A rolling resistance estimate using nonlinear finite element numerical analysis of a full three-dimensional tyre model

Abstract

In accordance with the worldwide trend for developing energy-efficient vehicles and meeting environmental regulations, there exists a large potential for decreasing energy losses due to tyre rolling resistance and significantly reduce fuel consumption and greenhouse gas emissions and also improve tyre tread durability. To achieve a quantitative estimate of tyre rolling resistance force, in the present paper, we carry out rolling resistance modelling in order to introduce a comprehensive relation for predicting rolling resistance force variations with speed taking into account the most influential parameters. To accomplish this goal, full three-dimensional finite element modelling of a visco-hyperelastic inflated rubber tyre under the deformation of vertical loading is performed and validated by making use of available test data. Free rolling simulations are performed and rolling resistance diagrams at various vehicle speeds and inflation pressures are extracted by analysing the results. According to the simulation results, a general formula is suggested to predict the tyre rolling resistance force in terms of the influential factors such as velocity, inflation pressure and tyre load. Results obtained using the proposed equation compared with recorded coast down test data clearly indicate excellent agreement between the results, confirming the validity of the relation. The presented solution can be built into models for comprehensive techno-economic evaluation of vehicle performance and fuel economy where changes in velocity, load and inflation pressure can be considered.

A novel method to improve vehicle energy efficiency: Minimization of tire power loss

“…As tire inflation pressure changes, tire slip stiffness would change due to increase or decrease of contact patch length. 47,48 An under inflated tire has a larger contact patch length and a smaller f l , according to equation (24). As it is shown in Figure 8, in case of a inflation pressure change, all of the normalized tire slip coefficients, i.e., f l , f l1 , and f l2 , show indistinguishable behavior.…”

“…Although the shape of F-l curve changes as coefficient of friction varies, the slope at the origin remains constant. It can be also figured out from equation (24) that the slope at origin does not depend on coefficient of friction. Changes of normalized tire slip coefficients are shown in Figure 6.…”

“…When normal force changes, the peak point in F-l diagram changes together with curve slope at the origin due to change of contact patch length. Recalling equation (24), it is obvious that f l decreases when the contact patch length (= 2a) increases due to a larger normal force. Therefore, normal force would affect f l2 as well as f l and f l1 .…”

“…In this field, the well-known tire rolling resistance has been investigated in detail. Several studies 22–24 have conducted experiments to evaluate rolling resistance. Studies in the field of tire influence on fuel efficiency 25–27 have concentrated on rolling resistance.…”

Experimental and theoretical analysis of high-speed radial tire standing waves

“…In the three-dimensional model, various rubber materials are represented by isotropic incompressible C3D8RH elements. The hyperelastic model is used to describe the stress-strain relationship of the rubber material [22]. The number of carcass rubber units in the finite element model is 10,721, and the number of belt and cord layer units is 10,102.…”