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TRT EVO: Advances in real-time thermodynamic tire modeling for vehicle dynamics simulations
Abstract
Vehicle performances, especially in motorsport, are deeply affected by tire behavior and in particular by tire compound proper working conditions. In this research activity, a series of innovations have been introduced on the Thermo Racing Tire (a physical-analytical tire thermal model, based on Fourier’s law of heat transfer applied to a three-dimensional domain) in order to take into account all the main aspects actively involved in the thermal behavior of the tire, as the presence of exhausted gases eventually impacting at the rear axle and the inhomogeneous distribution of local variables (pressure, stress and sliding velocity) within the contact patch, caused in example by the tire camber angle. The new model developed considers the presence of the sidewalls, actively involved in the convective heat exchanges, respectively, with the external airflow and the inner gas fluid, located inside the inflation chamber. The aim of the new version of the tire thermal model is a better physical comprehension of all the phenomena concerning the contact with the asphalt and the prediction of the link between the thermal state and the frictional performance, crucial for the definition of an optimal wheel and vehicle setup.
... Later, the original model, designed for vehicle handling applications, has been reformulated to include the internal pressure effect [21,22] and to extend the applicability in dynamic scenarios with higher frequency [23]. The MF model has been further enhanced in [24], where the authors have proposed an advanced multiphysical MF-based (MF-evo) realtime tyre model with the aim to extend the Pacejka's Magic Formula tyre model in the whole range of the tyre operating conditions, taking into account its internal temperature distribution [25,26], inflation pressure [22], tread wear [27,28], compound viscoelastic characteristics and road roughness [29,30]. The potential risks, related with the employment of empirical models, are linked with their parametrisation and the quality of data, since the adoption of numeric data-based techniques makes it possible to completely misinterpret the tyre behaviour even in case of a good fitting towards experimental results. ...
... To demonstrate the augmented reliability of the methodology, both standard MF and MF-evo have been calibrated and compared towards the experimental dataset acquired in dedicated handling track session, characterised by a typical measurement noise. In the case under study, the additional physical variables, consisting in temperature, pressure and compound wear level, have been co-simulated thanks to specific tyre thermal model [25,26] and a wear model [30], respectively. ...
... The vehicle has been equipped with a significant amount of instrumentation to evaluate the kinematics and the dynamics at each corner, as well as the thermodynamics of each tyre: The kinematic and dynamic quantities concerning a single corner can be reliably acquired and estimated [26,28,40]. Compound and carcass temperatures, inner air pressure and wear level are among the additional inputs of the MF-evo model, and they can be provided by means of both additional sensors and physical predictive models. ...
To cite this article: Aleksandr Sakhnevych (2021): Multiphysical MF-based tyre modelling and parametrisation for vehicle setup and control strategies optimisation, Vehicle System Dynamics, ABSTRACT Starting from the earliest phases of design of the vehicle and its control systems, the understanding of tyres is of fundamental importance to govern the overall vehicle dynamics. A properly charac-terised tyre-road interaction model is essential to achieve a reliable vehicle dynamics model on which more design variations can be studied directly in simulation environment optimising both cost and time. The possibility to count on computationally efficient and reliable formulations represents nowadays a great advantage, and the multiphysical Pacejka's Magic Formula (MF-evo) tyre model presented is one of the best trade-off solutions to meet the strict real-time requirements and to reproduce multiphysical variations of the tyre dynamic behaviour towards temperature, pressure and wear effects. A specific methodology has been developed to characterise and to identify the MF-evo parameters with a high grade of accuracy and reliability directly from experimental data. The proposed technique is based on a pre-processing procedure to remove non-physical outliers and to cluster the data, which allows to optimise the multidimensional parameterisation process. To the purpose of validation of the parametrisation routine, data from a motorsport case, exceptionally difficult to reproduce in simulation due particularly significant variations of the tyre dynamics during a single test, have been employed demonstrating the MF-evo model potential and robustness. ARTICLE HISTORY
... The same can be argued for the local deformation distribution within the tyre inner layers, resulting in specific local heating distributions within the meshed threedimensional domain. Starting from the TRT thermodynamic model, with its applications for both the performance optimization in racing field and in advanced control logics development for passenger vehicles, the physical modelling of the tyre behaviour can become particularly useful for the understanding of the tyre ideal working range and for the evolution of the control systems actions in emergency situations, thanks to the enriched dynamic vehicle state due to the availability of additional physical variables [19,20]. ...
... CFD analyses are performed with the aim to characterize the thermal behaviour of the tyre, deriving the 3D-related convective heat transfer coefficients of both inner liner and rim to be implemented in a 1D tyre thermal model, already developed by the authors in the recent years [19,20]. ...
... Starting from the full grid model configuration described in [19], a specific numerical study has been conducted to minimize the model computational cost without significantly altering the thermal dynamics of the tyre within the working range thanks to the adoption of simplified rib configuration described in [43], where the accuracy related results are also addressed comparing full three-dimensional model towards a simplified grid configuration. In [20] the authors have included the sidewalls and the wheel rim within the tyre model node layout, which represents the final model configuration adopted for this work. Since the thermal model can be employed for both the offline Software-in-the-Loop routines for vehicle performance analyses and the online hard real-time Driver-in-the-Loop applications, the number of nodes n can vary, depending on the particular tyre geometry under the investigation (motorsport, truck/bus or passenger tyre) and on the presence of eventual additional thermal sources (brakes, specifically designed cooling and warming systems or diffusers) to be considered, as addressed by the authors in [17,20]. ...
The characterization and reproduction of tyre behaviour for vehicle modelling is a topic of particular interest both for real-time driver in the loop simulations and for offline performance optimization algorithms. Since the accuracy of the tyre forces and moments can be achieved by the accurate physical modelling of all the phenomena concerning the tyre-road interaction, the link between the tyre thermal state and the tyre frictional performance turns into a crucial factor. An integrated numerical methodology, allowing to couple the full 3D CFD (Computational Fluid Dynamics) flux within the internal chamber of the tyre with an equivalent discrete 3D structure model, is proposed with the aim to completely represent the tyre thermodynamic convective behaviour in the steady-state operating conditions. 3D CFD model enables the evaluation of the internal distribution of the gas temperature and of the thermal powers exchanged at each sub-wall in detail. This allows to increase the reliability of the tyre thermodynamic modelling with a particular reference to the proper managing of the aero-thermal flow of the brake disc impact on the rim temperature and therefore on the internal gas dynamics in terms of temperature and pressure, being able to optimize the tyre overall dynamic performance in both warm-up and stabilized thermal conditions. The steady RANS (Reynolds Averaged Navier-Stokes) simulations have been performed employing the 3D CFD model in a wide range of angular velocities with the aim to calculate the convective thermal flux distributions upon rim and inner liner surfaces. The simulation results have been then exploited to derive the convective heat transfer coefficients per each sub domain to be employed within the real-time tyre physical thermal model, with the peculiar advantage of an enhanced model reliability for thermal characteristics. To validate the proposed methodology, the tyre thermal model outputs, in terms of temperatures of internal and external layers, have been validated towards the acquired ones within the specific routine performed on tyre force and moment test bench, confirming an excellent agreement with the experimental data in the entire range of operating conditions explored.
... Many phenomena occurring in the tyre/road interaction are largely dependent on the viscoelastic properties of the tyre tread [4][5][6][7][8][9][10], thus influencing the vehicle dynamics. Grip performance, rolling resistance and wear are some examples of events in which the viscoelasticity of the tread plays a fundamental role. ...
... This information would lead to an increased reliability and predictability of the vehicle behaviour analysis. It would also provide with physical inputs to tyre contact and friction models [4,5,7,8,14], generally parameterized starting from tribological experimental data by means of a reverse approach [10,15], and it would allow the study of the best suspensions setup in relation to the tyres optimal thermal working range [9,16]. ...
... The possibility to obtain the tyre tread viscoelastic response by means of a ND procedure, preserving the tyre integrity, represents an innovative topic that would define new scenarios for stakeholders, such as the monitoring of the tread characteristics during the entire tyres' lifecycle. A portable instrument, which can give a real-time characterization, allows to provide fundamental information to study the direct effects of tyre temperature variation [9] and tread wear [6,21], and it would also allow to select the compounds based on track and road dynamics, with the aim of improving performance and safety. The final target is the identification of the stiffness and damping parameters of the tested polymer, emphasizing that the instrument has been developed for tyre applications but the proposed methodology is general and can be potentially applied to any kind of material. ...
