No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
A physical-analytical model for a real-time local grip estimation of tyre rubber in sliding contact with road asperities
Abstract
This paper deals with the frictional behaviour of a tyre tread elementary volume in sliding contact with road asperities. Friction is supposed as composed by two main components: adhesion and deforming hysteresis. The target, fixed in collaboration with a motorsport racing team and with a tyre manufacturing company, is to provide an estimation of local grip for on-line analyses and real time simulations and to evaluate and predict adhesive and hysteretic frictional contributions arising at the interface between tyre tread and road. A way to approximate asperities, based on rugosimetric analyses on macro and micro scale, has been introduced. The adhesive component of friction has been estimated by means of a new approach based on two different models found in literature, whose parameters have been identified thanks to a wide experimental campaign previously carried out. The hysteretic component of friction has been estimated by means of an energy balance taking into account rubber viscoelastic behaviour, characterized by means of proper DMA tests, and internal stress / strain distribution due to indentation with road. Model results are finally shown and discussed and the validation experimental procedure is described. The correct reproduction of friction phenomenology and the model prediction capabilities are highlighted making particular reference to grip variability due to changes in working conditions.
... It is well known that the rubber friction coefficient is mainly originated by the contribution of three friction forces: one is referred to as the shearing deformation of the rubber surface in contact with the true road area. The other two forces are the viscoelastic force originated by the bulk deformation on substrate asperities and the cohesion losses linked to the rubber wear process [1][2][3][4][5]. ...
... Many researchers have discussed the impact of the wear phenomenon in different rubber friction contexts [3][4][5], and this contribution is considered much lower than the synergetic effect of adhesion and viscoelastic forces [6,7]. Therefore, it is commonly recognized that the main contributions to the rubber friction performance under dry conditions are a consequence of the adhesion and viscoelastic processes [1][2][3][4][5]. ...
... Many researchers have discussed the impact of the wear phenomenon in different rubber friction contexts [3][4][5], and this contribution is considered much lower than the synergetic effect of adhesion and viscoelastic forces [6,7]. Therefore, it is commonly recognized that the main contributions to the rubber friction performance under dry conditions are a consequence of the adhesion and viscoelastic processes [1][2][3][4][5]. ...
Two proposed methods to determine the adhesion friction coefficient were validated by experimental results of two types of rubber compounds at different sliding velocities under dry conditions. The experimental results were measured from a linear friction tester, while the viscoelastic friction coefficient was estimated using the Persson's contact theory. Adhesive friction (model 1) was derived from the deconvolution of dry friction coefficient in two Gaussian-like curves. Interesting results were obtained using the deconvoluted method in the range of intermediate sliding velocities where preponderant contribution to the adhesion friction is replaced by the viscoelastic friction. Fitting parameter results were in good general agreement with values derived from the literature, confirming the influence of the mechanical properties of the compound and substrate texture on the proposed adhesion frictional method. The second adhesive friction model (model 2) was based on the confinement rheology of rubber chains on the contact with the asperities of the road surface. We demonstrated that acceptable adhesion friction results were achieved from a dynamic viscosity test at low frequencies, confirming the applicability of the proposed rheological model. Moreover, the relationship between the rubber composition and the modified contact layer along with the likely interphase reaction are also discussed.
... 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]. ...
... To provide the friction coefficient modification due to thermal effects, compound viscoelastic characteristics, pressure and velocity distribution within the contact patch and the road texture, the physical grip model GrETA (Grip Estimation for Tyre Analyses) has been developed [7]. Its aim is to provide the friction coefficient value, as a combination of two main friction contributes: hysteretic term as a consequence of the power dissipated within the rubber compound indented by the road asperities and adhesive term, expressed by means of an original analytic formulation, whose formulation is identified thanks to dedicated experimental tests. ...
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 characterization of this sub-system is quite difficult and delicate because tyre forces show a complex and strongly nonlinear dependence on slip ratio, slip angle, camber angle, vertical load, tyre structure, inflation pressure, inner and surface temperature, wear [9][10][11][12]. Road conditions and properties are very relevant too [13]. ...
... In Fig. 17 the cloud shows that slip ratio and slip angle assume their maximum values at high camber angles, when the motorcycle is coming out from the curve: this phase is the most important to model and to proper fit because, in order to minimize the lap time, all the available grip should be employed, so the traction control needs a reliable and good fitting tyre-road interaction model [13]. ...
... Creation of virtual tyres obtained varying as desired the shape of the pure and combined interaction curves, useful to simulate the effect of tyre compound and structural variations on vehicle behaviour. Physical simulation of tyre/road interaction phenomena [35] by means of MF model integration with a physical grip model [13] and with a real-time tyre thermal model [10,33], able to reproduce local temperature distributions and their effect on tyre and vehicle performance. ...
Tyres play a key role in ground vehicles' dynamics because they are responsible for traction, braking and cornering. A proper tyre-road interaction model is essential for a useful and reliable vehicle dynamics model. In the last two decades Pacejka's Magic Formula (MF) has become a standard in simulation field.
This paper presents a Tool, called TRIP-ID (Tyre Road Interaction Parameters IDentification), developed to characterize and to identify with a high grade of accuracy and reliability MF micro-parameters from experimental data deriving from telemetry or from test rig. The tool guides interactively the user through the identification process on the basis of strong diagnostic considerations about the experimental data made evident by the tool itself. A motorsport application of the tool is shown as a case study.
... Such complex structure is necessary for supporting the interaction forces with the road. In literature there are different models able to describe tyre behavior both based on an physical approach [1][2][3][4][5][6][7][8][9][10][11][12] and based on an empirical one [13][14][15][16] . In order to parametrize physical based models [1][2][3][4][5][6][7][8][9][10][11][12] , it is very significant the knowledge about the thickness of the different tyre layers. ...
... In literature there are different models able to describe tyre behavior both based on an physical approach [1][2][3][4][5][6][7][8][9][10][11][12] and based on an empirical one [13][14][15][16] . In order to parametrize physical based models [1][2][3][4][5][6][7][8][9][10][11][12] , it is very significant the knowledge about the thickness of the different tyre layers. This aspect is particularly important as it concerns the physical models describing the tyre thermal behavior [8][9][10] , the tyre grip behavior [1,2,6,7] and the tyre wear [11] . ...
... In order to parametrize physical based models [1][2][3][4][5][6][7][8][9][10][11][12] , it is very significant the knowledge about the thickness of the different tyre layers. This aspect is particularly important as it concerns the physical models describing the tyre thermal behavior [8][9][10] , the tyre grip behavior [1,2,6,7] and the tyre wear [11] . ...
In this work is exploited the possibility to use two optical techniques and combining their measurements for the 3D characterization of different tyres with particular attention to the tyre's section. Electronic Speckle Pattern Interferometry (ESPI) and Laser Scanner (LS) based on principle of triangulation have been employed for investigating and studying the tyre's section and 3D shape respectively. As case studies two different racing tyres, Michelin S9H and Pirelli Diablo respectively, have been considered. The investigation has been focused at the aim to evaluate and measure the section's components in order to add to the 3D model obtained by Laser Scanning accurate information about the different layers along through the tyres sections. It is important to note that the assessment about the different layers along the section is a very difficult task to obtain by visual inspection or classical microscopy and even with the LS. Here we demonstrate that the different layers can be easily highlighted and identified by mean of the ESPI.
... An exhaustive analysis of the most widespread theoretical models emerged in recent years is beyond the scope of this work, but just the most common models will be mentioned specifying that they can be subdivided in empirical [6] and theoretical-numerical [7], [8]. ...
... (Fig. 10), identified by "NEW GA" code, whose surface is substantially "closed", i.e. lacking of the empty spaces due to the removal of bitumen consequent to wear. This asphalt is expected to exhibit higher values of the friction coefficient, both for better chemical attitude with SB polymers (friction adhesive component [8], [28]) and for a good indentation level due to asperities penetration into rubber tread (friction hysteretic component [8], [28]). ...
... (Fig. 10), identified by "NEW GA" code, whose surface is substantially "closed", i.e. lacking of the empty spaces due to the removal of bitumen consequent to wear. This asphalt is expected to exhibit higher values of the friction coefficient, both for better chemical attitude with SB polymers (friction adhesive component [8], [28]) and for a good indentation level due to asperities penetration into rubber tread (friction hysteretic component [8], [28]). ...
This paper deals with the experimental investigation about the sliding contact between tire tread and rough surfaces. To build and to validate reliable tire dynamical behaviour models it is fundamental the knowledge of the local grip in each point of the contact patch since in the contact patch points different conditions arise because of contact pressure, sliding speed, temperature, etc. In the paper after a brief description of the different methods usually adopted to experimentally test the tires with this aim, a new test machine, developed starting from a British pendulum at the Technical Centre Europe Bridgestone, as machine for tribological tests on rubber specimens in sliding contact with rough surface is presented. The scheme of the testing machine and the adopted measurement instruments are illustrated, together with the results of a typical test and the possible interpretations of the obtained results. © 2017, International Association of Engineers. All rights reserved.
