workspace usage. Using the stochastic nature of the ride metrics obtained, it is found possible to further penalize large excursions in the suspension working space. Weighting parameters in the ride metric are selected to match a given design to the US market condition, so that re-optimization assuming conditions relevant to the Indian market immediately provides trend directions for retuning the suspension. It is also shown how assumed increases in payload (passenger numbers etc.) or different driving speeds may be included in the tuning process. Future integration of durability and handling criteria is also discussed. The result is an efficient tuning tool that may be used to support more detailed studies in simulation and track testing, helping to reduce the time to market when suspension tuning is required. Copyright © 2012 SAE International.

Development of a two-dimensional model of a compliant non-pneumatic tire

An analytical model for a compliant non-pneumatic tire on frictionless, rigid ground is presented. The tire model consists of a thin flexible annular band and spokes that connect the band to a rigid hub. The annular band is modeled using curved beam theory that takes into account deformations due to bending, shearing and circumferential extension. The effect of the spokes, which are distributed continuously in the model and act as linear springs, is accounted for only in tension, which introduces a nonlinear response. The quasi-static, two-dimensional analysis focuses on how the contact patch, vertical tire stiffness and rolling resistance are affected by the stiffness properties of the band and the spokes. A Fourier series representation of the shear strain in the annular band and the complex modulus of the material were used to predict rolling resistance due to steady state rolling. From the analysis point of view, when the wheel is loaded at its hub, the following three distinct regions develop: (1) a support region where the hub hangs by the spokes from the upper part of the flexible band, (2) a free surface region where the spokes buckle and have no effect, and (3) a contact region where the flexible band is supported by the ground without the effect of the spokes. The angular bounds of these three regions are determined by the spoke angle and the contact angle, which are respectively the angle at which the spokes start to engage in tension and the angle that defines the edge of contact. Closed-form expressions of contact stress, stress-resultants and displacements at the centroids of the cross-sections of the flexible band are expressed in terms of these angles, which must be determined numerically. A thorough parametric analysis of quantities of interest for the tire is presented, which can be used to help support the optimal and rational design of compliant non-pneumatic tires. The model was validated by comparison with two computational models using the commercial finite element software ABAQUS and by experimental rolling resistance data.

타이어 압력 변화에 따른 1/4 MR 댐퍼 차량의 승차감 고찰

This paper presents ride comfort characteristics of a quarter-vehicle magneto-rheological(MR) suspension system with respect to different tire pressure. As a first step, controllable MR damper is designed and modeled based on both the optimized damping force levels and mechanical dimensions required for a commercial full-size passenger vehicle. Then, a quarter-vehicle suspension system consisting of sprung mass, spring, tire and the MR damper is constructed. After deriving the equations of the motion for the proposed quarter-vehicle MR suspension system, vertical tire stiffness with respect to different tire pressure is experimentally identified. The skyhook controller is then implemented for the realization of the quarter-vehicle MR suspension system. Finally, the ride comfort analysis with respect to different tire pressure is undertaken in time domain. In addition, a comparative result between controlled and uncontrolled is provided by presenting vertical RMS displacement.

Optimization of reinforcement turn-up effect on tyre durability and operating characteristics for racing tyre design

The damage occurring around the tyre bead region has been pointed out as one of the causes of critical failure during the service life of a tyre. This study investigates the influence of the carcass (body) ply turn-up and bead reinforcement turn-up around the bead region on tyre durability and operating characteristics using finite element analysis (FEA). A slick motorsport tyre with two carcass plies was modelled in ABAQUS based on the material properties obtained from tests and the profile provided by the tyre manufacturer. Various factors including the material property, the cross-section area, the spacing and angles of the reinforcement cords and the height of reinforcement turn-up, were characterized by numerical experiments using the design of experiment (DOE) method. The effects of these parameters on tyre durability and operating characteristics, in terms of mean response analysis of carcass stress, vertical stiffness, lateral stiffness, cornering stiffness and the strain energy density (SED) of elements in the critical region, were determined from the finite element tyre model. Similarly, optimum reinforcement turn-up heights were obtained and provided predictive information for tyre design purpose. Furthermore it was observed, from both experiment and prediction, that the vertical stiffness was rather high for the requirement of the Formula Student (FS) racing car. In order to reduce the tyre vertical stiffness and improve the tyre durability, an improved tyre based on the original design but with single carcass ply was proposed. The FEA results on tyre durability and operating characteristics from both the original and improved design tyres were compared. The FEA predictions indicated that the improved design model was capable of providing the required tyre characteristics as well as improved tyre durability. It is therefore proposed that the predictive technology using FEA can be utilized to optimize the tyre reinforcement turn-up effect in future tyre design.

