Tire Stiffness Research Articles

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.

A stochastic quarter-car model for dynamic analysis of vehicles with uncertain parameters

A quarter-car model is used to investigate the vibration response of cars with uncertainty under random road input excitations in this paper. The sprung mass, unsprung mass, suspension damping, suspension stiffness, and tyre stiffness are considered as random variables. The road irregularity is considered a Gaussian random process and modelled by means of a simple exponential power spectral density. The power spectral density, mean value, standard deviation, and variation coefficient of the vehicle's natural frequencies and mode shapes are obtained by using the Monte Carlo simulation method. The computational expressions for the numerical characteristics of the mean square value of the vehicle's random response in the frequency domain are developed by means of the random variable's functional moment method. The influences of the randomness of the vehicle's parameters on the vehicle's dynamic response are investigated in detail using a practical example, and some useful conclusions are obtained.

Friction and camber influences on the static stiffness properties of a racing tyre

Investigation of the stationary load—deflection behaviour of tyres reveals many details of the structure and the rubber-to-road friction properties. These characteristics are fundamental to the understanding of the behaviour of both the stationary and the rolling tyre. In connection with racing, tyre static stiffness characteristics are of interest as they reflect on the controllability of the vehicle to which they are fitted. In this paper, the construction of a finite element (FE) model capable of predicting the static tyre behaviour in great detail is presented. The model is validated against extensive experimental data, including contact pressure distributions and load—deflection characteristics. Static loading tests, which involve variations in the friction rules coupling tread rubber with the ground surface, and in wheel camber angle, are simulated with the tyre model. The results of the simulations reveal that a friction coefficient of 0.5 is sufficient to prevent sliding in static loading tests for this particular tyre. Lower levels of friction lead to tread sliding and reduced vertical tyre stiffness. Sliding is primarily lateral, leading to narrowing of the contact patch of the tyre. Narrowing also increases the local sidewall curvature, which is part of the softening mechanism for both upright and cambered tyres.

DESIGN OPTIMIZATION OF VEHICLE SUSPENSIONS WITH A QUARTER-VEHICLE MODEL

This paper presents a comparative study of three optimization algorithms, namely Genetic Algorithms (GAs), Pattern Search Algorithm (PSA) and Sequential Quadratic Program (SQP), for the design optimization of vehicle suspensions based on a quarter-vehicle model. In the optimization, the three design criteria are vertical vehicle body acceleration, suspension working space, and dynamic tire load. To implement the design optimization, five parameters (sprung mass, un-sprung mass, suspension spring stiffness, suspension damping coefficient and tire stiffness) are selected as the design variables. The comparative study shows that the global search algorithm (GA) and the direct search algorithm (PSA) are more reliable than the gradient based local search algorithm (SQP). The numerical simulation results indicate that the design criteria are significantly improved through optimizing the selected design variables. The effect of vehicle speed and road irregularity on design variables for improving vehicle ride quality has been investigated. A potential design optimization approach to the vehicle speed and road irregularity dependent suspension design problem is recommended.

Dynamic analysis of vehicles with uncertainty

The probabilistic and interval dynamic analysis of cars with uncertain parameters under random road input excitations by using a two-degree-of-freedom car model are presented in this paper. In the probabilistic analytical model, the vehicle parameters, including the sprung mass, unsprung mass, suspension damping, suspension, and tyre stiffness, are considered as random variables. The mean value, standard deviation, and variation coefficient of the vehicle's natural frequencies and mode shapes are obtained by using the Monte Carlo simulation method. Then, the computational expressions for the numerical characteristics of the mean square value of the vehicle's random response in the frequency domain are developed by means of the random variable's functional moment method. Considering the vehicle parameters as interval variables, the lower bound, upper bound, and interval change ratio value of the vehicle's random responses are obtained by means of the interval operations. The influences of the uncertainty of the vehicle parameters on the vehicle's natural frequencies, mode shapes, and dynamic responses are investigated in detail using a practical example. The comparison of the vehicle's dynamic characteristics using the probabilistic and interval analysis are also demonstrated.

Robust controller design for active suspensions using particle swarm optimisation

The paper presents a design technique for a fixed-structure PD robust controller of car active suspension systems. The design takes into consideration the uncertainty of system parameters, particularly tyre stiffness and body mass. Robustness is achieved by tuning the controller over a set of operating conditions covering the whole range of system parameters, e.g., body mass and tyre stiffness. Particle swarm optimisation (PSO) is used to attain different performance objectives of the system. Settling time of body displacement is minimised, system damping is maximised, and actuator saturation is avoided via control effort reduction. The design of controller parameters is cast in a multi-objective non-linear optimisation problem, and described to ensure the best possible performance. Simulation results show the superiority of the proposed system relative to the classical passive suspension, and signify robustness of the active controller design.

