Lateral tyre dynamic characteristics

The ability to model the ride vibration of unsuspended vehicles is at present seriously limited by lack of knowledge about the lateral and longitudinal dynamic characteristics of rolling tyres and the interaction of these characteristics with the ground surface. In this paper, models for the lateral dynamic behaviour of a rolling tyre are reviewed. The beam model, string model and spring-damper models are described and compared. A new lateral tyre model is introduced and tested against experimental results. This model comprises a parallel spring and hysteretic damping unit, representing the tyre carcass, in series with a viscous damper representing the interaction between the tyre and ground. Model justification was made against the measurements of lateral tyre response. The results showed that the proposed model provided more accurate prediction of lateral dynamic tyre response than the other spring-damper models.     

Analytical approach for the prediction of steady state tyre forces and moments under different normal pressure distributions

In general, all primary as well as disturbing forces acting on a vehicle (with the exception of aerodynamic forces) are generated at the tyre–road interface. The small size pneumatic tyres presented in this work are mostly used in lightweight vehicles like scooters, motor cycles and 3-wheelers that are extensively used for intercity transportation applications in India and other developing countries. Analytical approach is more advantage than experimental work due to many factors like it involves less cost, minimum time and little effort. Hence, Analytical tyre models are developed based on various normal pressure distributions with tyre contact patch as rectangle at the middle with part of circles at the ends. The tyre longitudinal and lateral force characteristic equations for proposed tyre models are developed. In addition, the equations for self – aligning moment and overturning moment characteristics for all tyre models are also derived. Results of proposed tyre models in the present study are compared with well-established earlier tyre models [4], [5], [6]. From the force and moment characteristics of all tyre models, unsymmetrical trapezoidal pressure distribution tyre model gives better performance than other models due to which better lateral stability of the vehicle can be obtained.     

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Parameterisation,validation and implementation of an all-terrain SUV FTire tyre model

This paper focuses on the parameterisation, validation and implementation of an FTire model of a Michelin LTX A/T² 235/85R16 tyre. This tyre is designed for both on- and off-road use and is commonly used on all wheel drive SUVs. Quasi-static laboratory and dynamic field tests were conducted to acquire parameterisation and validation test data for the FTire model. Quasi-static parameterisation tests include acquiring vertical tyre stiffness over a flat plate and cleats, tyre footprint sizes and shapes, longitudinal, lateral and torsional tyre stiffness for various tyre normal loads, as well as vibrational tyre responses. Dynamic parameterisation tests include dynamic cleat test data. An Adams model of the tyre testing equipment is implemented to simulate the FTire model and validate it against dynamic validation test results. Finally, the model is implemented on a fully nonlinear multi-body dynamics model of a Land Rover Defender. It is found that the FTire model is able to predict the lateral tyre behaviour well on a smooth road surface. The vertical and longitudinal tyre behaviour on a smooth road surface and on a rough surface are predicted accurately.     

TRT: thermo racing tyre a physical model to predict the tyre temperature distribution

In the paper a new physical tyre thermal model is presented. The model, called Thermo Racing Tyre (TRT) was developed in collaboration between the Department of Industrial Engineering of the University of Naples Federico II and a top ranking motorsport team. The model is three-dimensional and takes into account all the heat flows and the generative terms occurring in a tyre. The cooling to the track and to external air and the heat flows inside the system are modelled. Regarding the generative terms, in addition to the friction energy developed in the contact patch, the strain energy loss is evaluated. The model inputs come out from telemetry data, while its thermodynamic parameters come either from literature or from dedicated experimental tests. The model gives in output the temperature circumferential distribution in the different tyre layers (surface, bulk, inner liner), as well as all the heat flows. These information have been used also in interaction models in order to estimate local grip value.     