Performance evaluation of a quarter-vehicle MR suspension system with different tire pressure

This paper evaluates performance of a quarter-vehicle magneto-rheological (MR) suspension system with respect to different tire pressure. In order to achieve this goal, controllable MR damper that satisfies design specifications for a midsized commercial passenger vehicle is designed and manufactured based on the optimized damping force levels and mechanical dimensions. After experimentally evaluating the field-dependent characteristics of the manufactured MR damper, the quarter-vehicle suspension system consisting of sprung mass, spring, tire and the MR damper is constructed in order to investigate the ride comfort. After deriving the equations of the motion for the proposed quarter-vehicle MR suspension system, vertical tire stiffness with respect to different tire pressure is experimentally identified. The skyhook controller is then implemented for the realization of quarter-vehicle MR suspension system. Ride comfort characteristics such as vertical acceleration RMS (root mean square) and WRMS (weighted RMS) of sprung mass are evaluated under bump and random road conditions using a quarter-vehicle test facility.

Power dissipation in automotive suspensions

For a standard quarter-car vehicle model and a road disturbance whose velocity profile is white noise, it is shown that the power dissipated in the suspension is proportional to the tyre vertical stiffness and the noise intensity, but is independent of all masses and suspension parameters. The dependence of this result on the modelling assumptions is explored. It is shown that the road disturbance model is ill-posed for the computation of power dissipation in the tyre and a modification is suggested. Computational results then indicate that the total power dissipation is still very insensitive to variations in vehicle and suspension parameters, but not tyre parameters, even though the suspension power dissipation and the tyre power dissipation vary individually. The extension of the result to half-car vehicle models is also considered. For both the pitch-plane and roll-plane models, it is found from numerical examples that the broad conclusion of large dependence of the total power dissipation on tyre parameters and small dependence on all other parameters remains. A brief discussion is included on the contribution to power loss due to rolling resistance.

MR 댐퍼를 장착한 1/4차량의 타이어 공기압에 따른 성능분석

ABSTRACT This paper presents performance analysis of a quarter-vehicle magneto-rheological(MR) suspension system with respect to different tire pressure. As a first step, MR damper is designed and manufactured based on the optimized damping force levels and mechanical dimensions required for a commercial mid-sized passenger vehicle. After experimentally evaluating dynamic characteristics of the manufactured MR damper, the quarter-vehicle MR suspension system consisting of sprung mass, spring, tire and the MR damper is constructed in order to investigate the ride comfort. After deriving the equations of the motion for the proposed quarter-vehicle MR suspension system, vertical tire stiffness with respect to different tire pressure is experimentally identified. The skyhook controller is then implemented for the realization of quarter-vehicle MR suspension system. Ride comfort characteristics such as vertical acceleration RMS and weighted RMS of sprung mass are evaluated under various road conditions.

Ride comfort characteristics with different tire pressure of passenger vehicle featuring MR damper

This paper presents ride comfort characteristics of a quarter-vehicle magneto-rheological (MR) suspension system with respect to different tire pressure. As a first step, controllable MR damper is designed and manufactured based on the optimized damping force levels and mechanical dimensions required for a commercial mid-sized passenger vehicle. After experimentally evaluating dynamic characteristics of the manufactured MR damper, the quarter-vehicle suspension system consisting of sprung mass, spring, tire and the MR damper is constructed in order to investigate the ride comfort. After deriving the equations of the motion for the proposed quarter-vehicle MR suspension system, vertical tire stiffness with respect to different tire pressure is experimentally identified. The skyhook controller is then implemented for the realization of quarter-vehicle MR suspension system. Ride comfort characteristics such as vertical acceleration RMS of sprung mass are evaluated under bump road condition and presented in time domain.