Dynamic models and parameter identification of a heavy-duty autonomous vehicle

In this paper, we investigate the dynamic motion of an autonomous vehicle for container transportation. This vehicle has a configuration of four wheel steering and driving. It is used for transportation of containers up to 50 tons and in a seaport environment. Dynamic models are developed in three coordinate frames and parameters are identified using experimentally recorded data. Factors, such as tyre stiffness and friction, have been taken into account. Comparisons between the recorded data and model-based simulation results verify the developed models.

A Tire Stiffness Backstepping Observer Dedicated to All-Terrain Vehicle Rollover Prevention

Most active devices focused on vehicle stability concern on-road cars and cannot be applied satisfactorily in an off-road context, since the variability and the non-linearities of tire/ground contact are often neglected. In previous work, a rollover indicator devoted to light all-terrain vehicles accounting for these phenomena has been proposed. It is based on the prediction of the lateral load transfer. However, such an indicator requires the on-line knowledge of the tire cornering stiffness. Therefore, in this paper, an adapted backstepping observer, making use only of yaw rate measurement, is designed to estimate tire cornering stiffness and to account for its non-linearity. The capabilities of such an observer are demonstrated and discussed through both advanced simulations and actual experiments.

Second order sliding-mode observer for estimation of vehicle dynamic parameters

This paper uses second-order sliding mode observers to build up an estimation scheme allowing to identify the tyre longitudinal equivalent stiffness and the effective wheel radius using the existing ABS angular sensors. This estimation strategy, based on use of the proposed observer could be used with data acquired experimentally to identify the longitudinal stiffness and effective radius of vehicle tyres. The actual results show effectiveness and robustness of the proposed method.

New sidewall contour for evaluation of sidewall’s rotational stiffness of a radial tire

In this paper, we revisit the netting theory for the estimation of the rotational stiffness of sidewall of radial tires and suggest a new sidewall contour for evaluation of the rotational stiffness due to cord tension since the conventional theoretical curve does not fit the real curve in the interval near to a bead point. A new sidewall contour is constructed by combining the conventional curve in the interval near to the tread end and the quadratic curve in the interval near to the bead point. The new sidewall contour makes it possible to represent the real sidewall contour more accurately than the conventional one. The netting analysis using the new sidewall contour yields improved stiffness. We have illustrated the above facts by applying the new sidewall contour to a radial tire of P205/60R15 and have compared its rotational stiffness with an experimental one.

Truck fleet model for design and assessment of flexible pavements

The mechanistic empirical method of flexible pavement design/assessment uses a large number of numerical truck model runs to predict a history of dynamic load. The pattern of dynamic load distribution along the pavement is a key factor in the design/assessment of flexible pavement. While this can be measured in particular cases, there are no reliable methods of predicting the mean pattern for typical traffic conditions. A simple linear quarter car model which aims to reproduce the mean and variance of dynamic loading of the truck fleet at a given site is developed here. This probabilistic model reflects the range and frequency of the different heavy trucks on the road and their dynamic properties. Multiple Sensor Weigh-in-Motion data can be used to calibrate the model. Truck properties such as suspension stiffness, suspension damping, sprung mass, unsprung mass and tyre stiffness are represented as randomly varying parameters in the fleet model. It is used to predict the statistical distribution of dynamic load at each measurement point. The concept is demonstrated by using a pre-defined truck fleet to calculate a pattern of statistical spatial repeatability and is tested by using that pattern to find the truck statistical properties that generated it.

On the impact of cargo weight, vehicle parameters, and terrain characteristics on the prediction of traction for off-road vehicles