Off-road tyre modelling II: effect of camber on tyre performance

The problem of off-road vehicle tyre-terrain interaction is that it is difficult to model accurately. For an off-road vehicle over medium to firm terrain, the tyre load may be entirely supported by the tips of the lugs, or with a minimum carcass contact with the terrain. In this case, the effect of the lugs should be taken into consideration. The forces at the interface between lugged tyre and the soil, including normal and shear stresses, are discussed in this paper. The multi-spoke tyre model was developed to study the effect of tyre lugs on the forces between tyre and terrain and it has been extended to predict the tyre forces and moments in the case of combined lateral and longitudinal slip for a cambered tyre. The influence of slip angle, camber angle and soil hardness on off-road tyre performance has been investigated. A computer program was developed using MATLAB software. The results were derived as tyre forces and moments in the three directions along the tyre contact length. A comparison between the results of the multi-spoke tyre model of a smooth off-road tyre and an off-road tyre with straight lugs, in the cambered case, has been made. The results indicated that slip angle, camber angle and soil characteristics have a strong effect on off-road tyre performance. The modified mathematical model results help the off-road tyre engineering designers to predict accurate values of tyre forces and moments in this complex case.     

Net traction ratio prediction for high-lug agricultural tyre

A study was conducted to determine the accuracy of Wismer-Luth and Brixius equations in predicting net traction ratio of a high-lug agricultural tyre. The tyre was tested on a sandy clay loam soil in an indoor University Putra Malaysia (UPM) tyre traction testing facility. The experiment was conducted by running the tyre in driving mode. A total of 126 test runs were conducted in a combination consisting of three selected inflation pressures (i.e., 166, 193 and 221 kPa) and two wheel numerics (i.e., 19 and 29) representing two extreme types of soil strength under different levels of travel reduction ranging between 0% and 40%. Regression analysis was conducted to determine the prediction equation describing the tyre torque ratio. Marqurdt’s method used by Wismer-Luth for predicting non-linear equation was not found suitable in predicting the torque ratio of the test tyre awing its low coefficient of determination and inadequacy. The logarithmic model was found suitable in torque ration prediction. From analysis of covariance (ANCOVA) the mean effect of travel speed, tyre inflation pressure and wheel numeric on tyre net traction ratio were found to be highly significant, while the interaction of inflation pressure and wheel numeric was not significant. The 193 kPa inflation pressure was found the best, among the three inflation pressures used, in getting higher net traction ratio and higher maximum efficiency. Finally, two models were formulated for tyre net traction ratio; one in terms of wheel numeric and travel speed reduction and the other in terms of mobility number and travel reduction, to describe the tested tyre performance at different soil strengths.     

Green’s functions for a loaded rolling tyre

A new formulation to determine the unit impulse response (Green’s) functions of a loaded rotating tyre in the vehicle-fixed (Eulerian) reference frame for tyre/road noise predictions is presented. The proposed formulation makes use of the set of eigenfrequencies and eigenmodes for the statically loaded tyre obtained from a finite element (FE) model of the tyre. A closed-form expression for the Green’s functions of a rotating tyre in the Eulerian reference system as a function of the eigenfrequencies and eigenmodes of the statically loaded tyre is found. Non-linear effects during loading are accounted for in the FE model, while the frequency shift due to the rotational velocity is included in the calculation of the Green’s functions. In the literature on tyre/road noise these functions are generally used to determine the tyre response during tyre/road contact calculations. The presented formulation opens the possibility to solve the contact problem directly in the Eulerian reference frame and to include local tyre softening due to non-linear effects while keeping the computational advantage of describing the tyre dynamics as a set of impulse response functions. The advantage of obtaining the Green’s functions in the Eulerian reference system is that only the Green’s functions corresponding to the potential contact zone need to be determined, which significantly reduces the computational cost of solving the tyre/road contact and since the mesh is fixed in space, a finer mesh can be used for the potential contact zone, improving the accuracy of the contact force calculations. Although these effects might be less pronounced if a more accurate tyre model is used, it is found that using the Green’s functions of the loaded tyre in a contact force calculation leads to smaller forces than in the unloaded case, lower frequencies are present in the response and they decrease faster as the rotational velocity increases.     

Nonlinear optimization of a new polynomial tyre model

Tyre behaviour is strongly nonlinear. This article presents the validation of a new polynomial tyre model with real test data, analysing the convergence properties during the optimization process to calculate the values of the parameters. A multivariate model with 13 parameters is shown, including normal load and camber angle. The article reviews the methods of getting polynomial approximations of the magic formula tyre model used to develop the new polynomial model, the numerical optimization methods which calculate the parameters of the model from real test data, and it explains how the terms of the Jacobian matrix are modified when we impose constraints to the curve; this can be useful to improve the adjustment in some areas of the curve. The convergence properties are shown both for the magic formula tyre model and for this polynomial tyre model. The proposed model presents a fast convergence both in one and in three variables. This is an additional advantage to its excellent analytical properties, and the model is very easy to compute and can be easily derived and integrated. It is very well adapted for real-time computing.     