... Knowing the viscoelastic properties is a fundamental advantage in defining strategies and methods to maximize road grip, whose definition is "the maximum Knowing the viscoelastic properties is a fundamental advantage in defining strategies and methods to maximize road grip, whose definition is "the maximum available coefficient of friction between the surface of the tire and the surface of the road" (or of any other counter-surface in contact with the tread). Such friction depends on several factors [28], such as the roughness of the road/track, the relative speed and the contact pressure between the tire and road, the tire temperature and wear level, and, of course, the viscoelastic characteristics of the tread. As concerns the factors mainly taking part in friction as considered in the vehicle dynamics field, two mechanisms, shown in Figure 2, are involved at the rubber-road interface [29]: - ...
... available coefficient of friction between the surface of the tire and the surface of the road" (or of any other counter-surface in contact with the tread). Such friction depends on several factors [28], such as the roughness of the road/track, the relative speed and the contact pressure between the tire and road, the tire temperature and wear level, and, of course, the viscoelastic characteristics of the tread. As concerns the factors mainly taking part in friction as considered in the vehicle dynamics field, two mechanisms, shown in Figure 2, are involved at the rubber-road interface [29]: -The first is the frequency excitation due to the road texture. ...
The properties of tires related to their viscoelastic behavior have a significant impact in the field of vehicle dynamics. They affect the performance and safety of a vehicle based on how they change when the tire performs in variable thermal conditions, interacts with various kinds of road surfaces, and accumulates mileage over time. To analyze and understand such properties of viscoelastic materials, destructive tests like dynamic mechanical analysis (DMA) are used, which make the tire unusable after the test; these are usually carried out on specimens cut from the zone of interest. The development of an innovative testing methodology connected to a hardware device called VESevo allows the characterization of the viscoelastic properties of tire compounds belonging to tread or other parts in a fast and nondestructive way. This new device provides valuable information about the evolution of the tire’s viscoelastic properties, allowing it to monitor them throughout the whole lifecycle. In the paper, an overview of the possible sensitivities that can be investigated thanks to the VESevo is provided: The tread viscoelasticity was characterized and monitored for several tire tread compounds, over tire mileage, over tread thermal curing cycles, and as an index of the tread quality and uniformity in production. Preliminary results were collected and are presented. In the final paragraph, further recent applications developed from the tire field, which are not directly related, are reported.
... 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.
... 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. ...
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
... 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 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.
... There are many applications that delay conditions should be considered on their own dynamics [6][7][8][9][10]. It is also necessary in real-time estimation purposes [11][12][13][14]. ...
... For variable tyre/road adherence conditions, cornering coefficients can be updated using real-time estimation approaches [7,14]. Defining the above equation [5], 23 = ( 2 + 3 )/2 and 45 = ( 4 + 5 )/2, the above set of differential equations under assumptions 1, 2 and 3 can be expressed in the state space form as follows ...
In this paper, the dynamic stability analysis and control of an articulated heavy vehicle is investigated. First, lateral dynamics of an articulated heavy vehicle is described by a 3-DOF rigid body model. Then, it is considered as a linear system with steering input with delay. System states are the lateral and yaw motion of the tractor unit and the yaw motion of the semitrailer unit. Thus a less conservative stability criterion is developed for this system with time-varying delay. The key idea is constructing a new type of LKF containing a quadruple-integral term. Moreover, novel free-weighting matrices are introduced to increase the degree of freedom in the sufficient stability condition. The proposed delay-dependent stability measure is presented in the terms of linear matrix inequalities (LMIs). Numerical simulations are performed to show the performance of the proposed approach and demonstrate that the suggested scheme is remarkably less conservative compared to the available stability analysis approaches in the literature.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in Sharifzadeh et al. (2014a); Farroni et al. (2014bFarroni et al. ( , 2013 . For instance, in the case of adaptive cruise control, estimation of friction coefficient (µ) enables the braking distances to be adjusted in real time. ...
... As experimentally investigated by Farroni et al. (2014b), the friction coefficient can be modeled with semi-empirical formulas, which generate the steady-state wheels behavior. One of the widely-used models is the Burckhardt Model, which is easy to linearize for applying recursive least squares (RLS) identification method. ...
Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction parameters in real-time. The paper deals with the trust-region based method for on-line estimation of tyre/road friction parameters. This method provides an appropriate modeling (of a vehicle and the tyre/road contact) to observe the tyre/road friction coefficients directly using measurable signals in real-time. In this work, we present a new LuGre model-based nonlinear least squares (NLLS) parameter estimation algorithm using vehicle dynamic to obtain the parameters of LuGre model based on recursive nonlinear optimization of the curve fitting errors. The proposed estimation method can also be utilized in large-scale problems with similar conditions. Very promising results have been obtained in real-time simulations for most of the driving and road situations.
... Since the motion of a ground vehicle is primarily determined by the friction forces transferred from roads via tyres, information about the tyre/road interaction is critical to many active vehicle safety control systems, including longitudinal control, yaw stability control and rollover prevention control systems. In particular friction formation is crucial tool for Brake Assist Systems (BAS), Electronic Stability Control (ESC-ESP) and Adaptive Cruise Control (ACC) systems that have recently become essential for active safety systems, as shown in Sharifzadeh et al. (2014a); Farroni et al. (2014bFarroni et al. ( , 2013 . For instance, in the case of adaptive cruise control, estimation of friction coefficient (µ) enables the braking distances to be adjusted in real time. ...
... As experimentally investigated by Farroni et al. (2014b), the friction coefficient can be modeled with semi-empirical formulas, which generate the steady-state wheels behavior. One of the widely-used models is the Burckhardt Model, which is easy to linearize for applying recursive least squares (RLS) identification method. ...
Driving safety can be achieved by better understanding critical situations which may require the knowledge of interaction between vehicle tyres and the road surfaces. It is thus essential to have a good estimation of the tyre/road friction parameters in real-time. The paper deals with the trust-region based method for on-line estimation of tyre/road friction parameters. This method provides an appropriate modeling (of a vehicle and the tyre/road contact) to observe the tyre/road friction coefficients directly using measurable signals in real-time. In this work, we present a new LuGre model-based nonlinear least squares (NLLS) parameter estimation algorithm using vehicle dynamic to obtain the parameters of LuGre model based on recursive nonlinear optimization of the curve fitting errors. The proposed estimation method can also be utilized in large-scale problems with similar conditions. Very promising results have been obtained in real-time simulations for most of the driving and road situations.
Link: https://ifac.papercept.net/conferences/scripts/abstract.pl?ConfID=213&Number=81
... 2. Analysis of real thermal and frictional interaction effects: Tire test rigs bring some unavoidable alterations to the tire test conditions that sometimes result to be quite far from reality; an example can be the employment of sliding flat belts, able to keep the tire in rolling, but very different from real road in terms of roughness characteristics, stiffness and thermal conductivity. The possibility to test tires under real working conditions allows to take into account the real effect of frictional and thermal phenomena [14,15], usually neglected or misestimated. 3. Analysis of the test session results: Testing departments often work considering the opinion of specialized drivers as a unique instrument to evaluate tire performances; this essential subjective phase could be supported by a pure objective tool, able to provide an immediate comparison among the different tested tires. ...
... The described procedure is a part of a larger research activity, whose final target, fixed in collaboration with a motorsport racing team, with a high performance vehicle manufacturer and with a tire research and development technical center, is the realization of a physical tire model which can be employed in driving simulators and to predict tires behavior in a wide range of conditions. A key point to reach this target is the integration of the TRICK procedure with physical models [14,15], finally bringing about the realization of a procedure able to estimate tire interaction characteristics, taking into account the fundamental friction and thermal phenomena related to tire/road interaction.Fig. 16. ...