The non-destructive quantification of the mechanical properties of solid materials is a growing research topic for many applications. It could be used for monitoring material performance during the whole lifecycle of a component, for when sampling is limited or impossible or for applications that require sample identification. In this paper a portable instrument for non-destructive viscoelastic characterization of polymers, based on instrumented indentation, is presented, its aim is to allow a real-time assessment of viscoelastic storage and loss moduli (E’ and E”) directly in-situ. The designed architecture of the device is described in details alongside the procedure adopted for testing polymers, the corresponding signal processing procedure for the identification of materials stiffness and damping parameters is also described. For the scope of this paper the aforementioned procedure was tested on two different rubber compounds. Finally, the storage and loss moduli are calculated based on the linear viscoelasticity theory and the results are compared to the ones obtained with the standard Dynamic Mechanical Analysis technique (DMA): both these approaches show the same relative ranking between the compounds and a different trend in temperature due to the reached indentation depth. To overcome this limitation of linear viscoelasticity theory, normally valid for low indentation depths, a generalized formulation is proposed that takes into account the indentation depth on the moduli estimation. The results obtained with the generalized formulation show that this approach allows to evaluate accurately the trends and rankings of viscoelastic moduli, giving reliable results.
... This model is capable of simulating the temperature distribution in the tire layers and of relating this distribution to the heat exchange mechanisms. thermoRIDE model considers several critical heat-related phenomena, including heat generation and exchange processes within the tire structure and with the external environment [7]: ...
... The tire is considered to be parallelepiped-shaped and it is discretized by means of a grid, whose nodes represent the points in which the temperature will be determined instant by instant thanks to the written Fourier Equation 7. The discretization of the tire, which caters to its unique attributes such as dimensions, diffusivity, and inertia, can substantially vary. ...
Optimizing the performance of racing motorcycles is a central goal for competition teams. The necessity to ensure driver stability and a good level of grip in the widest possible range of riding conditions makes it necessary for tires to work in the right temperature window, capable of ensuring the highest interaction force between tire and road. Specifically, the internal temperature of the tire is a parameter that can be difficult to measure and control but has a significant impact on motorcycle performance and, also, on driver stability. Deepening knowledge of internal tire temperature in racing motorcycles can improve performance optimization on the track and finding the right motorcycle setup. In this work, a physical thermal model is adopted for an activity concerning the development of a moto-student vehicle, to predict the racing motorcycle setup allowing the tire to work in a thermal window that optimizes grip and maximizes tire life. More in detail, a focus has been placed on the effects of the motorcycle’s wheelbase and pivot height variations on internal tire temperatures. Indeed, the stability and handling of the vehicle are highly dependent on the geometric properties of the chassis. Several values of such quantities have been tested in a properly implemented vehicle model developed in the “VI-BikeRealTime” environment, validated by outdoor tests, able to provide forces acting on the tires, slip indices, and speeds, needed by the thermal model as inputs. Through the analysis of the internal temperatures calculated by the model, reached by the various layers of the tire, it has been possible to investigate which of the simulated conditions cause a too-fast thermal activation of the tire and which of them can avoid overheating and underheating phenomena. Lately, this research has delved into the correlation between motorcycle riders' paths and temperature fluctuations with the aim of comprehending how minor alterations in routine maneuvers may influence tire energy activation, particularly in the context of racing and qualifying conditions.
... The calibration results of the MF-evo have been inherited from a previous research work [12], employing handling data acquired on track. Pre-calibrated tire thermal and wear models [44,45] have been employed to obtain further physical channels per each dataset: temperature gradient, inflation pressure and wear variations. The parameterization of these models has been performed employing a non-destructive experimental methodology, including optical and ultrasound measurements to identify tire's thermal diffusivity and geometrical quantities [46,47]. ...
... Calibration of thermal and wear models [44,45] Data advanced processing ...
In the development of physical tire models, the complexity of the composite structure and the multiphysical variables require strongly nonlinear mathematical formulations to guarantee a desired degree of accuracy. The aim of the current work is to extend the applicability of the multiphysical magic formula-based tire model, already developed and presented by the authors, within a wider frequency range, interposing a rigid ring body between the contact patch and the wheel hub. The contact patch, varying in terms of size, shape, and relative position, is evaluated using instantaneous cams to define the effective plane. Here the advanced slip model, taking into account thermodynamic and wear effects, is then integrated. The adopted formulations have been mathematically and physically justified. They have been analytically compared to formulations related to the rigid-ring implementation available in the literature. Specific experimental activities concerning both the tire’s vertical kinematics and dynamics have been conducted to demonstrate the model’s improved physical consistency on small wavelength unevennesses.
... Therefore, the considerations made support the introduction and the calibration of additional dependencies able to express grip and stiffness variation towards temperature and pressure and to reproduce the trends shown by the experimental data [20,21]. The results of the calibration process are shown in Fig. 3, in which grip and stiffness dependencies towards temperature and pressure are represented. ...
... The aim of the study is not limited to a quantitative analysis on the effects of the variables variation on some specific KPIs or metrics, for which the DOE would have been a perfect solution, but one of the main intents is the analysis of the behavioral dynamics of the whole vehicle, due to the under/over-steering effects linked to tire state, as for example in terms of its trajectory. Another aspect to highlight is that varying the initial temperature on front tire means varying the initial state of all the layers in which the tire is radially discretized [21,35,37]; the same can be said for rear axle. Track and external air temperatures have been both set to 30 • C, defined as an arbitrary reference; the intention of the study, independently from the quantitative aspects related to the reference temperature values, aims to extrapolate relative deductions, useful to understand the global trends at decoupled boundary and starting conditions. ...
The handling behavior of a vehicle is one of its most important properties because of its relation to performance and safety and to its deep link with concepts such as “over-steer” or “under-steer”. Tire-road interaction models play a fundamental role in the vehicle system modelling, since tires are responsible for the generation of forces arising within contact patches, fundamental for both handling and ride/comfort. Among the models used to reproduce such forces, Pacejka’s Magic Formula (MF) is undoubtedly one of the most used ones in real-time automotive simulation environments because of its ability to fit quite easily a large amount of experimental data, but its original formulation did not take into account of the tire thermodynamics and wear conditions, which clearly affect tire and vehicle dynamics and are not negligible, especially for high level applications, such as motorsport competitions. Exploiting a multiphysical tire model, which consists in an evolved version of the standard MF model (MF-evo), and a vehicle model properly validated throughout experimental data acquired in outdoor testing sessions carried out with an industrial partner, the current work presents a study on vehicle behavior variation induced by thermodynamic and wear parameters, defining a series of metrics to analyze and show results. One of the elements of interest on which the focus is placed is the possibility to highlight how under-over-steering behavior of a car changes according to different thermodynamic states of tires; to do this, a commercial software VI CarRealTime has been used to perform a series of objective steady-state maneuvers and long runs, exploiting the logic of a lap time optimizer.
... The developed innovative MF-evo formulation is able to take into account of the pressure of the internal air, the temperatures of different tire layers, the road pavement characteristics and the compound viscoelasticity, varying instant by instant the dynamic characteristics of the tire starting from completely different initial working conditions. The additional physical variables are co-simulated thanks to specifically developed tire physical thermodynamic model [3][6], able to estimate in realtime respectively the tire layers' temperatures and the internal air pressure, meanwhile the road roughness characteristics and the compound viscoelasticity, considered respectively in terms of power spectral density resulting from optically acquired road profile, and of viscoelastic master curves describing the compound behaviour at different working frequencies and temperatures, are processed by physical grip model [7]. ...
... For this reason, at the current stage, a tire characterization suite including both the characterization procedures and the software set of tools have been developed to overcome the difficulties linked to the deeper understanding of the tire behaviour and to the identification of the physical quantities necessary to properly parameterise all the physical models. The developed set of tools comprises an interaction forces estimator based on vehicle outdoor acquisitions, called TRICK [10], a "smart" parameters identifier developed for Pacejka formulations, called TRIP-ID [4], a real-time physical thermal model, called TRT [3][6] and a physical grip model, called GrETA [7]. ...
The characterization and reproduction of tire behaviour for vehicle modelling is a topic of particular interest both for real-time driving simulations and for offline performance optimization algorithms. In such contexts, the Pacejka’s Magic Formula (MF) tire model [1] represents a standard that gained in the last 25 years a role of high relevance due to its low computational request and attitude to allow an efficient parameterization for a wide range of tires working conditions. Nevertheless, the original MF formulation was conceived with the aim to provide tire/road interaction forces and moments as a function of vertical load, longitudinal and lateral slip, and inclination (or camber) angle; such variables are fundamental but not totally satisfying in the description of the complex multi-physical phenomena occurring at tire/road interface [2]. In particular, the relationship between interaction forces and the cited input variables is highly influenced by further effects, linked to tire temperature, tread wear, compound viscoelastic characteristics and road roughness. Among these, the influence that the thermal conditions of the different layers constituting the global thickness of tires have on the friction and on their stiffness characteristics, is highly significant and definitely not negligible in case a full reliability of the vehicle dynamics simulations is required, especially in motorsport applications [4]. The paper illustrates the basic concepts linked to the development of a novel version of a MF-based formulation, able to take into account uncommon factors affecting tire/road interaction. Once described the structure and the parameters identification process [4], some results obtained with the MF-evo employed in a simulative loop with a thermal model are reported.