A realistic prediction of the traction capacity of vehicles operating in off-road conditions must account for stochastic variations in the system itself, as well as in the operational environment. Moreover, for mobility studies of wheeled vehicles on deformable soil, the selection of the tire model used in the simulation influences the degree of confidence in the output. Since the same vehicle may carry various loads at different times, it is also of interest to analyze the impact of cargo weight on the vehicle’s traction. This study focuses on the development of an algorithm to calculate the tractive capacity of an off-road vehicle with stochastic vehicle parameters (such as suspension stiffness, suspension damping coefficient, tire stiffness, and tire inflation pressure), operating on soft soil with an uncertain level of moisture, and on a terrain topology that induces rapidly changing external excitations on the vehicle. The analysis of the vehicle–soil dynamics is performed for light cargo and heavy cargo scenarios. The algorithm relies on the comparison of the ground pressure and the calculated critical pressure to decide if the tire can be approximated as a rigid wheel or if it should be modeled as a flexible wheel. It also involves using previously-developed vehicle and stochastic terrain models, and computing the vehicle sinkage, resistance force, tractive force, drawbar pull, and tractive torque. The vehicle model used as a case study has seven degrees of freedom. Each of the four suspension systems is comprised of a nonlinear spring and a viscous (linear or magneto-rheological) damper. An off-road terrain profile is simulated as a 2-D random process using a polynomial chaos approach [Sandu C, Sandu A, Li L. Stochastic modeling of terrain profiles and soil parameters. SAE 2005 transactions. J Commer Vehicles 2005-01-3559]. The soil modeling is concerned with the efficient treatment of the impact of the moisture content on relationships critical in defining the mobility of an off-road vehicle (such as the pressure–sinkage [Sandu C et al., 2005-01-3559] and the shear stress–shear displacement relations). The uncertainties in vehicle parameters and in the terrain profile are propagated through the vehicle model, and the uncertainty in the output of the vehicle model is analyzed [Sandu A, Sandu C, Ahmadian M. Modeling multibody dynamic systems with uncertainties. Part I: theoretical and computational aspects, Multibody system dynamics. Publisher: Springer Netherlands; June 29, 2006. p. 1–23 (23), ISSN: 1384-5640 (Paper) 1573-272X (Online). doi:10.1007/s11044-006-9007-5; Sandu C, Sandu A, Ahmadian M. Modeling multibody dynamic systems with uncertainties. Part II: numerical applications. Multibody system dynamics, vol. 15, No. 3. Publisher: Springer Netherlands; 2006. p. 241–62 (22). ISSN: 1384-5640 (Paper) 1573-272X (Online). doi:10.1007/s11044-006-9008-4]. Such simulations can provide the basis for the study of ride performance, handling, and mobility of the vehicle in rough off-road conditions.

The quantitative analysis and experimental verification of the tire static enveloping model using experimental modal parameters

Tire modal parameters reflect the natural properties of the tire. In the work by Dihua and Chengjian [Dihua, G. and Chengjian, F., 2003, Tire modeling for vertical properties including enveloping properties using experimental modal parameters. Vehicle System Dynamics, 40(6), 419–433], the tire-enveloping model established using experimental modal parameters can give a good quantitative description of the tire-enveloping phenomenon. On the basis of this description, this article deals with the quantitative analysis of the model with the modal order numbers taken into account and also considering the tire side wall non-linear stiffness. Comparison between the calculated results and those of an experiment specially carried out shows good agreement in every aspect. For example, the vertical stiffness errors are 4.67% and 10.6% for small (36% of load index) and very large (162% of load index) vertical loads, respectively; the maximum footprint length error is 6.48%; and the error of wheel center height fluctuation at the peak and valley of enveloping property characteristics with constant vertical load is 8%, and it is 9% of the vertical loads for corresponding characteristics with constant wheel center height. The analysis shows that the side wall non-linear stiffness plays an important role in the quantitative agreement between the calculations and the results of the experiment.

New evaluation and test of sidewall’s rotational stiffness of radial tire

In this paper, we have revisited the estimation of the rotational stiffness of sidewall of radial tire and have suggested a new method for evaluation of the rotational stiffness. Since thicknesses, and volume fractions of the constituents of sidewall are varied depending on radial position, the equivalent shear modulus of the sidewall also depends on radial position. For the estimation of rotational stiffness of sidewall’s rubber, we have divided its cross-section into sufficient numbers of small parts and have calculated the equivalent shear modulus of each part of sidewall. Using the shear moduli of divided parts, we have obtained the rotational stiffness by employing inplane shear deformation theory. This method is expected to be a useful tool in tire design since it relates such basic variables to the global stiffness of tire. Applying the calculation method to a radial tire of P205/60R15, we have compared its rotational stiffness with experimental one.

Computer modeling of lift trucks and operators to simulate lateral tipover

Lift truck lateral tipovers are mostly caused by its intrinsic instability. The objective of this paper was to develop a computer model of a parametric lift truck and its driver in order to simulate lateral tipover. For this, a biomechanical model of a driver (50th percentile Hybrid III dummy), a parametric lift truck (156 parameters), as well as the interface (contacts) between them and the ground were developed using the MADYMO multibody software. Two different rollover conditions were simulated: at rest (0 km/h) and high speed (20 km/h). Seven parameters (tire, ground and seat foam stiffnesses, lift truck angular and linear velocities, braking deceleration, and curve radius of a J turn) were tested to assess their influence on the vehicle and driver behaviors during rollover. Head and torso velocities and accelerations, as well as the Head Injury Criterion (HIC), were used to compare simulation results and to evaluate driver's possible traumatisms and survival probability. A realistic kinematic behavior of the models was obtained: Tire and ground stiffnesses have little influence on driver's behavior and safety. Soft foam seat has a more significant effect, but the HIC is always very high. Angular and linear velocities of the lift truck have a very large impact on operator injuries. Braking tends to minimize injury and lift truck never rolls over in larger curve radius (r > 4m).