The most powerful engine, the most sophisticated aerodynamic devices or the most complex control systems will not improve vehicle performances if the forces exchanged with the road are not optimized by proper employment and knowledge of tires. The vehicle interface with the ground is constituted by the sum of small surfaces, wide about as one of our palms, in which tire/road interaction forces are exchanged. From this it is clear to see how the optimization of tire behavior represents a key-factor in the definition of the best setup of the whole vehicle.Nowadays, people and companies playing a role in automotive sector are looking for the optimal solution to model and understand tire's behavior both in experimental and simulation environments. The studies carried out and the tool developed herein demonstrate a new approach in tire characterization and in vehicle simulation procedures. This enables the reproduction of the dynamic response of a tire through the use of specific track sessions, carried out with the aim to employ the vehicle as a moving lab.The final product, named TRICK tool (Tire/Road Interaction Characterization and Knowledge), comprises of a vehicle model which processes experimental signals acquired from vehicle CAN bus and from sideslip angle estimation additional instrumentation. The output of the tool is several extra "virtual telemetry" channels, based on the time history of the acquired signals and containing force and slip estimations, useful to provide tire interaction characteristics. TRICK results can be integrated with the physical models developed by the Vehicle Dynamics UniNa research group, providing a multitude of working solutions and constituting an ideal instrument for the prediction and the simulation of the real tire dynamics.
... For example, Rosen et al. presented a laboratory investigation on the variation of the tire sliding grip coefficient depending on the tire construction, inflation pressure, vertical load, and wheel camber [5]. Taking into account the rubber viscoelasticity, road randomness, pressure, temperature, and speed, Farroni et al. developed a friction model to evaluate the accurate sliding frictional coefficient under various conditions [6]. Boutylin et al. investigated the dependence between the friction coefficient and wheel slip as a function of deformation, adhesion, absolute slip velocity, and road roughness [7]. ...
The grip force of tires is crucial for vehicle security and drivability under different driving conditions. A small contact area and stress concentration in the contact patch of two-wheeled motorcycle (TWM) tires result in a reduction in grip performance and wear resistance. Even worse, improving the grip and wear resistance together is difficult to achieve. The purpose of the current study is to analyze the dynamic grounding characteristics and geometry of a cat paw pad and then apply its structure to the TWM tire to improve the contact area and wear resistance under different operating conditions. A nonlinear finite element tire model that could accurately reconstruct the tire structure and realistically reflect the mechanical response to different loads was employed. Then, the accuracy of the tire model was validated by a static test with a control tire. For cats, the dynamic grounding characteristics and topology of paw pads were determined using a pressure-sensitive walkway and a three-dimensional (3D) laser scanner. The results indicated that the cat forepaw third pad (CFTP) exhibited excellent grip capacity. According to similarity transformation, a bionic tire crown was designed according to the lateral fitting curve of the CFTP. Comparative results showed the enlargement of the contact area and decreases in peak pressure and frictional energy rate for the bionic tire under different conditions. With these improvements, the grip performance was improved, and the service life was extended synchronously. These research results can be applied for the design of TWM tires, especially cross-country motorcycle tires.
... As concerns the identification of the parameters of contact and friction physical models [5] [6], the availability of data on the thermal and structural behavior of the tread compounds provides an increase in the reliability and the predictivity of the proposed formulations, often parameterized in "reverse" basing on tribological experimental data [7] [8]. The possibility, moreover, to obtain such parameters by means of a non-destructive methodology would allow to preserve tire integrity and to exclude the boundary effects linked to the testing of small specimens. ...
The evaluation of the tire tread viscoelastic characteristics, especially by means of non-destructive procedures, is a particularly interesting topic for motorsport teams and companies, used to work with unknown and confidential compounds. The availability of such information would define new scenarios in vehicle analysis field, as the possibility to provide physical inputs to tire grip models or the study of the suspensions setup able to make tires work inside their optimal thermal working range. The employment of commercial devices allows to select by means of specific indices the optimal combination of tires to be installed on a vehicle, but it does not provide any information physically correlated with the tread polymers characteristics. The aim of the presented activity is the modelling of one of the cited devices, a dynamic dial indicator, interacting with a viscoelastic half-space. The obtained results allow, analyzing the signals acquired by the device, to identify the tread equivalent stiffness and damping as a function of tire working temperature, providing the basic guidelines for the development of an innovative procedure for a full non-destructive viscoelastic characterization of the tire compounds. Index Terms-Material non-destructive characterization, temperature effect, tire tread compound behavior, TSD, viscoelastic characteristics.
... There are several types of TCS in literature in addition to dedicated studies examining road-tyre friction characteristics focusing on temperature [5] and prolonged sliding conditions [6]. If the TCS application is narrowed down to EVs, one of the simplest form is model following controller (MFC) studied in [1]. ...
The application of traction control systems (TCS) for electric vehicles (EV) has great potential due to easy implementation of torque control with direct-drive motors. However, the control system usually requires road-tire friction and slip-ratio values, which must be estimated. While it is not possible to obtain the first one directly, the estimation of latter value requires accurate measurements of chassis and wheel velocity. In addition, existing TCS structures are often designed without considering the robustness and energy efficiency of torque control. In this work, both problems are addressed with a smart TCS design having an integrated acoustic road-type estimation (ARTE) unit. This unit enables the road-type recognition and this information is used to retrieve the correct look-up table between friction coefficient and slip-ratio. The estimation of the friction coefficient helps the system to update the necessary input torque. The ARTE unit utilizes machine learning, mapping the acoustic feature inputs to road-type as output. In this study, three existing TCS for EVs are examined with and without the integrated ARTE unit. The results show significant performance improvement with ARTE, reducing the slip ratio by 75% while saving energy via reduction of applied torque and increasing the robustness of the TCS.
... There are several types of TCS in literature in addition to dedicated studies examining road-tyre friction characteristics focusing on temperature [5] and prolonged sliding conditions [6]. If the TCS application is narrowed down to EVs, one of the simplest form is model following controller (MFC) studied in [1]. ...
The application of traction control systems (TCS) for electric vehicles (EV) has great potential due to easy implementation of torque control with direct-drive motors. However, the control system usually requires road-tire friction and slip-ratio values, which must be estimated. While it is not possible to obtain the first one directly, the estimation of latter value requires accurate measurements of chassis and wheel velocity. In addition, existing TCS structures are often designed without considering the robustness and energy efficiency of torque control. In this work, both problems are addressed with a smart TCS design having an integrated acoustic road-type estimation (ARTE) unit. This unit enables the road-type recognition and this information is used to retrieve the correct look-up table between friction coefficient and slip-ratio. The estimation of the friction coefficient helps the system to update the necessary input torque. The ARTE unit utilizes machine learning, mapping the acoustic feature inputs to road-type as output. In this study, three existing TCS for EVs are examined with and without the integrated ARTE unit. The results show significant performance improvement with ARTE, reducing the slip ratio by 75% while saving energy via reduction of applied torque and increasing the robustness of the TCS.
... The main differences among the illustrated methodologies, as confirmed by Fig. 7, regard the limit cornering behavior at high vertical loads, allowing consequently to consider the results, in terms of the estimation of the cornering stiffness, fully acceptable. In Fig. 8 a direct comparison among the three methodologies, expressed in terms of grip [45,46] (adimensionalization of the tangential interaction force respect to the applied normal load) is reported. The results observed from the friction point of view confirm the effectiveness of the procedure carried out considering the Principal Components for the evaluation of the tire cornering stiffness, enabling the possibility to implement an analytical real-time algorithm able to be run on-board with the aim to enhance the reliability of safety controls and the level of predictability and adaptability of the control logics to the variations due to wear, temperature and environmental boundary conditions. ...
... In the last decade the research is focusing on different types of ADAS concerning car occupant, pedestrian and/or cyclist safety such as Autonomous Emergency Braking (AEB), Lane Keeping Assistant (LKA), and Adaptive Cruise Control (ACC) [5,6,7]. As far as AEB is concerned, it combines sensing of the environment ahead of the vehicle with the automatic activation of the brakes [8] (without driver input) in order to mitigate or avoid an accident. The level of automatic braking varies and it may be up to full ABS braking capability. ...
The main idea of the present work is to define the domain in which it is possible to adopt very simple models of vehicle dynamics for applications in the testing of Advanced Driver Assistance Systems (ADAS) in lieu of complex models. The aim is to reduce the computational burden, and consequently the computing time. In particular, in the paper, the performances of a very simple model of vehicle dynamics, the Single Track with linear tires, have been compared with those of a complex and complete model, with non-linear tires, included in a commercial software (IPG CarMaker). For sake of shortness, the comparison has been carried out focusing on the lateral dynamical behaviour, and consequently the testing of a Lane Keeping Assistant (LKA) system has been carried out. Of course both the vehicle dynamic models, and the ADAS system have been integrated in a common simulation environment (Simulink), and tested in the standard traffic scenarios defined in EuroNCAP test protocols.
... The final goal of the research is the development of an analytical friction model able to take into account the described functionalities. This model of local grip, coupled with appropriate interaction models that are available in the literature and are able to provide the local operating conditions [10][11][12][13][14][15], will allow determination in real time of local interaction forces and, integrating them, also the global ones between tire and road, which can be compared with measurements made on the road. ...
The results of an experimental activity, carried out using a prototype of pin on disk machine and aimed at investigating the frictional behavior of visco-elastic materials in sliding contact with rigid asperities, are presented.