... The purpose of this work is the experimental analysis of the tire tread response, in different working condition, evaluated by a commercial dial indicator [2] considering the measured displacement values of the device. Experimental tests have been carried out on different tread compounds and, being the tire performance strictly affected by the working temperature, additional tests have been performed by heating and cooling each sample in a range of interest [3,4]. Moreover, the effects of aging on a tire has been studied. ...
... Hence, a real-time compounds characterization, which could be performed by means of a portable device [2], allows engineers to analyse directly the effects due to tire heating and cooling [3,14,15], tread wear [16,17], aging or winter and summer season compound choice on road so that the safety and handling performances can be improved by taking into account tire viscoelastic behaviour in friction coefficient evaluation for vehicle dynamics onboard algorithms. ...
The knowledge of tires tread viscoelastic behaviour plays a fundamental role in automotive to optimize vehicle performance and safety. These properties are usually characterized by means of Dynamic Mechanical Analysis [1] which implies the testing of compound sample that can be obtained by destroying the tire of interest or manufactured in different condition respect to the final product provided by tiremakers. Nowadays, the non-destructive analysis procedures are an attractive solution. These techniques are essentially advantageous for being employed in testing the whole tire, allowing the analysis of a great number of them without affects costs. The purpose of this work is the experimental analysis of the tire tread response, in different working condition, evaluated by a commercial dial indicator [2] considering the measured displacement values of the device. Experimental tests have been carried out on different tread compounds and, being the tire performance strictly affected by the working temperature, additional tests have been performed by heating and cooling each sample in a range of interest [3, 4]. Moreover, the effects of aging on a tire has been studied. The comparison of the testing activity results shows the reliability of the dynamic dial indicator to capture the tires tread different behaviour within the operating condition of interest. These encouraging results lead to next step of the research activity which will focus on the evaluation of properties characterizing the hysteretic behaviour of tires.
... In literature, the first approaches to such issue are related to the modelling of the Fourier equations applied to a three-dimensional domain, in some cases coupled with a mechanical model of the tire [15] [16], in other with stand alone tools able to work together with other interaction formulations, like Pacejka's MF [17], or with FEM [18]. During last years the focus has moved to highly discretized models able to work in real time [19], whose maximum level of complexity has been requested by motorcycle applications, for which tire contact patch moves along lateral direction of the tread, generating local stress [20] able to modify significantly the whole balance of energy respect to car tires [19]. ...
... In literature, the first approaches to such issue are related to the modelling of the Fourier equations applied to a three-dimensional domain, in some cases coupled with a mechanical model of the tire [15] [16], in other with stand alone tools able to work together with other interaction formulations, like Pacejka's MF [17], or with FEM [18]. During last years the focus has moved to highly discretized models able to work in real time [19], whose maximum level of complexity has been requested by motorcycle applications, for which tire contact patch moves along lateral direction of the tread, generating local stress [20] able to modify significantly the whole balance of energy respect to car tires [19]. ...
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 multi-layered 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.
... In literature, the first approaches to such issue are related to the modeling of the Fourier equations applied to a three-dimensional domain, in some cases coupled with a mechanical model of the tire [15,16], in other with stand-alone tools able to work together with other interaction formulations, like Pacejka's MF [17], or with FEM [18]. During the past years the focus has moved to highly discretized models able to work in real time [19], whose maximum level of complexity has been requested by motorcycle applications, for which tire contact patch moves along lateral direction of the tread, generating local stress [20] able to modify significantly the whole balance of energy with respect to car tires [19]. ...
... In literature, the first approaches to such issue are related to the modeling of the Fourier equations applied to a three-dimensional domain, in some cases coupled with a mechanical model of the tire [15,16], in other with stand-alone tools able to work together with other interaction formulations, like Pacejka's MF [17], or with FEM [18]. During the past years the focus has moved to highly discretized models able to work in real time [19], whose maximum level of complexity has been requested by motorcycle applications, for which tire contact patch moves along lateral direction of the tread, generating local stress [20] able to modify significantly the whole balance of energy with respect to car tires [19]. ...
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, requires 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 road. 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 because of rolling and to asphalt indentation, and for the cooling effects because of the air forced convection, to road conduction and to turbulences in the inflation chamber. The complex heat exchanges in the system are fully described and modeled, with particular reference to the management of contact patch position, correlated to camber angle and requiring the adoption of an innovative multi-ribbed and multi-layered 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. One of the most peculiar and challenging features of the model is linked with its topological and analytical structure, allowing to run in real-time, usefully for the application in co-simulation vehicle dynamics platforms, for performance prediction and setup optimization applications.
... The cylinder was cutinton smaller cylinders and vulcanized to give cylindrical specimens with a length of about 25 mm and a diameter of about 12 mm. Dynamic mechanical measurements were performed with an Instron dynamic device in the tractioncompression mode, at the following temperatures: 70 °C, 100 °C, and 120 °C, as reported in the literature [49]. An axial compressive pre-strain of 25% was applied on the specimen followed by a sinusoidal axial strain sweep having an amplitude of ±3.5% with respect to the applied pre-strain, with a 100 Hz frequency. ...
Driving a car at extreme speeds, road holding, and sustainability do not go together well. Formula 1 racing is exciting but is not an example of sustainability. The aim of this work was to use materials, suitable for the treads of high-performance racing tyres, that can favour both high performance and sustainability. In particular, the objective was to achieve high dynamic rigidity at high temperatures (>100 °C) and a stable crosslinking network. A copolymer from an industrial waste such as sulphur and a comonomer from a circular biosourced material were used as the crosslinking agent of an elastomer composite based on poly(styrene-co-butadiene) from solution anionic polymerization and a carbon black with a high surface area. The biosourced circular material was 1,6-bis(2,5-dimethyl-1H-pyrrol-1-yl)hexane (HMDP), the di-pyrrole derivative of hexamethylenediamine. Two poly(S-co-HMDP) copolymers, with different S/HMDP ratios (6 and 8.9, Copolymer 1 and Copolymer 2) were carefully characterized by means of 1H-, 13C-, 2D1H-1H-COSY and 2D 1H-13C HSQC NMR. The comparison of the spectra highlighted the substitution with sulphur of the β-position of the pyrrole ring: mono-substitution largely prevailed in Copolymer 1 and also bi-substitution in Copolymer 2. The copolymers were used as additives in the vulcanization system. Compared with a reference composite, they allowed us to achieve more efficient vulcanization, a higher density of the crosslinking network, higher dynamic rigidity, better ultimate tensile properties, and better stability of the crosslinking network at high temperatures. Compared with a traditional oil-based crosslinking agent for elastomer composites with high rigidity and a stable structure at high temperatures, such as the perthiocarbamate 6-((dibenzylcarbamothioyl)disulfaneyl)hexyl 1,3-diphenylpropane-2-sulfinodithioate, the poly(S-co-HMDP) copolymers led to higher dynamic rigidity and better ultimate tensile properties. These improvements occurring simultaneously are definitely unusual. This work paves the way for the upcycling of circular materials in a large-scale application such as in tyres.
... The activities of the Vehicle Dynamics research group, within the Applied Mechanics one, focus on testing, analyzing and modelling the interaction of road vehicles with the external environment, working with a particular emphasis on motorsport vehicles and tire/road interaction. Moreover, their dedication to advancing multiphysical models [ 17] and tread viscoelasticity testing and evaluation has led to groundbreaking research and two successful spin-off companies, originating from their tech transfer projects. ...
This chapter summarizes the main research activities and outcomes of the groups engaged in Mechanical Engineering, in the decade 2013–2023. The research topics are typical of the sectors Mechanical and Thermal Measurements, Applied Mechanics, Mechanical Design and Machine construction, Design Methods for Industrial Engineering.
... First, a tool called T.R.I.C.K. (Tire-Road Interaction Characterization & Knowledge) [10] is presented. This tool had been developed with the aim to process data acquired from experimental test sessions, estimating tires interaction forces, slip indices and inclination angle; the output of this tool is a sort of "virtual telemetry" which can be used to feed the thermoRIDE, a thermodynamic model [11][12][13] which provides in output the lateral and circumferential temperature distributions, in all the different tire layers: tread at three different depths, carcass and inner liner. Then, it is shown how this thermodynamic model can work coupled with a specific wear model [14], called weaRIDE, thanks to which it is possible to calculate tire tread thickness variation and to evaluate its effect on tire temperature and pressure. ...
... The tire's capacity to deliver optimal performance hinges on its complex structure and viscoelastic characteristics, which are, in turn, significantly governed by the temperatures experienced by various layers within the tire [7]. However, accurately measuring and controlling the internal temperature of a tire presents a formidable challenge. ...
