Fractional Calculus Approach to Reproduce Material Viscoelastic Behavior, including the Time–Temperature Superposition Phenomenon

The design of modern products and processes cannot prescind from the usage of viscoelastic materials that provide extreme design freedoms at relatively low cost. Correct and reliable modeling of these materials allows effective use that involves the design, maintenance, and monitoring phase and the possibility of reuse and recycling. Fractional models are becoming more and more popular in the reproduction of viscoelastic phenomena because of their capability to describe the behavior of such materials using a limited number of parameters with an acceptable accuracy over a vast range of excitation frequencies. A particularly reliable model parametrization procedure, using the poles-zeros formulation, allows researchers to considerably reduce the computational cost of the calibration process and avoid convergence issues typically occurring for rheological models. The aim of the presented work is to demonstrate that the poles-zeros identification methodology can be employed not only to identify the viscoelastic master curves but also the material parameters characterizing the time-temperature superposition phenomenon. The proposed technique, starting from the data concerning the isothermal experimental curves, makes use of the fractional derivative generalized model to reconstruct the master curves in the frequency domain and correctly identify the coefficients of the WLF function. To validate the methodology, three different viscoelastic materials have been employed, highlighting the potential of the material parameters' global identification. Furthermore, the paper points out a further possibility to employ only a limited number of the experimental curves to feed the identification methodology and predict the complete viscoelastic material behavior

Review on friction and wear test rigs: An overview on the state of the art in tyre tread friction evaluation

The future evolution of autonomous mobility and road transportation will require substantial improvements in tyre adherence optimization. As new technologies being deployed in tyre manufacturing reduce total vehicle energy consumption, the contribution of tyre friction for safety and performance enhancement continues to increase. For this reason, the tyre’s grip is starting to drive the focus of many tyre developments nowadays. This is because the tread compound attitude to maximize the interaction forces with the ground is the result of a mix of effects, involving polymer viscoelastic characteristics, road roughness profiles and the conditions under which each tyre works during its lifespan. In such a context, mainly concerning the automotive market, the testing, analysis and objectivation of the friction arising at the tread interface is performed by means of specific test benches called friction testers. This paper reviews the state of the art in such devices’ development and use, with a global overview of the measurement methodologies and with a classification based on the working and specimen motion principle. Most tyre friction testers allow one to manage the relative sliding speed and the contact pressure between the specimen and the counter-surface, while just some of them are able to let the user vary the testing temperature. Few devices can really take into account the road real roughness, carrying out outdoor measurements, useful because they involve actual contact phenomena, but very complex to control outside the laboratory environment

Cross-combined UKF for vehicle sideslip angle estimation with a modified Dugoff tire model: design and experimental results

Abstract: The knowledge of key vehicle states is crucial to guarantee adequate safety levels for modern passenger cars, for which active safety control systems are lifesavers. In this regard, vehicle sideslip angle is a pivotal state for the characterization of lateral vehicle behavior. However, measuring sideslip angle is expensive and unpractical, which has led to many years of research on techniques to estimate it instead. This paper presents a novel method to estimate vehicle sideslip angle, with an innovative combination of a kinematic-based approach and a dynamic-based approach: part of the output of the kinematic-based approach is fed as input to the dynamic-based approach, and vice-versa. The dynamic-based approach exploits an Unscented Kalman Filter (UKF) with a double-track vehicle model and a modified Dugoff tire model, that is simple yet ensures accuracy similar to the well-known Magic Formula. The proposed method is successfully assessed on a large amount of experimental data obtained on different race tracks, and compared with a traditional approach presented in the literature. Results show that the sideslip angle is estimated with an average error of 0.5 deg, and that the implemented cross-combination allows to further improve the estimation of the vehicle longitudinal velocity compared to current state-of-the-art techniques, with interesting perspectives for future onboard implementation

Study on the generalized formulations with the aim to reproduce the viscoelastic dynamic behavior of polymers

Appropriate modelling of the real behavior of viscoelastic materials is of fundamental importance for correct studies and analyses of structures and components where such materials are employed. In this paper, the potential to employ a generalized Maxwell model and the relative fraction derivative model is studied with the aim to reproduce the experimental behavior of viscoelastic materials. For both models, the advantage of using the pole-zero formulation is demonstrated and a specifically constrained identification procedure to obtain the optimum parameters set is illustrated. Particular emphasis is given on the ability of the models to adequately fit the experimental data with a minimum number of parameters, addressing the possible computational issues. The question arises about the minimum number of experimental data necessary to estimate the material behavior in a wide frequency range, demonstrating that accurate results can be obtained by knowing only the data of the upper and low frequency plateaus plus the ones at the loss tangent peak