The pin is a rubber specimen coming from three different passenger automotive tires, while the disk is covered with glass, marble, or 3M anti-slip tape surfaces. Tests, performed both in dry and wet conditions, highlighted that the friction coefficient is strongly influenced by the effect that surface roughness plays on friction mechanisms of adhesion and hysteresis. The results confirmed the theoretical dependence of friction on vertical load, sliding velocity, rubber characteristics, and track conditions.
... stability control systems, intelligent driver support systems, adaptive cruise control, collision-avoidance systems and other intelligent vehicle safety systems [9,3,4]. ...
It is well recognized in the automotive research community that knowledge of the real-time tyre-road friction conditions can be extremely valuable for intelligent safety applications, including design of braking, traction, and stability control systems. This paper presents a new development of an on-line tyre-road adherence estimation methodology and its implementation using both Burckhardt and LuGre tyre-road friction models. The proposed strategy first employs the recursive least squares to identify the linear parameterization (LP) form of Burckhardt model. The identified parameters provide through a Takagi-Sugeno (T-S) fuzzy system the initial values for the LuGre model. Then, it is presented a new large-scale optimization based estimation algorithm using the steady state solution of the partial differential equation (PDE) form of LuGre to obtain its parameters. Finally, real-time simulations in various conditions are provided to demonstrate the efficacy of the algorithm.
... Over the past decades, many efforts have been focused on the study of pneumatic tyre modelling [6][7][8][9][10] and the dynamic interaction between the tyre and the soil. [11][12][13] A precise tyre modelling method is an important part of understanding and estimating the tyre-soil interaction. ...
An innovative non-pneumatic tyre called the mechanical elastic wheel is introduced; significant challenges exist in the prediction of the dynamic interaction between this mechanical elastic wheel and soil containing an obstacle owing to its highly non-linear properties. To explore the mechanical properties of the mechanical elastic wheel and the soil, the finite element method is used, and a non-linear three-dimensional finite element wheel–soil interaction model is also established. Hyperelastic incompressible rubber, which is one of the main materials of the mechanical elastic wheel, is analysed using the Mooney–Rivlin model. The modified Drucker–Prager cap plasticity constitutive law is utilized to describe the behaviour of the soil, and the obstacle is represented as an elastic body. Simulations with different rotational speeds of the mechanical elastic wheel were conducted. The stress distribution and the displacement of the mechanical elastic wheel and the soil were obtained, and the effects of different rotational speeds on the displacement, the velocity and the acceleration of the hub centre are presented and discussed in detail. These results can provide useful information for optimization of the mechanical elastic wheel.
... 35 The dynamic frictional coefficient is an important factor in contact mechanics and is often influenced by the road roughness, the stiffness characteristics of the materials, the temperature dependences, etc.; also, there have been many studies on exact friction models. [37][38][39] For simplification, a simple model for slip friction coefficients, in which the effects of both the slip velocity and the static friction coefficient were considered, was employed according to ...
This paper focuses on invetigating the relationship between the contact features of the tyres and the tyre wear in a quantitative sense as a function of the tyre structure and the manoeuvre parameters by utilizing a modified theoretical tyre wear model. The modified tyre wear model was developed by combining a modified ring model for the tyres and a modified brush model and was validated. The model parameters were also identified by physical experiments. Moreover, the contact features were characterized as the contact length, the asymmetry factor and the rolling resistance shift in order to investigate the influence of the contact features on the tyre wear. The amount of wear versus the three key variables of the contact features with variations in the tyre parameters was plotted and analysed. The results show that the maximum normal contact pressure does not play the most important role in the tyre wear. An increase in the damping coefficient can lead to an increase in the tyre wear, whereas increases in the effective elastic constant, the effective bending density and the effective bending stiffness result in a decrease in wear. The three key variables of the contact features increase with increasing vertical load, increasing rolling velocity and increasing damping coefficient and with decreasing inflation pressure and decreasing effective bending stiffness. The tyre wear follows the same trend when the three key variables increase or decrease synchronously. This analysis provides a quantitative indication of the relationship between the contact features and the tyre wear in order to obtain guidelines for tyre manufacturers on how to achieve less tyre wear.
... The total braking and driving torques are obtained as output of 'Control Logic' subsystem, acting on all four wheels of the vehicle. It is very relevant to properly take in account tyres' behaviour on the road [26,27], and in our case the 'Magic formula' by Hans Pacejka [28] was implemented, which solves the dynamics of the wheels and assesses the forces actually exchanged between the tyres and the road (taking into account the available grip and the vertical load acting on all four tires). In the 'Vehicle Dynamics' subsystem the equilibrium in the longitudinal direction is considered: ...
The research presented here is framed in the area of the design of Advanced Driving Assistance Systems (ADAS), carried out in the so-called automotive V-Cycle. In particular we concentrated our effort at the Model In the Loop (MIL) level. Indeed we developed an additional component for the fuel consumption evaluation at the MIL stage. The developed component has been based on the combination of a simplified model of the vehicle dynamics, and a fuel consumption model calibrated in previous experiments. The developed module is used for tuning the parameters of an Ecological fully Adaptive Cruise Control System.
... Grip Estimator for Tyre Analysis (GrETA) 20 is a physical-analytical tire grip model developed with the aim to satisfy motorsport and tiremakers requests, providing the calculation of the power dissipated in a polymeric material indented by a road asperity, taking into account the adhesive/hysteretic effects and the viscoelastic experimental characteristics. 21 In order to model the complex interactions between tire and asphalt at a microscopic level, the model focuses on the behaviour of an elementary volume of rubber in sliding contact with a limited portion of road. ...
The tire and vehicle setup definition, able to optimise grip performance and thermal working conditions, can make the real difference as for motorsport racing teams, used to deal with relevant wear and degradation phenomena, as for tire makers, requesting for design solutions aimed to obtain enduring and stable tread characteristics, as finally for the development of safety systems, conceived in order to maximise road friction, both for worn and unworn tires. The activity discussed in the paper deals with the analysis of the effects that tire wear induces in vehicle performance, in particular as concerns the consequences that tread removal has on thermal and frictional tire behaviour. The physical modelling of complex tire–road interaction phenomena and the employment of specific simulation tools developed by the Vehicle Dynamics UniNa research group allow to predict the tire temperature local distribution by means of TRT model and the adhesive and hysteretic components of friction, thanks to GrETA model. The cooperation between the cited instruments enables the user to study the modifications that a reduced tread thickness, and consequently a decreased SEL (Strain Energy Loss) and dissipative tread volume, cause on the overall vehicle dynamic performance.
... Nowadays everyone playing a role in automotive sector is looking for the optimal solution in order to model and to understand the tyres behaviour in both experimental and simulation environments. The ability to predict the interior temperature distribution, and thus the grip behaviour of the tyre [3], is fundamental in terms of the vehicle handling improvement and of the asset optimization according to highly variable outdoor testing conditions [4]. ...
New structure elements have been developed and implemented in the TRT thermo-dynamic tyre model. The updated model aims to provide a complete tool to study and understand all the phenomena concerning the tyre behaviour in thermal transient conditions, since all the elements constituting its structure are modelled. The computational cost, connected to a more complex model to manage, has been decreased by simplifying the mesh of the previous model version and, thus, by reducing the state vector length so making it suitable for real time analyses.
... Thanks to ABS logic, it is even possible to take into account the possibility of tyres locking, following the very intense application of braking and/or poor traction driving conditions (e.g. on snow, ice, rain etc.). As regards the variations in road frictional conditions, fundamental in ABS actuation, a specific physical grip model was employed [28]. In the ABS block two proportionalintegral controllers were used to estimate the magnitude of the action to be performed on the vehicle's systems to let it move according to the ADAS control logics. ...
This paper presents some results on the development and testing of new solutions in the field of driving automation. The introduction of increasing levels of vehicle automation aimed at enhancing road safety requires a renewed approach to the research and development process and needs a multi-actor environment where the innovation can be tested. Indeed, vehicle automation spans several scientific disciplines and it is becoming exceedingly difficult and too costly for a single research innovation team to go in depth into all technologies and solutions. This is shifting the innovation process toward a multidisciplinary approach in which the only way to ensure an easy, rapid, efficient and scalable introduction of the required innovation is to adopt integrated and complex testing platforms for the simulation of automation solutions, based on a modular architecture, where independent components can be developed and then integrated and tested in a multi-actor environment. A platform for virtual testing is presented herein and employed to assess the performance of an integrated driving assistance solution based on computing appropriate surrogate measures of safety that allow for the transition between different automation logics in free-flow, car-following and emergency braking conditions.