Optimizing the performance of racing motorcycles is a central goal for competition teams. The necessity to ensure driver stability and a good level of grip in the widest possible range of riding conditions makes it necessary for tires to work in the right temperature window, capable of ensuring the highest interaction force between tire and road. Specifically, the internal temperature of the tire is a parameter that can be difficult to measure and control but has a significant impact on motorcycle performance and, also, on driver stability. Deepening knowledge of internal tire temperature in racing motorcycles can improve performance optimization on the track and finding the right motorcycle setup. In this work, a physical thermal model is adopted for an activity concerning the development of a moto-student vehicle, to predict the racing motorcycle setup allowing the tire to work in a thermal window that optimizes grip and maximizes tire life. More in detail, a focus has been placed on the effects of the motorcycle’s wheelbase and pivot height variations on internal tire temperatures. Indeed, the stability and handling of the vehicle are highly dependent on the geometric properties of the chassis. Several values of such quantities have been tested in a properly implemented vehicle model developed in the “VI-BikeRealTime” environment, validated by outdoor tests, able to provide forces acting on the tires, slip indices, and speeds, needed by the thermal model as inputs. Through the analysis of the internal temperatures calculated by the model, reached by the various layers of the tire, it has been possible to investigate which of the simulated conditions cause a too-fast thermal activation of the tire and which of them can avoid overheating and underheating phenomena. Lately, this research has delved into the correlation between motorcycle riders' paths and temperature fluctuations with the aim of comprehending how minor alterations in routine maneuvers may influence tire energy activation, particularly in the context of racing and qualifying conditions.
... The necessity to ensure driver stability and a good level of grip in the widest possible range of riding conditions makes it necessary for tires to work in the right temperature window, capable of ensuring the highest interaction force between tire and road (Farroni 2022). Indeed, the magnitude of the tire-road interaction forces of the motorcycle tackling a specific dynamic maneuver is strictly influenced by the tire structure and the tire compound viscoelastic characteristics, which in turn is strongly influenced by the tire's layers' temperatures (Farroni 2018). Specifically, the internal temperature of the tire is a parameter that can be difficult to measure and control but has a significant impact on motorcycle performance and, also, on driver stability. ...
... Despite these difficulties, it remains abundantly clear that tire temperature profoundly impacts the performance and the handling on the track. To address this critical challenge, a physical-analytical model, known as thermoRIDE [22], can be used. This model has proven its mettle by faithfully replicating the thermal dynamics of tires across diverse operational conditions. ...
In the world of motorsports engineering, improving brake performance is a crucial goal. One significant factor that affects this performance is the increase in brake disc temperature due to reduced cooling airflow, a phenomenon called “blanking”. This temperature increase also impacts the rim and the air inside the tire, causing changes in tire temperature and pressure, which affects the vehicle’s performance. Properly adjusting the brake blanking can be essential to keep the tire running at the right temperature, resulting in maximization of the performance on track. To address this complex problem, this study describes the problem of cooling brake discs, and this problem is then used as an opportunity to introduce a new variable in order to optimize the performance of the vehicle. By changing the thermal evolution of the brake disc, through the blanking, it can change a large percentage of heat that heats the tire. When combining an existing brake model in the literature with a tire thermal model in a co-platform simulation, it was seen that it is possible to work these two models together with the aim of being able to obtain the prediction of the optimal blanking value to be adopted before proceeding on track, thus saving time and costs.
... To date, there is no evidence that the value 1.2 × 10 4 W/(m 2 K), even if it is the most used, is the correct one, because as far as the authors' knowledge goes, there is not an extensive validation of such a number for all of the possible tyre use conditions. Farroni et al. [30] considered Hc a function of the thermal characteristics of the compound only, but as far as the authors' knowledge goes, there is not a relation or an equation that permits calculating the coefficient on the basis of known parameters related to actual vehicle conditions. There is a lack of knowledge about the phenomenon. ...
Featured Application: Advanced thermo-mechanical tyre models, real time vehicle dynamic simulation , heat transfer calcualtion. Abstract: Tyres are one of the most important elements of a vehicle because they are the link to the road and have a huge impact on traffic-related pollution. Knowing their behaviour, thus being able to use them at their best and reducing their wear rate, is one of the means of improving their lifetime, which means decreasing traffic environmental impact. In order to understand how tyres behave and to predict the real-time tyre-road coefficient of friction, which is strongly influenced by the temperature, in the last few years several complex thermo-mechanical models of heat transfer inside the tyre have been developed. However, in the current state of the art of the literature and practice, there is still an important parameter regarding such models that is not deeply studied. This parameter is the heat transfer coefficient between the tyre and the road at the contact patch, which usually is considered as a constant. The current research paper allows understanding that such an approximation is not always valid for all of the speeds and tyre loads of city and race cars; instead, it is developed an equation that, for the first time, calculates the real-time, dynamic tyre-road heat transfer coefficient, taking into account the tyre's travelling speed and the footprint length. The equation results are in good agreement with the empirical values coming from the literature and permit understanding how much such a parameter can vary, depending on the tyre use range. The formulation is simple enough to be easily implemented in existing thermodynamic tyre models without requiring meaningful computational time.
... This process involved the measurement of the footprint extension's variations concerning vertical load, camber, and inflation pressure for a reference bicycle tire. Additionally, measurements of the thermal conductivity and specific heat of the various layers and materials constituting the bicycle tire were conducted via a non-destructive procedure [9]. ...
Bicycle mobility has become increasingly popular as a sustainable and healthy means of transportation. Bicycles are not only a cost-effective transportation mode but also help reduce traffic congestion and air pollution. However, the efficiency and safety of bicycling largely depend on the optimization of bicycle components, such as the tires. The importance of bike tire optimization cannot be underestimated as it can affect both bicycle dynamics and bicycle performance. Due to the lack of multi-physical mathematical models able to analyze and reproduce complex tire/road contact phenomena, useful to predict the wide range of working conditions, this research aims to the development of a bicycle tire thermal model. The main outcome is to provide the full temperature local distribution inside the tire’s inner rubber layers and the inflation chamber. Such kind of information plays a fundamental role in the definition of the optimal adherence conditions, for both safety and performance maximization, and as an indicator of the proper tire design for various applications, each requiring specific heat generation and management. The experimental validation has been carried out thanks to an innovative test-rig developed at Politecnico di Milano. It is known as VetyT (acronym of Velo Tyre Testing), and it complies with the standard ISO 9001-2015. It has been specifically instrumented for the activity, acquiring the external tire temperatures to be compared with the respective simulated ones, under various workingconditions.
... Further, Motorsport racing teams use to face with the restrictions due to the employment of confidential tires and not available to invasive testing. Therefore, an innovative procedure for the acquisition of the data for tire viscoelasticity characterization within the working thermal range could be very useful for vehicle setup optimization and definition of vehicle simulation tools [8] [9]. ...
... Furthermore, the thermal conductivity and the specific heat of the various layers and materials constituting the tire was measured with a nondestructive procedure (Farroni, 2018). Data input and outputs are schematized in Figure 2. The experimental validation has been carried out thanks to an innovative test-rig developed at Politecnico di Milano (Figure 3). ...
Bicycle mobility has become increasingly popular as a sustainable and healthy means of transportation. Bicycles are not only a cost-effective mode of transportation but also help to reduce traffic congestion and air pollution. However, the efficiency and safety of bicycling largely depend on the optimization of bike components, such as the tires. The importance of bike tire optimization cannot be underestimated as it can affect both the bicycle dynamics and bicycle performance. In recent years, research has focused on improving the design and materials used in bike tires to enhance their efficiency and safety, mainly investing on empirical correlation activities (Steyn, 2014) and FEA models (Kumar, 2018). Due to the lack of multi-physical mathematical models able to analyze and reproduce complex tire/road contact phenomena, useful to predict the wide range of working conditions, this research aims to the development of a bicycle tire thermal model. With the know-how gained in motorcycle applications (Farroni, 2020), the main outcome is to provide the full temperature local distribution inside the tire inner rubber layers and the inflation chamber. Such kind of information plays a fundamental role in the definition of the optimal adherence conditions, for both safety and performance maximization, and as an indicator of the proper tire design for various applications, each requiring specific heat generation and management. Figure 1. The conceptual scheme of the tire thermal model, and of its internal structure The model, based on the thermodynamics Fourier Differential Equations applied to a three dimensional domain, has been parameterized measuring for a reference bicycle tire the variation of the footprint extension due to vertical load, camber and inflation pressure.