A real-time thermal model for the analysis of tire/road interaction in motorcycle applications

While in the automotive field the relationship between road adherence and tire temperature is mainly investigated with the aim to enhance the vehicle performance in motorsport, the motorcycle sector is highly sensitive to such theme also from less extreme applications. The small extension of the footprint, along with the need to guarantee driver stability and safety in the widest possible range of riding conditions, require that tires work as most as possible at a temperature able to let the viscoelastic compounds - constituting the tread and the composite materials of the whole carcass structure - provide the highest interaction force with soil. Moreover, both for tire manufacturing companies and for single track vehicles designers and racing teams, a deep knowledge of the thermodynamic phenomena involved at the ground level is a key factor for the development of optimal solutions and setup. This paper proposes a physical model based on the application of the Fourier thermodynamic equations to a three-dimensional domain, accounting for all the sources of heating like friction power at the road interface and the cyclic generation of heat due to rolling and to asphalt indentation, and for the cooling effects due to air forced convection, to road conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are fully described and modelled, with particular reference to the management of contact patch position, correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multilayered tire structure. The completely physical approach induces the need of a proper parameterization of the model, whose main stages are described, both from the experimental and identification points of view, with particular reference to non-destructive procedures for thermal parameters definition

Multi-Physical Approach for Tyre Contact and Wear Mechanisms Modelling

Tyres represent one of the most important and complex parts in a vehicle, providing the only connection between the vehicle and the road and being responsible for the motion transfer within the tire-road interface in order to guarantee their optimal use in all the vehicle operating conditions. The invention and the enhancement of a pneumatic tyre has made it possible to realize fast and comfortable road vehicles. The pneumatic tyre is a crucial component of a vehicle: among its main features as low mass and flexibility, the purpose of a good-designed tyre has become not only to sustain the vehicle weight, properly filtering the road unevennesses, but also to ensure the highest possible grip level in the whole of its operating range. A tyre is an integrated multi-physical system: from only a mechanical point of view, tyres are represented by highly composite multi-layered structures, consisting of a multitude of different materials, covering synthetic and natural rubbers, carbon black, steel cords and bead wire, polyester and nylon fibre, mixed with chemicals, waxes, oils, pigments, silicas and clays. During the tyre motion, due to the multi-material interaction and to the viscoelastic rubber matrix compositions, the dynamic characteristics of a tyre may vary considerably, even considering to modify only one parameter among inner pressure, track and ambient temperatures, pavement surface, etc. . Taking into account of the tyre temperature influence upon the tyre characteristics, both of the structural part expressed in terms of interaction stiffnesses and the compound viscoelastic behaviour, function of temperature, sliding speed and road granularity, the approach to a tyre dynamic analysis and therefore to a correct modelling of both transient and steady-state conditions can only be multi-physical. Rubber friction is a topic of huge practical importance, e.g. for tyres. In the latter case, rubber-asphalt friction is influenced by a great number of variables and parameters, particularly hard to control and to measure, as for example macro and micro roughness range of bodies in contact, pressure distribution arising at their interface, materials stiffness characteristics, and their temperature-frequencies dependence, relative motion direction and speed. Another variable to take into account is time. The tyre structure and compound characteristics inevitably change within the life-cycle because of ageing, leading to a modification of cornering characteristics and to a decrease of the level of available grip. These degradation time and ambient dependent phenomena have to be taken into account within the vehicle control logics in order to optimize both safety and performance targets. Tyre model requirements for vehicle dynamics, indeed, have to accurately predict the forces arising at the tyre-road interface to be transmitted to the wheel spindle, remaining easily to characterize from the experimental point of view, requiring low computational efforts and being widely applicable. Since wear affects the tyre thermo-dynamic characteristics, it is absolutely crucial to improve the understanding and to scrutinize all the aspects of ageing. This project is focused on the analysis related to the behaviour of high performance tyres in order to comprehend which physical phenomena are responsible for the wear tread abrasive and compound degradation terms

A Non-Destructive Methodology for the Viscoelastic Characterization of Polymers: Toward the Identification of the Time–Temperature Superposition Shift Law