... With the aim to analyze and understand the complex phenomena concerning with local contact between viscoelastic materials and rough surfaces [9], GrETA grip model has been developed [10]. The main advantage the employment of the grip model represents is the possibility to predict the variations induced by different tread compounds or ground textures on vehicle dynamics, leading to the definition of a setup able to optimize performances as a function of the tyre working conditions. ...
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.
... Thanks to the ABS logic, it is even possible to take into account the possibility of tyres' locking, following to very intense application of braking and/or to poor traction driving conditions (e.g. on snow, ice, rain etc.). As concerns the variations in road frictional conditions, fundamental in ABS actuation, a specific physical grip model has been employed [30]. In ABS block two proportional-integral controllers have been used in order to estimate the magnitude of the action it is necessary to perform on the vehicle's systems to let it move according to the ADAS control logics. ...
This paper presents some preliminary analyses on the development of new tools for the transport industry, able to deal with the introduction of increasing levels of vehicle automation. Driving assistance is aimed at increasing road safety, but it needs a renewed approach to the research and development process. Indeed, vehicle automation spans several scientific disciplines and it's becoming exceedingly difficult and too costly for a single research innovation team to " go deep " across all technologies and solutions. The only way to ensure an easy, fast, efficient, and scalable introduction of the required innovation is to adopt integrated and complex testing platform for the simulation of automation solutions. To this aim virtual-testing platforms should be conceived to allow different actors to work on different components, possibly at different levels of detail, any of the actors being allowed to sophisticate with a particular simulation issue (e.g. the driver behaviour in presence of Advanced Driving Assistance Systems) knowing that the other components (e.g. the vehicle dynamics) have been (or will be) simulated at the required sophistication level, possibly by another actor of the innovation process. In this paper the authors wishes to contribute to the development of these new-generation tools. Analyses will be carried out in order to identify the key opportunities and criticalities in the development of virtual testing platform for testing driving automation. From these analyses research perspectives will be identified and proposed for future developments.
... In the event of low-friction situations, it is advantageous to control the vehicle sideslip angle, preventing it from assuming unexpected values [9], [10]. However, despite the absolute benefits deriving from the direct measurement of Manuscript the sideslip angle and absolute vehicle velocity, these values are not usually directly measured on production cars and therefore must be estimated [11], [12]. ...
Accurate measurement of the vehicle sideslip angle is fundamental to improve reliability of the vehicle dynamics control systems focused on stability and developed both for safety and performance optimization. Many experimental procedures to estimate the vehicle sideslip angle have been proposed in the last years, mainly based on GPS, INS and physical models. The aim of this paper is to compare different methods to estimate sideslip angle employing an instrumented vehicle, equipped with a system for data acquisition and time-synchronized storage capabilities, a stand-alone GPS, a GPS aided MEMS-based Attitude and Heading Reference System (AHRS) and specific sensors to collect data on the steering wheel angle and on the position of brake, throttle and clutch pedals. Further information is collected by capturing the available data at the OBD port of the vehicle. Data acquisitions (from all sensors) are synchronized by means of an external triggering signal. After driving sessions performed with specific manoeuvres in order to highlight the main phenomena concerned with the dynamic behaviour of the vehicle, the different estimation procedures have been applied, discussing on the advantages and the degree of reliability of each one of them.
... Specifying that the DMA test has been carried out at a frequency of 1Hz, notably di erent from common tread stress frequencies, a quick calculation, hypothesizing an average road macro-roughness wavelength λ equal to 0.01m and an average sliding speed Vs of 5m/sec, enables the real tire temperature at which the tan δ maximum can be experienced by the driver to be estimated. Applying a simpli ed version of the WLF equation, 8 it is possible to obtain which, added to the starting 42°C, gives a temperature of 63.6°C, in accordance with the experimental value shown in the analyses already presented. ...
The automotive sector is looking for the optimal solution in modeling and understanding tire behavior in
experimental and simulation environments.1,2,3 !e studies and tools described here represent a new
approach in tire characterization and vehicle simulation procedures, leading to the complete reproduction of the dynamic response of a tire and of its frictional and thermodynamic behavior simply by means of specific
track sessions and a few laboratory measurements. !is represents a bridge between a robust and widespread approach, like Pacejka’s, and purely physical modeling, that satis"es predictive requests and the need for deeper knowledge about complex phenomena.
In this paper, we present a Boundary Element methodology to numerically investigate the operation of a viscoelastic rolling element bearing in steady-state conditions. The methodology is fully general, able to deal with any real linear viscoelastic material, and relies on the ad hoc definition of steady-state viscoelastic Green’s functions that intrinsically take into account the circular geometry of the domain. From an applicative point of view, the assessment of this contact problem is crucial: we show that the distribution of the load among the rollers is really different from what is predicted in purely elastic conditions, with some rollers eventually losing the contact with the raceways for some speed values. This has dramatic consequences not only on the rolling element bearing durability but may impact the rotor dynamics of the system supported by the bearing. Furthermore, our analysis assesses the viscoelastic torque pointing out the sources of hysteretic dissipation. Finally, to corroborate our model, numerical predictions for a rolling element bearing with the outer ring made of Polytetrafluoroethylene (PTFE) are compared, with good agreement, to experimental outcomes.
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.
Uncertainties in parameters can affect racing car performance. In this study, a nonlinear interval suspension damping optimization method is proposed to improve the road holding of a racing car. To evaluate the dynamic responses of racing cars under a random road input and a bump input with interval uncertain parameters, a quarter car model with a two-stage asymmetric damper is established. Then, a quadratic approximation model with second derivative terms is developed by second-order Taylor series expansion and dimension reduction to calculate the nonlinear dynamic response of the vehicle. Interval analysis of the objective function and constraints is carried out using interval arithmetic to eliminate nesting optimization and make the optimization efficient. The results show that the proposed optimization method can improve road holding performance, effectively suppress the fluctuation range of the road holding performance evaluation index, and ensure the robustness of the design scheme.
Optimal control is used to study the management of tyre performance for a Formula One car. Tyre friction is compromised by accumulated wear and operation outside the tyre design temperature window – inappropriate thermal operation accelerates tyre wear. In this study tyre wear is modelled as a function of the tyre surface temperature and the power dissipated at the road contact. The tyre's frictional performance is modelled as a function of temperature and accumulated wear. A previously developed thermodynamic model is modified by the addition of a state representing the tyres' carcass temperature. Optimal control calculations are used to optimise (multi-lap) performance by improving grip and extending the life of the tyres. In combination, tyre wear and friction control can be used to schedule tyre changes and minimise race times.
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.
Abstract— The article discusses a possibility of using fiber-optic sensors based on address fiber Bragg structures (AFBS) to assess a dynamic of tire. A motivation for a study is to develop an economically sound sensor system for measuring forces acting on a wheel. A description of a multisensor measuremets technology of continuous monitoring of the tire state was presented and disscused. Information from the sensors is used as input parameters of an algorithms that allow evaluating key characteristics, such as longitudinal and lateral friction forces. One of the advantages of this new technology is the fact that an optical photodetector is used as an interrogator, which greatly simplifies the system.
In this chapter, the dynamic stability analysis and control of an articulated heavy vehicle is investigated. First, lateral dynamics of an articulated heavy vehicle is described by a 3-DOF rigid body model. Then, it is considered as a linear system with steering input with delay. System states are the lateral and yaw motion of the tractor unit and the yaw motion of the semitrailer unit. Thus a less conservative stability criterion is developed for this system with time-varying delay. The key idea is constructing a new type of LKF containing a quadruple-integral term. Moreover, novel free-weighting matrices are introduced to increase the degree of freedom in the sufficient stability condition. The proposed delay-dependent stability measure is presented in the terms of linear matrix inequalities (LMIs). Numerical simulations are performed to show the performance of the proposed approach and demonstrate that the suggested scheme is remarkably less conservative compared to the available stability analysis approaches in the literature.
A relatively new technology for the electric vehicles considers the use of brushless permanent magnet motors directly connected to the car wheels (in-wheel motors or hub motors). In order to evaluate the performance that can be obtained, a complete dynamic model of a four-wheel drive (4WD) electric vehicle equipped with four in-wheel motors is developed and a correspondent parametric simulator is implemented in Matlab/SimulinkTM. The simulator is also employed for designing, testing and comparing various control logics which reproduce the handling behavior of a real vehicle.
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.