Tyre load capacity and energy loss with respect to varying soil support stiffness

An analytical model is developed to predict the tyre deformation and the resultant energy loss due to tyre flexibility relative to various soil stiffnesses ranging from rigid unyielding support to soft soil. The analysis allows for examination of a pneumatic tyre with respect to the wheel load to be carried, the supporting ground rigidity and the rigidity of the tyre casing. The important tyre characteristics in providing for wheel load capability under motion are demonstrated to be the tyre carcass construction, dimension, inflation pressure and the ability of the tyre casing to recover some of the resultant energy losses incurred by the tyre under motion.     

Modelling in FEM the soil pressures distribution caused by a tyre on a Rhodic Ferralsol soil

Tyre traffic over soil causes non-uniform ground pressures across the tyre width and along the soil–tyre contact area. The objective of this paper was to obtain in the topsoil the shape, magnitudes, distribution and transmission in depth of the ground pressures from a finite element model of soil compaction. The influence of tyre inflation pressure, tyre load and soil water content over the pressures propagation in the soil was analysed. The model shows how to low inflation pressure the tyre carcass supports most of the total load and the biggest peak pressures are distributed in the tyre axes when it traffics over firm soil. For high inflation pressure the incremented stiff causes that pressure is distributed with parabolic shape. In wet soil the inflation pressure does not influence on the ground pressure distribution, this depends only on the tyre load. The inflation pressure and tyre load changed the shape of the vertical pressures distribution on the surface of a hard dry soil, but these variables did not affect the distribution of vertical stresses in a soft wet soil or below a depth of 0.15 m.     

Effect of inflation pressure on motion resistance ratio of a high-lug agricultural tyre

A single wheel tyre facility at University Putra Malaysia (UPM) was used to check the validity of Wismer–Luth and Brixius equations in predicting the motion resistance ratio of a high-lug agricultural tyre and to investigate the effect of inflation pressure. A Bridgestone 5-12, 4 ply, lug M was tested on sandy-clay-loam soil. The experiments were conducted by running the tyre in towing mode. Three inflation pressures (i.e., 166, 193 and 221 kPa) were investigated and wheel numerics ranging between 0 and 70. The analysis of covariance (ANCOVA) revealed that both inflation pressure and wheel numeric have significant effects on tyre motion resistance ratio. Regression analysis was also conducted to determine the closeness of fit for Wismer–Luth’s and Brixius’ equations in predicting the motion resistance ratio of the tested tyre. Finally, three new logarithmic models for tyre motion resistance were formulated. The advantage of reducing tyre inflation pressure from 221 (nominal pressure) to 193 kPa on the motion resistance ratio of the high-lug agricultural tyre was pronounced. However, the tyre’s motion resistance ratio deteriorated with further reduction in tyre inflation pressure from 221 (nominal pressure) to 166 kPa.     

The Hohenheim Tyre Model: A validated approach for the simulation of high volume tyres – Part I: Model structure and parameterisation

The applied tyre model influences significantly the accuracy of vehicle simulations. This is especially the case for farm machinery that is equipped with high volume tyres and mostly suspended on one axle only. In order to account for the special properties of these tyres – such as the nonlinearities that come along with high deflections – a new tyre model was developed at the University of Hohenheim. During the development phase the main requirements to fulfil were short computation times, an easy to apply parameterisation process and a high model quality. In order to attain these goals an all new multi-spoke tyre model was developed. Various adaptations were made to the model structure in order to achieve a real-time factor of 0.6. All eighteen parameters have a physical meaning and can be determined with two in-house tyre test stands. Validation comprises aspects relevant to both handling and ride quality and will be addressed in part two of this publication series.     

Tractive characteristics of radial ply and bias ply tyres in a California soil

Four tyres (18.4-38, 18.4R38, 14.9-28, 14.9R28) were tested using the UCD single wheel traction tester. Each tyre was tested at two different inflation pressures and three different vertical loads at each inflation pressure. All tests were conducted in a well tilled Yolo loam soil. A dimensional analysis procedure was used to design and analyse the experiment. Two models were considered: (A) using inflation pressure as a variable, and (B) using tyre deflection as a variable. The effect of tyre type, tyre size, tyre inflation pressure and dynamic load on (1) net traction ratio at 20% slip and (2) average tractive efficiency in the 0–30% slip range were investigated using an ANOVA technique. An estimate of the possible energy savings due to the use of radial ply tyres instead of bias ply tyres in California agriculture was made.     