... Furthermore, the parameterised vehicle is rear-wheel drive with front steering and internal combustion engine. The tyre model is described by Pacejka's magic formula evolved model and is coupled with the validated high-fidelity multi-physical tyre described in Section 2.1 and thermal model described in [15] called 'TRT: Thermo Racing Tyre', whereas the prediction model inside the controller includes a 5-DOF vehicle longitudinal model (Section 2.3.2) coupled with the same myTyre as used in the case of the quarter-car. The whole controller was modelled in Simulink, and Simulink was the environment for the simulations with the full-car model. ...
Vehicle dynamics can be deeply affected by various tyre operating conditions, including thermodynamic and wear effects. Indeed, tyre temperature plays a fundamental role in high performance applications due to the dependencies of the cornering stiffness and potential grip in such conditions. This work is focused on the evaluation of a potentially improved control strategy’s performance when the control model is fed by instantaneously varying tyre parameters, taking into account the continuously evolving external surface temperature and the vehicle boundary conditions. To this end, a simplified tyre thermal model has been integrated into a model predictive control strategy in order to exploit the thermal dynamics’ dependents within a proposed advanced ABS control system. We evaluate its performance in terms of the resulting braking distance. In particular, a non-linear model predictive control (NMPC) based ABS controller with tyre thermal knowledge has been integrated. The chosen topic can possibly lay a foundation for future research into autonomous control where the detailing of decision-making of the controllers will reach the level of multi-physical phenomena concerning the tyre–road interaction.
... Several authors have already tackled the problem describing different techniques and modelling approaches [63][64][65]. The authors plan also to include the impact of the road bank angle and slope, the tire combined interaction characteristics, as well as, the variations of the vehicle dynamic behaviour due to the tire intrinsic multi-physics (i.e., wear and temperature effects) [66,67]. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. ...
In recent years, autonomous vehicles and advanced driver assistance systems have drawn a great deal of attention from both research and industry, because of their demonstrated benefit in reducing the rate of accidents or, at least, their severity. The main flaw of this system is related to the poor performances in adverse environmental conditions, due to the reduction of friction, which is mainly related to the state of the road. In this paper, a new model-based technique is proposed for real-time road friction estimation in different environmental conditions. The proposed technique is based on both bicycle model to evaluate the state of the vehicle and a tire Magic Formula model based on a slip-slope approach to evaluate the potential friction. The results, in terms of the maximum achievable grip value, have been involved in autonomous driving vehicle-following maneuvers, as well as the operating condition of the vehicle at which such grip value can be reached. The effectiveness of the proposed approach is disclosed via an extensive numerical analysis covering a wide range of environmental, traffic, and vehicle kinematic conditions. Results confirm the ability of the approach to properly automatically adapting the inter-vehicle space gap and to avoiding collisions also in adverse road conditions (e.g., ice, heavy rain).
... Further, Motorsport racing teams use to face with the restrictions due to the employment of confidential tires and not available to invasive testing. Therefore, an innovative procedure for the acquisition of the data for tire viscoelasticity characterization within the working thermal range could be very useful for vehicle setup optimization and definition of vehicle simulation tools [8] [9]. ...
The evaluation of the viscoelastic properties is a key topic for the analysis of the dynamic mechanical behaviour of polymers. In vehicle dynamics field, the knowledge of the viscoelasticity of tread compound is fundamental for tire-road contact mechanics modelling and friction coefficient prediction for the improvement of vehicle performance and safety, i.e. motorsport field. These properties are usually characterised by means of Dynamic Mechanical Analysis, which implies testing a compound sample obtained by destroying the tire of interest or a slab manufactured in different conditions respect to the final product provided by tiremakers. In this scenario, the non-destructive procedures are an advantageous solution for the analysis of the tread viscoelasticity, without affecting the tire integrity, allowing a great number of tests in the shortest possible time. For this reason, the authors propose an innovative instrument, called VESevo, for viscoelasticity evaluation by means of non-destructive and user-friendly technique. The purpose of the following work is the preliminary analysis of the dynamic response of the tires tested employing the VESevo in order to determine viscoelastic behaviour indexes for mechanical properties evaluation.
... Moreover, other researchers have been developed a tire models that taking into account also the thermodynamic effect [17] and tire wear [18] which are fundamental phenomena in tire-road interaction. ...
The implementation of a tire model in a simulation environment is fundamental to characterize the vehicles and to predict the dynamic behaviour during the design phase, e.g. to test automotive control systems like ADAS [1] or different parameters or working conditions like tire compound, pressure, and speed. Moreover, the output of a tire model can be employed also to predict its temperature distribution [2]. This paper deals with the comparison between different Pacejka formulations, differing for the sensitivity to physical factors, like inflation pressure and slight analytical variations. Since the discussed tire models are different version of the same formulation, the microparameters concerning specific physical effects have been zeroed, in order to make the comparison more reliable. In particular, a Pacejka’s MF 5.2 has been compared towards the MF 6.1 tire model employing a tire vehicle in specific dynamic manoeuvres. Some longitudinal (braking and acceleration) and lateral manoeuvres (spiral, steering pad, fishhook, line change, constant speed curve) have been adopted to compare the results of the implemented tire model influence on the overall vehicle dynamics. Finally, to evaluate the effect of different tire configurations, a sensitivity test was carried out.
... • Tire characterization without expensive indoor tests: most of the times, studies on tires are carried out through complex and bulky test benches [7]; the proposed tool allows to use the vehicle as a moving lab, collecting data from it • Analysis of frictional interaction and thermal phenomena [8]: the possibility to process data from outdoor tests allows to consider a series of frictional and thermal phenomena often neglected or misestimated • Performance evaluation: tires play a crucial role in vehicle dynamics; a detailed analysis of normal and tangential interactions is vital for a better understanding of vehicle's behavior • Tire models' parameters identification: a wide dataset acquired from the track allows to identify physical [9,10] and empirical tire models' parameters [11,12], tuning their output in order to fit experimental data • Objective test session results' analysis: driver's subjective opinion can be supported or integrated by an objective tool, aimed at comparing different tested products TRICK4TRUCK tool comprises of a vehicle model which processes experimental signals acquired from vehicle CAN bus or from dedicated instrumentation (explained in paragraph 2.1). The output of the tool provides a sort of "virtual telemetry" containing forces and slips estimation, so that tires interaction characteristics can be obtained. ...
The tire behavior optimization is crucial for the definition of the best setup of the whole vehicle; in fact, its interface with the ground is constituted by the sum of small surfaces in which tire-road interaction forces are exchanged. The fundamental role that in the last years tires have played in automotive industry and the growing need to reproduce with a high level of detail the phenomena concerning with vehicle dynamics have given a strong impulse to the research in the field of vehicle systems and modelling.
... Since the vehicle motion is determined by the interaction between the tyres and the road surface, knowledge of the tyre/surface friction forces and grip condition is a crucial tool which can be used in vast number of applications including longitudinal/lateral stability and rollover avoidance systems. In particular grip information is crucial tool for Advanced Driver-Assistance System (ADAS) and Autonomous Emergency Braking system (AEB) as shown in [1][2][3][4]. For instance, in the case of ADAS, estimation of friction coefficient provides an enough data for Adaptive Cruise Control unit during the slippery roads. ...
The Department of Industrial Engineering was established on 1 January 2013 in application of Law 240/2010 which has reframed the organization of the Italian university system. This chapter summarizes the efforts and the main achievements of the Department in the research, management of research and technology transfer activities in the decade 2013–2023.
In steady-state conditions, explicit expressions for tyre characteristics may be derived using the theoretical framework provided by the brush theory. This chapter is, thus, dedicated to addressing the stationary problem from both the local and global perspectives. The fundamental concepts of critical slip and spin are introduced with respect to an isotropic tyre, and the deformation of the bristles inside the contact patch is investigated for different operating conditions of the tyre. Analytical functions describing the tyre forces and moment acting inside the contact patch are obtained for the particular case of a rectangular contact patch. The analysis is qualitative in nature.
The brush theory constitutes the simplest, full-physical approach to model the tyre-road interaction. It describes the tyre-wheel system as a rigid body equipped with bristles, which undergo tangential deformations in their attempt to stick to the ground. This chapter introduces the governing equations of the brush models. These may be divided into four separate sets: the friction model, the constitutive relationships, the tyre-road kinematic relationships and the equilibrium equations. The fundamental assumptions behind the proposed formulation are outlined, and the boundary and initial conditions are stated in a general manner.
At a high level of description, the tyre may be thought of as a nonlinear dynamical system, which produces certain outputs, often referred to as tyre characteristics, when subjected to opportune inputs. This interpretation allows defining some fundamental quantities that contribute to determining both the steady-state and the transient response of the tyre. Amongst these, the slip variables play the most important role. In steady-state conditions, the tyre characteristics may be described as real analytic functions of the slips, which may be defined in three main different ways. The Jacobians of the steady-state characteristics with respect to the slip variables are often called matrices of generalised slip stiffnesses. The local properties of the steady-state tyre characteristics may be deduced from the entries of these matrices.