Pneumatic tyres are used in vehicles since the beginning of the last century. They generate braking and steering forces for bicycles, motor cycles, cars, busses, trucks, agricultural vehicles and aircraft. These forces are generated in the usually very small contact area between tyre and road and their performance characteristics are of eminent importance for safety and comfort. Much research has been addressed to optimise tyre design with respect to footprint pressure and friction. In this context, the development of virtual tyre prototypes, that is, simulation models for the tyre, has grown to a science in its own. While the modelling of the structural dynamics of the tyre has reached a very advanced level, which allows to take into account effects like the rate-independent inelasticity of filled elastomers or the transient 3D deformations of the ply-reinforced tread, shoulder and sidewalls, little is known about the friction between tread-block elements and road. This is particularly obvious in the case when snow, ice, water or a third-body layer are present in the tyre–road contact. In the present paper, we give a survey on the present state of knowledge in the modelling, simulation and experimental validation of tyre tread-block friction processes. We concentrate on experimental techniques.
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.
The results of an experimental activity carried out with the aim to investigate on the adhesive behaviour of visco-elastic materials in sliding contact with road asperities are presented. Experiments are carried out using a prototype of pin on disk machine in which pin is constituted by a specimen of rubber coming from a commercial tire, while different disks are realized in glass, marble, steel and in abrasive paper of different roughness. Tests are performed in both dry and wet conditions. Roughness of the test surfaces is evaluated by a rugosimeter, while pressure is evaluated, off-line, analysing the extension of the contact patch left by the pin on a sheet of graph paper under known applied loads. Slide velocity is imposed by an inverter controlled motor driving the disk. Basing on well known theoretical hypotheses, adhesive component of friction coefficient is estimated making the specimens slide on surfaces characterized by low values of macro-roughness, in order to underline the differences in rubber behaviour respect to micro-roughness surface variations. The results confirmed adhesion dependence on pressure and sliding velocity in both cases of smooth surfaces, where the main friction mechanism is the adhesive one, and of rough surfaces, where the main friction mechanism is the hysteretic one. Analysing various surfaces roughness it is possible to notice a maximized adhesive contribution on flat surfaces; it reduces with increasing roughness, while hysteretic friction comes over instead of it because of asperities penetration into rubber sliding surface. Moreover in the case of rough surfaces the separation between static and dynamic friction coefficient is evident and the static coefficient is greater than the dynamic one. On the other hand in case of smooth surface the absence of indentation phenomena doesn't allow to recognize, in the measured force time history, the "classical" peak usually associated to the static friction coefficient. Dry and wet tests performed on different micro-roughness profiles highlighted that friction coefficient in dry conditions is greater on smoother surfaces, while an opposite tendency is shown in wet condition, when asperities are greater enough to break the thin water layer, providing a certain degree of indentation. A proposal for a methodology able to estimate the only adhesive friction component, developed thanks to wet contact tests, is expressed in the end of the paper.
In this paper the results of an experimental activity carried out with the aim to investigate on the frictional behaviour of visco-elastic materials in sliding contact with road asperities is presented.
Experiments are carried out using a prototype of pin on disk machine whose pin is constituted by a specimen of rubber coming from a commercial tyre while the disk may be in glass, marble or abrasive paper. Tests are performed both in dry and wet conditions.
Roughness of the disk materials is evaluated by a tester and by a laser scan device. Temperature in proximity of the contact patch is measured by pyrometer pointed on the disk surface in the pin trailing edge, while room temperature is measured by a thermocouple. Sliding velocity is imposed by an inverter controlled motor driving the disk and measured by an incremental encoder. Vertical load is imposed applying calibrated weights on the pin and friction coefficients are measured acquiring the longitudinal forces signal by means of a load cell.
As regards to the road roughness, the experimental results show a marked dependence with road Ra index.
Dry and wet tests performed on different micro-roughness profiles (i.e. glass and marble) highlighted that friction coefficient in dry conditions is greater on smoother surfaces, while an opposite tendency is shown in wet conditions.
Although affected by uncertainties the results confirm the dependence of friction on temperature, vertical load and track conditions.
Surface roughness evaluation is very important for many fundamental problems such as friction, contact deformation, heat and electric current conduction, tightness of contact joints and positional accuracy. For this reason surface roughness has been the subject of experimental and theoretical investigations for many decades. The real surface geometry is so complicated that a finite number of parameters cannot provide a full description. If the number of parameters used is increased, a more accurate description can be obtained. This is one of the reasons for introducing new parameters for surface evaluation. Surface roughness parameters are normally categorised into three groups according to its functionality. These groups are defined as amplitude parameters, spacing parameters, and hybrid parameters. This paper illustrates the definitions and the mathematical formulae for about 59 of the roughness parameters. This collection of surface roughness parameter was used in a new software computer vision package called SurfVision developed by the authors. In the package, these definitions were extended to calculate the 3D surface topography of different specimens.
The contact friction characteristic between a tyre and the road is a key factor that dominates the dynamics performance of a vehicle under critical conditions. Vehicle dynamics control systems, such as anti-lock braking systems, traction control systems, and electronic stability control systems (e.g. Elektronisches Stabilitäts Programm (ESP)), need an accurate road friction coefficient to adjust the control mode. No time delay in the estimation of road friction should be allowed, thereby avoiding the disappearance of the optimal control point. A comprehensive method to predict the road friction is suggested on the basis of the sensor fusion method, which is suitable for variations in the vehicle dynamics characteristics and the control modes. The multi-sensor signal fusion method is used to predict the road friction coefficient for a steering manoeuvre without braking; if active braking is involved, simplified models of the braking pressure and tyre force are adopted to predict the road friction coefficient and, when high-intensity braking is being considered, the neural network based on the optimal distribution method of the decay power is applied to predict the road friction coefficient. The method is validated through a ground test under complicated manoeuvre conditions. It was verified that the comprehensive method predicts the road friction coefficient promptly and accurately.
In this article, a logic for vehicle dynamics control during partial braking while turning a corner is presented, which only requires knowledge of the instantaneous speed of the four wheels. For this reason, the proposed control algorithm can be adopted on all ABS equipped cars. A scheme of the simulation program for logic validation is described, which is constituted by a loop of software models of the principal vehicle subsystems which are singly illustrated. The proposed logic has been tested both in closed and open-loop maneuvers. The results are provided in the form of time histories of the principal analyzed quantities. The analysis of the results confirms the goodness of the proposed control strategy.
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 novel aspects regarding the physically motivated modelling of rubber stationary sliding friction on rough surfaces. The description of dynamic contact is treated within the framework of a generalized Greenwood–Williamson theory for rigid/soft frictional pairings. Due to the self-affinity of rough surfaces, both hysteresis and adhesion friction components arise from a multi-scale excitation of surface roughness. Beside a complete analytical formulation of contact parameters, the morphology of macrotexture is considered via the introduction of a second scaling range at large length scales which mostly contribute to hysteresis friction. Moreover, adhesion friction is related to the real area of contact combined with the kinetics of interfacial peeling effects. Friction experiments carried out with different rubbers on rough granite and asphalt point out the relevance of hysteresis and adhesion friction concepts on rough surfaces. The two scaling ranges approach significantly improves the description of wet and dry friction behaviour within the range of low sliding velocity. In addition, material and surface effects are predicted and understood on a physical basis. The applicability of such modelling is of high interest for materials developers and road constructors regarding the prediction of wet grip performance of tyres on road tracks.
Surface roughness has a huge impact on many important phenomena. The most
important property of rough surfaces is the surface roughness power spectrum
C(q). We present surface roughness power spectra of many surfaces of practical importance,
obtained from the surface height profile measured using optical methods and the atomic
force microscope. We show how the power spectrum determines the contact area
between two solids. We also present applications to sealing, rubber friction and
adhesion for rough surfaces, where the power spectrum enters as an important input.
We study the heat transfer between elastic solids with randomly rough surfaces.We include both the heat transfer from the area of real contact, and the heat transfer between the surfaces in the non-contact regions.We apply a recently developed contact mechanics theory, which accounts for the hierarchical nature of the contact between solids with roughness on many different length scales. For elastic contact, at the highest (atomic) resolution the area of real contact typically consists of atomic (nanometer) sized regions, and we discuss the implications of this for the heat transfer. For solids with very smooth surfaces, as is typical in many modern engineering applications, the interfacial separation in the non-contact regions will be very small, and for this case we show the importance of the radiative heat transfer associated with the evanescent electromagnetic waves which exist outside of all bodies.