Polymers find widespread applications in various industries, such as civil engineering, aerospace, and industrial machinery, contributing to vibration control, dampening, and insulation. To accurately design products that are able to predict their dynamic behavior in the virtual environment, it is essential to understand and reproduce their viscoelastic properties via material physical modeling. While Dynamic Mechanical Analysis (DMA) has traditionally been used, innovative non-destructive techniques are emerging for characterizing components and monitoring their performance without deconstructing them. In this context, the Time–Temperature Superposition Principle (TTSP) represents a powerful empirical procedure to extend a polymer’s viscoelastic behavior across a wider frequency range. This study focuses on replicating an indentation test on viscoelastic materials using the non-destructive Viscoelasticity Evaluation System evolved (VESevo) tool. The primary objective is to derive a unique temperature–frequency relationship, referred to as a “shift law”, using characteristic curves from this non-invasive approach. Encouragingly, modifying the device setup enabled us to replicate, virtually, three tests under identical initial conditions but with varying indentation frequencies. This highlights the tool’s ability to conduct material testing across a range of frequencies. These findings set the stage for our upcoming experiment campaign, aiming to create an innovative shift algorithm from at least three distinct master curves at specific frequencies, offering a significant breakthrough in non-destructive polymer characterization with broad industrial potential

A three-dimensional multibody tire model for research comfort and handling analysis as a structural framework for a multi-physical integrated system

A tire is an extremely integrated and multi-physical system. From only a mechanical point of view, tires are represented by highly composite multi-layered structures, consisting of a multitude of different materials, synthesized in peculiar rubber matrices, to optimize both the performance and the life cycle. During the tire motion, due to the multi-material thermodynamic interaction within the viscoelastic tire rubber matrix, the dynamic characteristics of a tire may alter considerably. In the following paper, the multibody research comfort and handling tire model is presented. The main purpose of the research comfort and handling tire is to constitute a completely physical carcass infrastructure to correctly transmit the generalized forces and torques from the wheel spindle to the contact patch. The physical model structure is represented by a three-dimensional array of interconnected nodes by means of tension and rotational stiffness and damper elements, attached to the rim modeled as a rigid body. Research comfort and handling tire model purpose is to constitute a structural physical infrastructure for the co-implementation of additional physical modules taking into account the modification of the tire structural properties with temperature, tread viscoelastic compound characteristics, and wear degradation. At the stage, the research comfort and handling tire discrete model has been validated through both static and dynamic shaker test procedures. Static test procedure adopts contact sensitive films for the contact patch estimation at different load and internal pressure conditions, meanwhile the specifically developed sel test regards the tire dynamic characterization purpose at the current stage. The validation of the tire normal interaction in both static and dynamic conditions provided constitutes a necessary development step to the integration of the tangential brush interaction model for studying the handling dynamics and to the analysis of the model response on the uneven surfaces

Development of a Grip and Thermodynamics Sensitive Procedure for the Determination of Tyre/Road Interaction Curves Based on Outdoor Test Sessions

Designers and technicians involved in vehicle dynamics face during their daily activities with the need of reliable data regarding tyres and their physical behaviour. The solution is often provided by bench characterizations, rarely able to test tyres in real working conditions as concerns road surface and the consequential thermal and frictional phenomena. The aim of the developed procedure is the determination of the tyre/road interaction curves basing on the data acquired during experimental sessions performed employing the whole vehicle as a sort of moving lab, taking into account effects commonly neglected

Physical Modelling of Tire Wear for the Analysis of the Influence of Thermal and Frictional Effects on Vehicle Performance

The tire and vehicle setup definition, able to optimise grip performance and thermal working conditions, can make the real difference as for motorsport racing teams, used to deal with relevant wear and degradation phenomena, as for tire makers, requesting for design solutions aimed to obtain enduring and stable tread characteristics, as finally for the development of safety systems, conceived in order to maximise road friction, both for worn and unworn tires. The activity discussed in the paper deals with the analysis of the effects that tire wear induces in vehicle performance, in particular as concerns the consequences that tread removal has on thermal and frictional tire behaviour. The physical modelling of complex tire–road interaction phenomena and the employment of specific simulation tools developed by the Vehicle Dynamics UniNa research group allow to predict the tire temperature local distribution by means of TRT model and the adhesive and hysteretic components of friction, thanks to GrETA model. The cooperation between the cited instruments enables the user to study the modifications that a reduced tread thickness, and consequently a decreased SEL (Strain Energy Loss) and dissipative tread volume, cause on the overall vehicle dynamic performance