This book provides an in-depth understanding of tyre dynamics. In the first three chapters, new concepts are introduced in respect to the classic theory. Analytical results are derived step-by-step to guide the reader through the governing equations of the model. Transient phenomena are explained in a relatively simple way according to the brush theory. The analysis is extended to cover the case of large camber angles, which is often disregarded. The principal mechanisms behind the transient generation of tyre forces and moment are discussed in general terms, and exact solutions to the rolling contact problem are given for simple contact geometries.
The last part of the book is dedicated to the approximated theories of transient generation of tyre forces and moment. Two different models, suitable for use in vehicle dynamics applications, are presented and compared.
This chapter deals with tyre mechanics and it has a particular focus on thermal effects on its dynamical behaviour. In the first part the typical tyre structure is introduced together with the tyre mechanical/dynamical behaviour according to a classical approach, so recalling the main kinematic and dynamic quantities involved in tyre pure and combined interactions. The core of this chapter is the description of a physical-analytical tyre thermal model able to determine the thermal status in each part of the tyre useful for vehicle dynamics modelling and driving simulations in order to take into account thermal effects on tyre interactions and consequently on vehicle dynamical behaviour. Successively also the tyre wear modelling is faced, after a brief introduction to the different models available in literature some considerations are reported concerning the thermal effects on wear.
In this work, a combined numerical/experimental analysis is performed for an automotive tyre. A preliminary experimental activity is realized on examined tyre to measure the temperatures of its layers under various operating conditions. In a second stage, a 3D CFD model of tyre is developed in a commercial code and steady RANS simulations are performed in the full range of angular velocity with the aim to refine the prediction of convective thermal power and heat transfer coefficient. CFD simulation results are passed to a user-defined 3D thermodynamic model to furnish a detailed and reliable tyre thermal output with the advantage of a low computational time. Tyre thermodynamic model, enhanced by CFD-related thermal characteristics, demonstrates the capability to properly forecast the measured temperature of tyre layers in a wide range of investigated operating conditions. The proposed numerical approach represents a valuable tool supporting the optimization of tyre behavior and the development of advanced control rules for optimal tyre management.
Vehicle dynamics is largely influenced by the phenomena occurring in the tire-road interface, and a great portion of these phenomena is mainly conditioned by the viscoelastic properties of the tire tread compound. It is not surprising that the possibility of obtaining the viscoelastic response of a compound by means of a nondestructive procedure is a growing research topic that affects application fields ranging from monitoring of the material performance during its entire life cycle to the quantitative analysis of product quality and repeatability of production processes. In this article, a novel nondestructive procedure for the viscoelastic characterization of tire tread compound is proposed. A portable instrument, based on instrumented indentation, was designed and prototyped with the aim to allow a real-time assessment of moduli directly on site. The testing procedure adopted to perform the test on three different compounds was described. A signal-processing procedure was developed for the identification of compound stiffness and damping parameters from which viscoelastic moduli were estimated. The results were also compared with the DMA characterization showing the same relative ranking between the compounds with a different trend in temperature due to the amount of the tests' indentation depth.
The use of computer simulations in motorcycle engineering makes it possible both to reduce designing time and costs and to avoid the risks and dangers associated with experiments and tests. The multi-body model for computer simulations can be built either by developing a mathematical model of the vehicle or by using commercial software for vehicle system dynamics. Even though the first method is more difficult and time-consuming than the second, maximum flexibility in the description of the features of the model can be obtained only by using an analytical model. Moreover, mathematical modelling has a high computation efficiency, whereas multi-body software requires a lot of time to carry out simulations. For the reasons above, the aim of this work was to develop a mathematical model of a motorcycle.
In this paper, we discuss three improved brush models. The first one
deals with the coupling between the slip and spin parameters and
is valid for relatively high steering speed and small camber angles;
the second one is more complex and considers the presence of a
two-dimensional velocity field inside the contact patch due to large
camber angles; the third one is more general and combines both
the previous formulations. For the last two models, the investigation
is conducted with respect to a rectangular contact patch, for
which we show that three different regions can be identified, each
of them corresponding to a different steady-state solution for the
deflection of the bristle. Furthermore, from the transient analysis it
emerges that each region can be in turn separated into an area in
which steady-state conditions reign and another one in which the
transient solution takes place. An asymptotic analysis is carried out
for the three models and it is shown that the solutions are equivalent
to the ones predicted by the standard brush theory for small values of
the spin ratio and camber angle. Finally, a comparison is performed
amongst the models to highlight the differences in the predicted tyre
characteristics.
In this paper the capability to reproduce the mechanical behaviour of viscoelastic materials is investigated comparing the response of a generalized Maxwell model and a relative fraction derivative model towards the experimental behavior of a selected viscoelastic material. In particular, the rheological models are mathematically described illustrating the advantages of the pole-zero formulation for a constrained parameters’ identification procedure. The effectiveness of the both models’ is then compared focusing on the ability of the models to adequately fit the experimental data with a minimum number of parameters, also addressing the possible computational issues.
The vehicle dynamic behaviour analysis is a crucial step for the evaluation of performance in terms of stability and safety. Tires play an important role by generating the interaction forces at each road-tire contact patch. The longitudinal and lateral dynamics are analysed by using instrumented vehicles with expensive high precision sensors to get a measurement of estimates of physical parameters of interest. This paper deals with the evaluation of vehicle under/oversteering behaviour and of braking performance using a Real-time (RT) simulator. The simulations were performed by using an efficient 15 Degrees of Freedoms (DOFs) Lumped-Parameter Full Vehicle Model (LPFVM), comprising a tire model with temperature-dependent properties. A virtual Driver-in-the-Loop (vDiL) scheme was used to perform test manouvers. The virtual driver is based on two PID regulators for speed and steering control. Finally, this paper reports the results of constant radius tests as defined by standard ISO4138 and of a braking manoeuvre. In both tests, a type-A road profile as defined by ISO 8608 standard was simulated.
Soft robots have been extensively studied for their ability to provide both good performance and safe human-robot interaction. In this paper, we present and compare the performance of two model-based control techniques with the common aim to independently and simultaneously control position and stiffness of a pneumatic soft robot’s joint. The dynamic system of a robot arm with flexible joints actuated by a pneumatic antagonistic pair of actuators, so-called McKibben artificial muscles, will be regarded, while its dynamic parameters will be considered imprecise. Simulation results are provided to verify the performance of the algorithms.
The understanding and control of tire wear, preventing tread degradation and irregular wear has been a challenge to tire product engineers, and an important issue for fleet management. There is not a simple equation to analyze and predict it. The optimal wear, and consequent mileage performance, depends not only on the tire, but also on its interaction with the vehicle and the road. It varies with operational conditions and, furthermore, with vehicle and tire maintenance. This paper aims to show the preliminary analysis useful for the development of a tool able to predict tire wear performances in the truck & bus environment, anticipating the results coming from a standard field evaluation. A predictive tool is important for both tire manufacturer and final customers: the advantage for tire manufacturer is the possibility to drastically reduce time-to-market and to have reliable and controlled results; for OEMs, the possibility to receive tire models based on outdoor tests using their own vehicle as a moving lab; for final customer, the advantage of having smart-tire able to predict wear performances, generating valuable advices for maintenance and fleet control. Such aspects will be explained in this paper covering the first results obtained during an outdoor session where a reference vehicle has been instrumented in order to evaluate longitudinal behavior.
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.
In the paper new structure elements have been developed and implemented in the already-existing TRT thermo-dynamic tyre model. The updated model aims to provide a complete tool to study and understand all the phenomena concerning the tyre in thermal transient conditions, since all the elements constituting its structure are finally modelled. The computational cost, connected to a more complex model to manage, was decreased by simplifying the mesh of the previous version of the model and, thus, by reducing the state vector length.
In investigation and development of road tires within passenger car development, temperature dependency of tire characteristics is often neglected. This research however explicitly focuses on investigation and identification of temperature dependency of tire characteristics and its interaction with other inner tire states. To this extent, a novel method using a thermographic camera for measurement of both tire core and surface temperature is used. On the basis of these measurements, the dependency of cornering stiffness, relaxation length and lateral coefficient of friction on either core or surface temperature is presented. Moreover, the effect of tire core temperature on inner pressure is investigated. By choice of appropriate operating conditions, the effects of temperature and inner pressure on tire characteristics is investigated separately. A mechanical-analytical analysis forms the basis for derivation of the relationship between material attributes and tire characteristics. Material measurements of a sample taken from the tire under investigation are performed utilizing a hydropulser test rig. The aim of this analysis is identification of rubber storage and loss moduli, i.e. material master curves. The relationship of these material attributes to tire behavior is then shown for the tire characteristics under investigation. Finally, the transferability of the presented findings regarding temperature dependency from a test rig environment to real road conditions is discussed and recommendations are made for tire and vehicle measurements.