The influence of tyres on the dynamic behaviour of a lawn mower

Agricultural tractors are used for on-road and off-road transport purposes, for supplying the necessary power during field operations and for controlling the mounted implements. Unfortunately, soil undulations induce tractor and machine vibrations, reducing driver's comfort and their capability of controlling the linked machinery. In this introductory study, the effect of some characteristics parameters, such as tyre pressure, and herewith related tyre stiffness, and mass addition on the dynamic behaviour and, more specifically, on the resonance frequencies of a lawn mower, are analysed by experimental modal analysis. After adapting the modal model, field unevenness instead of disturbance forces could be introduced as excitation inputs. A final validation of the adapted modal models shows good agreement with measured lawn mower vibrations.     

Experimental observations of tyre deformation characteristics on heavy mining vehicles under static and quasi-static loading

Due to large sidewall and bead thicknesses, multi-piece rims are necessary for use with large off-the-road (OTR) tyres. This paper presents the testing protocol and observed load/deflection and vertical/sidewall deflection characteristics of three Goodyear OTR tyre assemblies, namely, (1) a radial 29.5R29 (2) a bias-ply 29.5-29, and (3) a bias-ply 26.5-26. Localized tyre deformations and rim displacements were measured using optical displacement transducers and post-processing high-speed camera images using digital image analysis software. A validation analysis illustrated a maximum difference of 4.05% of vertical wheel displacements between the aforementioned methods. Quasi-static tests show the maximum values of vertical rim displacement and lateral tyre deflection are in the range of 72.2–78.9 mm and 23.3–27.1 mm, respectively, for a severe excitation condition. Differences ranging from 0.2% to 21.5% for maximum vertical and lateral tyre deflections were found between static load tests and engineering data provided by the tyre manufacturer. Linear relationships were observed for both vertical wheel displacement and lateral tyre deflection versus load for all tests. This study demonstrates a thorough methodology to study deflection characteristics of heavy duty OTR tyres and the collected data could be very useful in the development of numerical models of wheel and tyre assemblies for mining vehicles.     

Tyre Wear Model: Validation and Sensitivity Analysis

Due to their many economic and ecological implications the possibility to predict tyre wear is of major importance to tyre manufacturers, fleet owners and governments. Based on these observations, in 2000 a three-year project named Tyre and Road Wear and Slip assessment (TROWS) was started. One of the TROWS objectives was to provide a tool able to numerically predict tyre global wear as well as to qualitatively determine the wear distribution. The proposed methodology combines a mathematical model of the tyre with an experimentally determined local friction and wear law. Thus, tyre abrasion due to each single manoeuvre can be determined. Full-scale experimental tests were carried out with two Peugeot 406 cars on a public road course in Italy. Each car was equipped with a different set of tyres: one car was equipped with four all-season tyres (from now on called A tyres) and the other car was equipped with four winter tyres (from now on called B tyres). Both sets of tyres had a 195/65 R15 size. The collected data was used to validate the model. The methodology proved to give qualitatively good tyre wear predictions.     

Nonlinear analysis of a shimmying wheel with contact-force characteristics featuring higher-order discontinuities

In this study, the yaw dynamics of a towed caster wheel system is analysed via an in-plane, one degree-of-freedom mechanical model. The force and aligning torque generated by the elastic tyre are calculated by means of a semi-stationary tyre model, in which the piecewise-smooth characteristic of the tyre forces is also considered, resulting in a dynamical system with higher-order discontinuities. The focus of our analysis is the Hopf bifurcation affected by the non-smoothness of the system. The structure of the analysis is organised in a similar way as in case of smooth bifurcations. Firstly, the centre-manifold reduction is performed, then we compose the normal form of the bifurcation. Based on the Galerkin technique an approximate, semi-analytical method to calculate the limit cycles is introduced and compared with the method of collocation. The analysis provides a deeper insight into the development of the vibrations associated with wheel shimmy and demonstrate how the non-smoothness due to contact-friction influences the dynamic behaviour.