Die Bedeutung der Reibung in unserem Alltag ist nicht zu unterschätzen. Vom Entfachen eines Feuers durch Aneinanderreiben von Stöckchen bis hin zu den heutigen Bemühungen, nanoelektromechanische Systeme herzustellen, hat die Reibung eine zentrale Rolle in der Technologieentwicklung der Menschheitsgeschichte gespielt. Reibung ist ein komplexes Phänomen, das sich auf vielen verschiedenen Längenskalen abspielt. Es hängt stark von den atomaren Wechselwirkungen innerhalb der Kontaktflächen, den makroskopischen elastischen und inelastischen Eigenschaften der Materialien sowie der unvermeidbaren stochastischen Rauigkeit realer Oberflächen ab. Trotz großer Fortschritte in der Tribologie -- der Reibungswissenschaft -- sind noch viele interessante Fragen offen. Diese Arbeit befasst sich unter Zuhilfenahme numerischer Methoden mit der Rolle der Oberflächenrauigkeit in der Tribologie auf den verschiedenen Längenskalen, von der atomaren bis zur makroskopischen Größenordnung. Wir haben verschiedene Aspekte der Kontakte rauer Oberflächen untersucht, zum Beispiel Adhäsions- und Reibungseigenschaften sowie die Leckströmungen von Flüssigkeiten an einer Dichtung. Außerdem haben wir wir das Benetzungsverhalten von Nanotröpfchen auf stochastisch rauen Oberflächen betrachtet. Für eine aussagekräftige Untersuchung der Mechanik des Kontaktes ist es notwendig, die Dicke des elastischen Materials vergleichbar mit der größten Wellenlänge der Oberflächenrauigkeit zu wählen. Obwohl man prinzipiell eine atomistische Beschreibung verwenden sollte, ist der numerische Aufwand bereits bei kleinen Systemen zu hoch. Deshalb haben wir eine Multiskalen-Molekulardynamik-Methode entwickelt, bei der wir eine atomistische Beschreibung nur in den kritischen Regionen, nämlich in den Nanokontakten und an der Oberfläche, verwenden; in den übrigen Gebiete wird die Physik der langreichweitigen elastischen Response durch ein gröberes Modell wiedergegeben. Die Kontaktfläche und die Grenzflächenseparation werden als Funktion des auf das System ausgeübten Drucks ohne und mit Adhäsion analysiert. Die tatsächliche Kontaktfläche beeinflusst die Reibungs- und Hafteigenschaften und die Abnutzung entscheidend. Die Grenzflächenseparation ist dagegen verantwortlich für Effekte wie die Kapilarität, optische Interferenz und die Leckrate einer Abdichtung. Durch numerische Simulationen konnten wir zeigen, dass bei kleinem Druck und ohne anziehende Wechselwirkung die effektive Kontaktfläche linear vom angewandten Druck abhängt, während die Grenzflächenseparation logarithmisch von diesem abhängt. Ferner haben wir das Gleiten von elastischen Materialien mit adhäsivem Kontakt bei glatten und rauen Oberflächen untersucht. Dabei haben wir eine starke Abhängigkeit der Gleitreibung vom Elastizitätsmodul festgestellt; dies ist eine der Hauptursachen der Gleitinstabilität. Bei elastisch harten Materialien mit glatten Oberflächen und inkommensurablen Gitterstrukturen beobachteten wir eine extrem niedrige Reibung (superlubricity), die bei sinkendem Elastizitätsmodul des Festkörpers abrupt ansteigt. Dieser Effekt wird allerdings schon durch eine kleine Oberflächenrauigkeit oder durch eine geringe Konzentration eines Adsorbats zerstört. Des weiteren haben wir das Benetzungsverhalten von Nanotröpfchen auf rauen hydrophilen wie hydrophoben Oberflächen untersucht. Dieses Problem ist relevant in der Nanoelektromechanik und der Nanofluiddynamik, die beide von großem aktuellen Interesse sind. Aufgrund thermischer Fluktuationen wurde für Nanotröpfchen auf hydrophoben Oberflächen keine Berührungswinkel-Hysterese gefunden. Der Kontaktwinkel steigt mit der mittleren quadratische Abweichung der Rauigkeit der Oberfläche und ist nahezu unabhängig von ihrer fraktalen Dimension. Wir konnten feststellen, dass thermische Fluktuationen auf der Nanoebene sehr wichtig sind. Auf hydrophilen Oberflächen ist die thermische Fluktuation allerdings nicht ausreichend, um die Hysterese des Kontaktwinkels zu beseitigen.
Tyre–road friction characteristics are deeply interlaced with all vehicle safety oriented control systems as road conditions strongly affect the controlled system behaviour. Thus, the capability of estimating in real-time the friction conditions may provide a valuable source of information for any active vehicle control system. In particular, friction information can be used to enhance the performance of wheel slip control systems.
In this chapter we address three different problems related with friction estimation. Specifically, Section 8.2 illustrates an approach that is capable of estimating the sign of the slope of the friction curve, thereby allowing one to detect if the system is operating in the stable or in the unstable region of the friction curve. In fact, as largely discussed in this book, the equilibrium points associated with the wheel braking dynamics are stable for values of the wheel slip before the peak and unstable for those beyond the peak.
Hence, an online detection of the slope of the friction curve can be exploited to adapt and to optimise the closed-loop performance of wheel slip control systems. The advantage of this identification method is that it can be implemented also with a very limited set of sensors.
Secondly, in Section 8.3 an approach to the problem of estimating both the slip value corresponding to the peak of the friction curve and the parameters of the Burckhardt friction model (see Section 2.1) is presented. This is done by setting up a curve fitting problem which is then solved by two different identification approaches, namely a least squares and a maximum likelihood approach, arising from different parametrisations of the friction curve. A detailed analysis of the merits and drawbacks of the two approaches is also provided, which considers both the obtained accuracy in the estimated parameters and the convergence issues which have to do with the length of the available data set.
Finally, Section 8.4 presents an approach for estimating the instantaneous vertical and longitudinal forces from in-tyre acceleration measurements. Specifically, an appropriate set of sensors and regressors is illustrated, based on the measurements provided both by standard vehicle sensors (wheel encoders) and an accelerometer mounted directly in the tyre. Such estimates are based on the idea of extracting information from the phase shift between the wheel hub and the tyre, which is due to the transmission of traction and braking forces exerted on the tyre itself.
The paper presents an analysis of tangential interaction between flexural properties of tyres and frictional properties of the tyre-road interface. Using simple models to represent tyre structure and friction, the traction-slip characteristics are derived for various situations of practical interest: a standing tyre subjected to monotonic and oscillatory loading, a stationary rolling tyre and especially that of the transition from standing to steady rolling. To gain deeper insight into the requirements for modelling flexural and the complex friction properties, the study examines the influence of the normal pressure profile, tyre structural properties and friction in the contact region on the overall and detailed characteristics of tyre traction. The analysis presented serves as a basic framework for modelling the complex tyre-road interactions such as that encountered in the snap-start problem of road vehicles.
This article presents the results of a numerical dynamic analysis of two
bodies in sliding contact. The 2D model consists of two finite elastic
media separated by a contact interface, governed by classical Coulomb
friction law. The aim of this work is to investigate the instability
scenarios occurring when friction forces excite the mechanical systems
during the relative motion; simulation results show that the coupling
between the frictional behaviour at the contact and the global dynamic
of the system can bring to either stick-slip phenomena, or mode coupling
instability. Complex eigenvalue analysis and transient non-linear
simulations highlight how system parameters, like structural damping,
affect the macroscopic frictional behaviour, switching from stick-slip
phenomena to harmonic vibrations (due to mode coupling instability), up
to the stable sliding state. The presented results allow for
generalizing the instabilities due to mode coupling, named in brake
squeal literature "lock-in" instability, to any mechanical system with
frictional contact. The analyses show how maps of the instability
scenarios can be drawn as a function of different parameters to help the
design of systems in frictional contact.
Stick–slip behaviour is a common but not entirely understood tribological phenomenon. The sliding motion of a rubber sample was studied on a glass plate. The local sliding velocity field of the contact area was calculated by means of Digital Image Correlation and compared to the measured friction force. It was observed that the sliding of individual sipes nucleates from the side edge, whereas the sliding of a tread block propagates from the leading edge. Phase shifts between tread block detachments were observed. Furthermore, a velocity field for a precursor is presented which indicates only the local sliding of the contact without the triggering of a global detachment. The relevance of the result for rougher surfaces is discussed.
This paper proposes a comparative study of three observers: a second-order sliding mode observer, a third-order sliding mode observer, and an adaptive observer. The observers are designed for tyre—road friction coefficient μ estimation during a braking manoeuvre in an automotive vehicle. The second-order sliding mode observer and the third-order sliding mode observer reconstruct the friction coefficient μ using equivalent output error injection ideas, while the adaptive observer uses explicit estimates of the road condition parameter as part of the scheme. The new second-order observer that is proposed in this paper is based on a quarter-vehicle representation and is independent of the model used to represent the tyre—road friction. The paper considers a dynamic LuGre friction model, a pseudostatic LuGre friction model, and a parameter-based friction model as a basis for a comparative study.
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.