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.
A new analytical–physical tyre model for which the paternity has to be ascribed to Professor Giuseppe Capone was developed at the Department of Mechanical Engineering for Energetics at Naples University ‘Federico II’ with the support of the Bridgestone Technical Centre Europe. The whole model allows to obtain the road–tyre interactions so it can be used in vehicle dynamic simulations. The model has been named Ph.An.Ty.M.H.A., acronym of ‘PHysical ANalytical TYre Model for Handling Analysis’ and it includes the normal, longitudinal and lateral tyre–road interaction. Considering that Ph.An.Ty.M.H.A. is an analytical ‘deductive’ model, it is necessary to develop it starting just from the normal interaction, described in this paper, and then the other ones will be described in future papers. In fact, the normal interaction, i.e. the relationship between the normal load and the normal deflection, influences the tangential (longitudinal plus lateral) one, which determines the vehicle handling behaviour. The parameters used in this model are physical and geometrical so they can be measured on the real tyre. This property allows to better understand the tyre–road interaction mechanism. The tyre behaviour is modelled by analytical expressions based on equilibrium conditions and geometrical relations. To reproduce the experimental normal interaction and the pressure distribution, once the tyre geometrical quantities are known, it is necessary to identify some parameters, related to the tyre structure, by a comparison with the experimental data. Moreover, the predictive ability of the whole model, combined with a vehicle model, is very careful in analysing the vehicle handling [J.C. Dixon, Tyres, Suspensions and Handling, Cambridge University Press, Cambridge, 1991].
This paper presents a method to predict the relative objective weighting scheme necessary to cause arbitrary members of a
Pareto solution set to become optimal. First, a polynomial description of the Pareto set is constructed utilizing simulation
and high performance computing. Then, using geometric relationships between the member of the Pareto set in question, the
location of the utopia point and the polynomial coefficients, the weighting of the performance metrics which causes a particular
member of the Pareto set to become optimal is determined. The use of this technique, termed the scaling method, is examined
via using a sample problem from the field of vehicle dynamics optimization. The scaling method is based on the collinearity
theorem which is also presented in the paper.
Sometimes it is necessary to test how repair affects the properties of the car. These tests are carried out using a cylinder test stand. During the test the tyre is rolling between two cylinders of a small diameter. The question arises whether the rolling resistance of the tyre is the same as the rolling resistance when the wheel is rolling on the plane. If it is not the same what is the reliation between tyre resistances in these two cases? It is an important answer because the change of rolling resistance can affect consumption, the highest speed, engine power and other results of measurement. The paper gives the answer to these questions and describes the method of getting this information.
We present a simple theory of crack propagation in viscoelastic solids. We calculate the energy per unit area, G(v), to propagate a crack, as a function of the crack tip velocity v. Our study includes the non-uniform temperature distribution (flash temperature) in the vicinity of the crack tip, which has a profound influence on G(v). At very low crack tip velocities, the heat produced at the crack tip can diffuse away, resulting in very small temperature increase: in this "low-speed" regime the flash temperature effect is unimportant. However, because of the low heat conductivity of rubber-like materials, already at moderate crack tip velocities a very large temperature increase (of order of 1000 K) can occur close to the crack tip. We show that this will drastically affect the viscoelastic energy dissipation close to the crack tip, resulting in a "hot-crack" propagation regime. The transition between the low-speed regime and the hot-crack regime is very abrupt, which may result in unstable crack motion, e.g. stick-slip motion or catastrophic failure, as observed in some experiments. In addition, the high crack tip temperature may result in significant thermal decomposition within the heated region, resulting in a liquid-like region in the vicinity of the crack tip. This may explain the change in surface morphology (from rough to smooth surfaces) which is observed as the crack tip velocity is increased above the instability threshold.
The TRT model, developed to accurately reproduce the tire thermal dynamics in all the vehicle working conditions, has to be physically characterized [1][2]. An appropriate non-destructive procedure, that allows to obtain the thermal diffusivity of completely different tire layers, is described. The heat is directly supplied on the tire tread surface trough a specifically powered laser, while two thermal cameras acquire temperatures reached on both the outer and the inner layers. Using the above instrumentation layout to acquire the tire radial and circumferential temperature gradients and a specifically developed mathematical TRTLab model based on the use of Fourier's equation of diffusion applied to a three dimensional domain, allows to estimate the tire thermal diffusivity.
Most of the equations governing the problems related to science and engineering are nonlinear in nature. As a result, they are inherently difficult to solve. Analytical solutions are available only for some special cases. For other cases, one has no easy means but to solve the problem must depend on numerical solutions. Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions presents the current theoretical developments of boundary layer theory, a branch of transport phenomena. Also, the book addresses the theoretical developments in the area and presents a number of physical problems that have been solved by analytical or numerical method. It is focused particularly on fluid flow problems governed by nonlinear differential equations. The book is intended for researchers in applied mathematics, physics, mechanics and engineering. Addresses basic concepts to understand the theoretical framework for the method Provides examples of nonlinear problems that have been solved through the use of numerical method Focuses on fluid flow problems governed by nonlinear equations.
The optimal tire temperature is a determining factor to get quick lap times in motorsport, because the tire rubber compound characteristics decay very rapidly outside a given temperature range. The characteristics of road car tires also vary with temperature, although such a variation is smaller than the one of racing cars; however, the performance of sport cars is still massively influenced by tire temperatures. The heat coming out of high performance driving is transferred in different ways throughout the tires, resulting in very big temperature variations within the tire parts. The tire surface in contact with the road can get warm very quickly because of friction energy in the contact patch, and can also cool down rapidly because of air convection and heat conduction into the track. On the other hand, the inner liner has much smaller and slower variations in temperature, partly because of the relatively low thermal conductivity of the rubber compound. These two spots where the tire temperature is usually detected have an influence on tire characteristics which are relevant for vehicle dynamics: the surface temperature correlates with grip, the inner liner temperature with cornering stiffness [1]. The measurement of these quantities requires additional (and reliable) sensors, setting a tough task.
Direct yaw moment control (DYC) is an active safety technique developed in recent years to improve vehicle handling dynamics. Delayed or excessive intervention is a common problem in traditional logic threshold control algorithm due to the vehicle inertia. To improve the control effect, model predictive control (MPC) is applied in stability control which relies significantly on the accuracy of reference model. In this paper, a MPC stability controller with tire cornering stiffness estimation is proposed. The reference model is modified online by correcting tire cornering stiffness. In this way, yaw rate can be better predicted which improves the control effect. The effectiveness of the proposed algorithm is compared with a MPC controller with constant tire cornering stiffness and a traditional logic threshold controller through numeric simulation. The simulation result indicates that the handling performance of the proposed controller is improved from that without tire cornering stiffness estimation.
The Nature of Viscoelastic Behavior. Illustrations of Viscoelastic Behavior of Polymeric Systems. Exact Interrelations among the Viscoelastic Functions. Approximate Interrelations among the Linear Viscoelastic Functions. Experimental Methods for Viscoelastic Liquids. Experimental Methods for Soft Viscoelastic Solids and Liquids of High Viscosity. Experimental Methods for Hard Viscoelastic Solids. Experimental Methods for Bulk Measurements. Dilute Solutions: Molecular Theory and Comparisons with Experiments. Molecular Theory for Undiluted Amorphous Polymers and Concentrated Solutions Networks and Entanglements. Dependence of Viscoelastic Behavior on Temperature and Pressure. The Transition Zone from Rubberlike to Glasslike Behavior. The Plateau and Terminal Zones in Uncross-Linked Polymers. Cross-Linked Polymers and Composite Systems. The Glassy State. Crystalline Polymers. Concentrated Solutions, Plasticized Polymers, and Gels. Viscoelastic Behavior in Bulk (Volume) Deformation. Applications to Practical Problems. Appendices. Author & Subject Indexes.
This paper presents an axisymmetric layerwise finite element formulation for dynamic analysis of laminated structures with embedded viscoelastic material whose constitutive behavior is represented by the Prony-generalized Maxwell series. To account the time dependence of the constitutive relations of linear viscoelastic materials, the incremental formulation in the temporal domain is used. Layerwise finite element has been shown to provide an efficient and accurate tool for the simulation of laminated structure. Most of the previous work on numerical simulation of laminated structures has been limited to elastic material behavior. Thus, the current work focuses on layerwise finite element analysis of laminated structures with embedded viscoelastic material. A computer code based on the presented formulation has been developed to provide the numerical results. The present approach is verified by studying its convergence behavior and comparing the numerical results with those obtained using the ABAQUS software. Finally, and as an application of the presented formulation, the effects of load duration on the dynamic structural responses of multilayered pavements are studied. © The Society of Theoretical and Applied Mechanics, R.O.C. 2014.