Effect of Truck Suspension and Tire Properties on Pavement Damage Spatial Distribution

Strain energy is stored within pavement by a measured distribution of heavy vehicle traffic. A simulation methodology based on this strain energy is proposed to study the spatial distribution of pavement damage. Stored energy in the model depends on the magnitude and speed of the tire loads and on the pavement response. Pavement response is a function of different asphalt binder and mix properties, including temperature, softening temperature, void content, and penetration index. Aggregated stored energy for measured heavy vehicle traffic is obtained in terms of suspension stiffness and damping and tire stiffness properties. A pavement-traffic model is derived after linear in-plane vehicle models are integrated with the distributed pavement model. The accumulated stored energy is compared with AASHO test data to validate the proposed methodology. Results for the spatial concentration of the potential road damage revealed that normalized-to-average difference between the maximum and minimum values for pave...

Effect of Truck Suspension and Tire Properties on Pavement Damage Spatial Distribution

Strain energy is stored within pavement by a measured distribution of heavy vehicle traffic. A simulation methodology based on this strain energy is proposed to study the spatial distribution of pavement damage. Stored energy in the model depends on the magnitude and speed of the tire loads and on the pavement response. Pavement response is a function of different asphalt binder and mix properties, including temperature, softening temperature, void content, and penetration index. Aggregated stored energy for measured heavy vehicle traffic is obtained in terms of suspension stiffness and damping and tire stiffness properties. A pavement–traffic model is derived after linear in-plane vehicle models are integrated with the distributed pavement model. The accumulated stored energy is compared with AASHO test data to validate the proposed methodology. Results for the spatial concentration of the potential road damage revealed that normalized-to-average difference between the maximum and minimum values for pavement potential damage along the road profile is a function of pavement roughness, with average values of approximately 45%, 20%, and 11.5% for rough, medium-rough, and smooth pavements, respectively. Variations in normalized road damage concentration because of changing suspension and tire properties are from 40% to 50% for a rough pavement, from 18% to 22% for a medium-rough pavement, and from 9% to 14% for a smooth pavement.

Consistent nonlinear estimation of longitudinal tire stiffness and effective radius

This paper presents two effectively unbiased nonlinear estimation schemes which identify tire longitudinal stiffness and effective radius using Global Positioning System (GPS) and antilock braking system (ABS) wheelspeed sensors. A nonlinear approach is taken as one possible approach of eliminating the well known biases that linear least squares algorithms introduce for this problem. These new estimation strategies are then used to experimentally identify the longitudinal stiffness and effective radius of a summer tire and a winter tire under several different test conditions. The data clearly shows that there are several important parameters which govern tire longitudinal stiffness behavior in the low slip region. At a minimum, inflation pressure, tread depth, normal loading and temperature have a strong influence on longitudinal stiffness estimates; the change from dry to wet asphalt had the smallest effect on longitudinal stiffness estimates.

A Simplified Model for Predicting the Pneumatic Stiffness of Conventional and Multi-Cell Inflation Mechanisms for Off-Road Tires

Abstract An efficient yet reliable model is developed to predict the static stiffness of pneumatic off-road motorcycle tires inflated by both traditional and non-traditional inflation mechanisms. The model does not include tire sidewall or carcass structural stiffness effects; instead, only the pneumatic component resulting from pressure and volume changes is considered. Model predictions are verified via experimentally measured static stiffness and internal tire pressure data. The analytical and experimental data presented compare the static stiffness behavior of an off-road motorcycle tire inflated with a traditional inner tube to the static stiffness behavior of the same tire inflated by a novel flat-proof inflation system composed of discrete air cells. Results show that the flat-proof inflation system produces performance enhancing static stiffness characteristics over those of the conventional inner tube.

A static-output-feedback design procedure for robust emergency lateral control of a highway vehicle

A linear matrix inequality (LMI)-based procedure for the design of robust static-output-feedback controllers is demonstrated on the problem of emergency lateral control of a highway vehicle with bounded time-varying uncertainties. A linear time-varying (LTV) tire model is used with a yaw-plane model of a highway vehicle to express the problem of emergency lateral control. The vehicle system is parameterized for variation in speed between (15 m/s and 30 m/s) and independent variation of front and rear effective lateral tire stiffnesses (between 30 kN/rad and 60 kN/rad) to form a polytope of linear systems. A stabilizing static-output-feedback controller is designed and its gains are reduced while guaranteeing robust stability.