Analytical and finite element modelling of the dynamic interaction between off-road tyres and deformable terrains

Automotive tyres are one of the main components of a vehicle and have an extremely complex structure consisting of several types of steel reinforcing layers embedded in hyperelastic rubber materials. They serve to support, drive – accelerate and decelerate – and steer the vehicle, and to reduce transmitted road vibrations. However, driving is associated with certain types of pollution due to CO2 emissions, various particles due to tyre wear, as well as noise. The main source of CO2 emissions is the tyre rolling resistance, which accounts for roughly 30% of the fuel consumed by cars. The phenomenon becomes more pronounced in off-road conditions, where truck vehicles are responsible for about a quarter of the total CO2 emissions. Appropriate legislation has been introduced, to control all of these pollution aspects. Therefore, tyre simulation (especially in off-road conditions) is essential in order to achieve a feasible design of a vehicle, in terms of economy and safety. [Continues.

Pneumatic tyres interacting with deformable terrains

In this study, a numerical model of a deformable tyre interacting with a deformable road has been developed with the use of the finite element code ABAQUS (v. 6.13). Two tyre models with different widths, not necessarily identical to any real industry tyres, have been created purely for research use. The behaviour of these tyres under various vertical loads and different inflation pressures is studied, initially in contact with a rigid surface and then with a deformable terrain. After ensuring that the tyre model gives realistic results in terms of the interaction with a rigid surface, the rolling process of the tyre on a deformable road was studied. The effects of friction coefficient, inflation pressure, rebar orientation and vertical load on the overall performance are reported. Regarding the modelling procedure, a sequence of models were analysed, using the coupling implicit – explicit method. The numerical results reveal that not only there is significant dependence of the final tyre response on the various initial driving parameters, but also special conditions emerge, where the desired response of the tyre results from specific optimum combination of these parameters

Finite element modelling of a pneumatic tyre interacting with rigid road and deformable terrain

In this study, the dynamic interaction between a pneumatic P235/75R17 tyre and a rigid and/or deformable rolling surface is analysed using the finite element method. After a footprint analysis of the tyre, two models were developed: (a) tyre rolling on rigid road with bumps and (b) tyre rolling on the surface of a soft soil layer, appropriate for off-road vehicle handling. In the first model, a steady-state transport analysis is performed to obtain the free rolling conditions of the tyre, which are then used to simulate the impact of the tyre on a rigid bump, typical of a road cleat or speedbump. In the second model, the transient rolling response of the tyre on a soft cohesive soil layer was simulated under towed and driven conditions. Along with a concise literature review and detailed description of the numerical models considered, various response quantities along with deformed geometries are provided throughout the text. It is finally shown that the dynamic response of the rolling tyre and its interaction with the deformable soil is inherently complex and depends on many parameters, whereas it is proven that the overall performance of the off-road tyres depends on significantly different parameters from that of the on-road tyres

Dynamic response of rigid wheels on deformable terrains

Off-road vehicle performance, such as vehicle mobility, maneuverability, and traction performance is generally affected by the pneumatic tyre-off-road terrain interaction. Modelling of such cases is usually based on empirical and semi-empirical solutions, which have limited applicability in real situations due to their inherent weaknesses. In this study, numerical simulation of the dynamic mobility of a rigid wheel on a deformable terrain is performed through a series of transient nonlinear dynamic finite element analyses with the use of the finite element code ABAQUS (v. 6.13). The dynamic interaction of a rigid wheel with the underlying soil during off-road vehicle travel is simulated. The effects of the vertical load carried by the wheel, the tread pattern, the longitudinal and lateral tread parameters, and the slip ratio of the wheel on the wheel performance are investigated and useful results are extracted. The numerical results reveal that the effects of the tread pattern, particularly tread depth and the terrain constitutive properties, such as soil cohesion can be of high importance for the general wheel response

Development of accurate pneumatic tyre finite element models based on an optimization procedure

A novel method for extracting the geometric and constitutive material properties of pneumatic tyres from available numerical or experimental data for the development of realistic and reliable tyre numerical models is proposed. This method involves an optimization procedure, which incorporates a finite element model as a solver (ABAQUS) properly coupled with an optimiser function (MATLAB). Following that, an initial tyre model (P235/75R17) is developed, and then its properties are suitably adjusted via the optimization process, in order for the former to best fit a target model available in the literature, with respect to eigenfre-quency analysis results. After the termination of the algorithm, the “optimum” tyre model (i.e. the model which best conforms to the target model) is obtained, the response of which is further investigated to ensure its realistic behaviour, which warrants its use for various numerical simulations. The results of this study show clearly the efficiency of the optimization procedure proposed, as well as the realistic response of the tyre model developed

Dynamic response of rigid wheels on deformable terrains

Off-road vehicle performance, such as vehicle mobility, maneuverability, and traction performance is generally affected by the pneumatic tire-off-road terrain interaction. Modeling of such cases is usually based on empirical and semi-empirical solutions, which have limited applicability in real situations due to their inherent weaknesses. In this study, numerical simulation of the dynamic mobility of a rigid wheel on a deformable terrain is performed through a series of transient nonlinear dynamic finite element analyses with the use of the finite element code ABAQUS (v. 6.13). The dynamic interaction of a rigid wheel with the underlying soil during off-road vehicle travel is simulated. The effects of the vertical load carried by the wheel, the tread pattern, the longitudinal and lateral tread parameters, and the slip ratio of the wheel on the wheel performance are investigated and useful results are extracted. The numerical results reveal that the effects of the tread pattern particularly tread depth and the terrain constitutive properties, such as soil cohesion can be of high importance for the general wheel response

Off-road tire-terrain interaction: an analytical solution

A novel semi-analytical solution has been developed for the calculation of the static and dynamic response of an off road tire interacting with a deformable terrain, which utilizes soil parameters independent of the size of the contact patch (size-independent). The models involved in the solution presented, can be categorized in rigid and/or pneumatic tires, with or without tread pattern. After a concise literature review of related methods, a detailed presentation of the semi-analytical solution is presented, along with assumptions and limitations. A flowchart is provided, showing the main steps of the numerical implementation, and various test cases have been examined, characterized in terms of vertical load, tire dimensions, soil properties, deformability of the tire, and tread pattern. It has been found that the proposed model can qualitatively capture the response of a rolling wheel on deformable terrain