Owing to elastic and viscous characteristics of embedded rubber compounds, some of the supplied mechanical energy to composite structure of a rolling tire is dissipated as heat. As a result, the tire may have different body temperatures for different operating conditions. In most performed studies, just temperature distribution is investigated and the mechanical behavior of tire structure, which is highly temperature-dependent, is ignored. In this study a 3D finite element model is developed for evaluating the effects of loading conditions and the body temperature on mechanical behavior of the tire. The obtained results are compared with related published works to evaluate the accuracy of the analysis.
In this paper, we investigate the vehicle lateral dynamics stabilisation problem to enhance vehicle handling by considering time-varying longitudinal velocity. The longitudinal velocity is described by a polytope with finite vertices and a novel technique is proposed to reduce the number of vertices. Since the tyre dynamics is nonlinear, the cornering stiffness is represented via the norm-bounded uncertainty. Concerning the time-varying velocity and the nonlinear tyre model, a linear parameter-varying vehicle model is obtained. As the velocity and the states are measurable, a gain-scheduling state-feedback controller is introduced. In the lateral control, the sideslip angle is required to be as small as possible and the yaw rate is constrained to a certain level. Thus, the control objective is to minimise the sideslip angle while the yaw rate is under a prescribed level or constrain both the sideslip angle and the yaw rate to prescribed levels. To consider the transient response of the closed-loop system, the [Inline formula]-stability is also employed in the energy-to-peak control. The optimal controller can be obtained by solving a set of linear matrix inequalities. A nonlinear vehicle model is utilised to illustrate the design procedure and the effectiveness of the proposed design method. Finally, simulations and comparisons are carried out to show the significant advantage of the designed controller. Compared to the open-loop system, the closed-loop system with the designed controller can achieve much smaller sideslip angle and the yaw rate is closer to the desired yaw rate from a reference model. Therefore, the vehicle safety and the handling are both improved in our simulation cases.
In response to the current and future energy and environment challenges, the automotive industry is strongly focusing on improving the fuel efficiency of vehicles. Although the electrification of automotive powertrains is clearly the principal path towards sustainable transportation, many opportunities still exist to improve the fuel economy of conventional vehicles. However, some of the technical solutions representing the state of the art in research and advanced development are difficult to benchmark in terms of their potential benefits for fuel consumption improvement. A greater understanding of the fuel energy utilization on the vehicle (here intended as a ‘system’ ) is therefore necessary in order to identify the readily available opportunities for efficiency improvements and, ultimately, to develop automobiles which are more fuel efficient. To this extent, this paper presents a review of the state of the art and technology trends in the field of energy management and recovery for automotive systems, with the primary focus on conventional powertrains. An understanding of the fuel energy utilization and dissipation associated with the vehicle subsystems (the engine, transmission, and chassis) is provided, as well as an overview of the opportunities and potential challenges in improving the fuel economy through system-level energy management, recovery, and harvesting. Finally, an overview of the most important solutions for managing energy dissipation, energy recovery, and harvesting is presented, discussing their potential for fuel economy improvement, technical readiness, and challenges. Wherever possible, projections on fuel economy improvements, based on either experimental data or simulations, are reported to provide opportunity for the assessment and comparison of current and future technologies.
A Numerical–physical tyre model was developed . The whole model allows to obtain the road–tyre interactions so it can be used in vehicle dynamic simulations. In this article are presented its capabilities in normal interaction analysis.
The normal interaction, i.e. the relationship between the normal load and the normal deflection, influences the tangential (longitudinal plus lateral) one, which determines the vehicle handling behaviour. The parameters used in this model depend on the structure of the tyre and they can be measured on the real tyre.
The tyre has been schematized as composed by a flexible belt , the sidewalls and a rigid ring (Rim). The flexible belt is composed by a number of lumped masses linked by extensional and bending stiffnesses and dampers. The tyre model has been developed using the finite segment method. Using these method could be possible to include in the tyre simulations various non-linear structural effects due to large displacements and rotations. The model allows to simulate both steady state and transient conditions.
When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review the basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggests a new explanation for puzzling experimental results [L. Bureau, T. Baumberger, C. Caroli, arXiv:cond-mat/0510232 v1] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.
Contact phenomena which occur at the tire-ground interface play a crucial role in most issues related to optimal performances of the vehicle, safety, comfort, and energy consumption. Thus, it is essential to have available experimental tools capable of supplying detailed information about the main contact parameters (size and shape of nominal contact area and contact pressure distribution), especially when unknown or unpredictable external conditions make it difficult to use numerical tools in assessing them. Although a number of laboratory techniques have been devised to address this problem, here we propose a novel approach that exploits the property of ultrasonic waves to be differently reflected by a contact interface depending on its stress state. This noninvasive method is capable of supplying in real-time detailed maps of contact conditions as well as quantitative information with regard to geometric features of the contact area and contact pressure distribution values after suitable postprocessing procedures.
This study reports the results of the application of the ultrasonic method in the case of contact of a motor-bicycle tire on a rigid surface. A number of tests were carried out under different conditions with regard to inflation pressure and applied load. In each case, the raw reflection data were converted into graphic maps that display the contact area features and contain information about contact pressure. Moreover, to assess the quantitative reliability of the technique, ultrasonic data were compared with those obtained by means of a commercial pressure-sensitive film. The results are discussed to evaluate the capability of the ultrasonic method to correctly capture contact patch features.
Vehicle Dynamics and Control provides a comprehensive coverage of vehicle control systems and the dynamic models used in the development of these control systems. The control system topics covered in the book include cruise control, adaptive cruise control, ABS, automated lane keeping, automated highway systems, yaw stability control, engine control, passive, active and semi-active suspensions, tire models and tire-road friction estimation. In developing the dynamic model for each application, an effort is made to both keep the model simple enough for control system design but at the same time rich enough to capture the essential features of the dynamics.
The effect of service temperature on chemical structure and mechanical properties of polyamide 6 & 66 tyre cords was studied
over the broad range of 50–200°C and for a period of 16h. The heat treatment of cords at below 100°C and above 120°C was
found to reduce their tensile properties considerably. The changes in properties above 120°C were caused by increase in width
of the molecular weight distribution curve as ascertained by gel permeation chromatography (GPC) studies and increase in irregularity
of the polymeric chains as ascertained by birefringence studies; this appears to be due to the fact that, by raising the temperature,
both chain folding and chain scission occur. Since there was deformation of the amorphous regions as ascertained by FTIR spectroscopy
and birefringence studies, the changes in properties below 100°C were attributed mainly to the effectiveness of thermal oxidation
and annealing in the amorphous phase. In other words, the degree of crystallinity increased, the tyre cord became brittle,
and breaking load and elongation at break were decreased. The lower reduction of tensile properties at an intermediate temperatures
of 100–120°C was caused by the lower polydispersity and irregularity in the polymeric chains, in comparison with higher temperatures
and less crystallinity than lower temperature treatments.
KeywordsHeat treatment–Tyre cord–Polyamide–Mechanical properties–Molecular weight distribution
Tire inflation pressure influence on a vehicle stopping distances
- V Rievaj
- J Vrabel
- A Hudak
Measurement of the thermal diffusivity of a tire compound by mean of infrared optical technique
- F Timpone
- C Allouis
- A Amoresano
Ph.An.Ty.M.H.A.: a physical analytical tyre model for handling analysis—the normal interaction
- G Capone
- D Giordano
- M Russo
- Ph
- An
- M H A Ty
Tire Inflation Pressure on a vehicle Stopping Distances
- V Rievaj
- J Vrabel
- A Hudak
V. Rievaj, J. Vrabel, A. Hudak (2013). Tire Inflation Pressure on a vehicle Stopping
Distances. International Journal of Traffic and Transportation Engineering, 2(2), p.9-13.
Testing of a Race Car in a Full Scale Climatic Wind Tunnel. SAE Technical Paper
- Aero-Thermal
Aero-Thermal Testing of a Race Car in a Full Scale Climatic Wind Tunnel. SAE
Technical Paper, No. 2016-01-1588.
Integrated Aero-Thermal Testing of a Race Car in a Full Scale Climatic Wind Tunnel
- A Abdel-Rahman
- M Agelin-Chaab
- G Elfstrom
- J Komar
A. Abdel-Rahman, M. Agelin-Chaab, G. Elfstrom, J. Komar (2016). Integrated
Aero-Thermal Testing of a Race Car in a Full Scale Climatic Wind Tunnel. SAE
Technical Paper, No. 2016-01-1588.
Investigating Temperature Effects on
- H Golbakhshi
- M Namjoo
H. Golbakhshi, M. Namjoo (2014). Investigating Temperature Effects on
- Rievaj V
- Board on Energy Environmental Systems and Transportation Research Board