Formulae for the estimation of any stress tensor component at some point in an elastic half-space are presented. With these formulae, the normal and maximum tangential stress distributions in the deep layers are studied in detail. The sinusoidal indenter may be used as a model for surface roughness. Some suppositions about possible destruction mechanisms of conjugate bodies under frictional contact are suggested. Surface roughness causes deep plastic deformation of surface layers. With rough surfaces high frequency oscillations occur and even with low sliding velocities the oscillations may achieve high frequencies.
A theory of the adhesional friction of rubber is developed by considering adhesion as a time-dependent process in which a tangential force helps to overcome an energy barrier of the work of adhesion. The frictional phenomenon, as a consequence of such adhesion, would arise primarily from the deformation of the rubber aggregates in contact with a smooth, hard surface constituting the “top layer”. The existence and importance of such a highly-deformed layer has been shown by Schallamach1 in his studies on surface conditions. The true area of contact is considered to increase with time of adhesion as is generally observed in quasi-static behaviour of viscoelastic materials. The deformational characteristics describing the time temperature dependence of mechanical properties would then be reflected in the frictional behaviour. A simple phenomenological approach is taken here instead of a complicated one with the theory of rate processes applied to basic molecular activity. The variation of the frictional force with viscoelastic properties is in fair agreement with the experimentally-obtained results of Grosch2. The static coefficient of friction equals the dynamic coefficient at extremely low speeds. The analysis is confined to steady-state conditions and the influence of frictional heating is considered negligible.
Using the general solution of the periodic contact problem of elasticity theory a perturbation which models surface roughness was considered for the stressed state in the surface layer of an elastic material due to the action of a periodic sinusoidal indenter. Equations were derived for the calculation of normal, tangential and maximum tangential stresses at any point of the contact area. Plots are presented to illustrate the stressed state. It was shown that stress perturbation in the compressed rough bodies spreads to a thin surface layer of thickness comparable with the space between projections on the rough surface. As a result of the analysis of the maximum tangential stress regions the occurrence of a continuous layer under the surface of the compressed bodies in which the material is in a plastic state is possible.
The stress distribution outside the contact-induced plastic zone can be estimated by the superposition of a Hertzian field and the field for an embedded center of dilatation (ECD) in a half-space, while the residual stress distribution can be estimated by the ECD field alone. This model has a simple closed-form analytical expression, matching with finite element results nearly perfectly.
Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict the real area of contact which affects friction and wear of an interface. The contact of two macroscopically flat bodies with microroughness is reduced to the contact at multiple asperities of arbitrary shapes. Most of deformation at the asperity contact can be either elastic or elastic-plastic. In this paper, a comprehensive review of modeling of a single asperity contact or an indentation problem is presented. Contact analyses for a spherical asperity/indenter on homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented. The analyses reviewed in this paper fall into two groups: (a) analytical solutions, primarily for elastic solids and (b) finite element solutions, primarily for elastic-plastic problems and layered solids. Implications of these analyses in friction and wear are discussed.
Material Properties That Influence Surface Interactions. Surface Interactions. Friction. Types of Wear. Adhesive Wear. Abrasive and Other Types of Wear. Lubrication. Adhesion. Appendix. Sample Problems. Index.
The periodic sinusoidal indenter, which models the microroughness of a rough surface, was used to study the effect of the strain energy due to distortion and the volume strain energy at any point of an elastic half-space on the total mechanical energy generated. It is shown that the distribution of the total mechanical energy generated by the contact of elastic bodies with rough surfaces depends principally on Poisson's ratio. There are two areas within the contact zone where the origin of destruction is most likely to occur. One is located on the surface and the other at a specific subsurface depth. The possible existence of a deeply located source of heat caused by friction is suggested.
Thermal analysis using mechanical property measurementTheoretical considerationsPractical considerationsInstrument details and calibrationExample dataThermomechanical analysisAppendix: sample geometry constantsReferences
Thermal Analysis techniques are used in a wide range of disciplines, from pharmacy and foods to polymer science, materials and glasses; in fact any field where changes in sample behaviour are observed under controlled heating or controlled cooling conditions. The wide range of measurements possible provide fundamental information on the material properties of the system under test, so thermal analysis has found increasing use both in basic characterisation of materials and in a wide range of applications in research, development and quality control in industry and academia. Principles and Applications of Thermal Analysis is written by manufacturers and experienced users of thermal techniques. It provides the reader with sound practical instruction on how to use the techniques and gives an up to date account of the principle industrial applications. By covering basic thermogravimetric analysis (TGA), differential scanning calorimetry (DSC) including the new approach of Fast Scanning DSC, together with dynamic mechanical analysis (DMA /TMA) methods, then developing the discussion to encompass industrial applications, the book serves as an ideal introduction to the technology for new users. With a strong focus on practical issues and relating the measurements to the physical behaviour of the materials under test, the book will also serve as an important reference for experienced analysts.
This paper describes a study of the adhesion and friction of elastomers in dry and lubricated conditions under normal and tangential forces. Data are provided for the area of contact, in which the experiments were carried out between optically smooth concave elastomers and a glass substrate. Data for the corresponding frictional forces area also provided, in which the experiments were carried out between an optically smooth elastomeric strip and a glass indenter. The conclusion for the areas of contact is that adhesion plays a significant role in dry contacts under normal load as well as under a combined normal/tangential action, though the role of adhesion in the mechanism of surface separation upon the action of an imposed tangential force is still unclear. In lubricated conditions adhesion is greatly reduced and the classical theory of elasticity accounts for the areas of contact. Results for the corresponding frictional forces show a sharp decrease in the coefficient of friction in lubricated contacts, compared to its value for dry contacts, a trend which remained unaffected in all regimes of lubrication detected, namely “boundary”, hydrodynamic and elastohydrodynamic (EHL) lubrication. Finally, from the results of the areas of contact and the corresponding frictional forces, a first order calculation of the interfacial shear strength, s, of the elastomer was made and it was shown that s is a strong function of the sliding velocity and depends also on the normal load.
Contact modeling of two rough surfaces under normal approach and with relative motion is carried out to predict real area
of contact and surface and subsurface stresses affecting friction and wear of an interface. When two macroscopically flat
bodies with microroughness come in contact, the contact occurs at multiple asperities of arbitrary shapes, and varying sizes
and heights. Deformation at the asperity contacts can be either elastic and/or elastic-plastic. If a thin liquid film is present
at the interface, attractive meniscus forces may affect friction and wear. Historically, statistical models have been used
to predict contact parameters, and these generally require many assumptions about asperity geometry and height distributions.
With the advent of computer technology, numerical contact models of 3-D rough surfaces have been developed, particularly in
the past decade, which can simulate digitized rough surfaces with no assumptions concerning the roughness distribution. In
this article, a comprehensive review of modeling of multiple-asperity contacts in dry and wet conditions is presented. Contact
models for homogeneous and layered, elastic and elastic-plastic solids with and without tangential loading are presented.
The models reviewed in this paper fall into two groups: (a) analytical solutions for surfaces with well-defined height distributions
and asperity geometry and (b) numerical solutions for real surfaces with asperities of arbitrary shape and varying size and
height distributions. Implications of these models in friction and wear studies are discussed.
Measurements of Young's modulus as a function of pressure up to 10 000 bars at 20°C show that the glass‐transition temperature in natural and synthetic rubbers is raised by pressure. For natural gum rubber, the transition occurs at 5100 bars at 20°C and Young's modulus increases 1000‐fold on passing through the transition.
We study the role of rubber friction in tire traction with special emphasis on the load and velocity dependence of the friction coefficient. In the first part, we present some basic concepts of contact mechanics of slipping tires and analyze the influence of energy dissipation due to tread deformation on the friction force.Then, we apply a recently developed model of hysteresis and adhesion friction of rubber on self-affine road surfaces for estimating the load dependence of the kinetic friction coefficient in the contact area of slipping tires. In this context the impact of track morphology (sharp or blunt) on the kinetic friction characteristics is demonstrated.Finally, using the brush model for slipping tires we discuss consequences of the load dependence of the kinetic friction coefficient with respect to the overall tire friction and slip characteristics. We show that due to the presence of a load dependence of the local rubber-road friction coefficient the tread contact patch is globally never entirely in a fully sliding situation.The presented results yield a contribution to an improved physical understanding of the dynamic frictional contact of tires with road tracks during cornering and braking, especially in the case of cars equipped with Anti-Blocking Systems (ABSs).
A theoretical model for the adhesive friction between elastomers and rough solid surfaces is proposed on the basis of opening crack propagation processes at the boundary of the contact interfaces and the rate processes of formation of molecular bonds on the solid surface. This model, which is expressed as a product of the terms related to the two abovementioned processes, requires some measurable and fitted parameters such as the frictional shear strength expressed as a function of viscoelastic dissipation, rate-dependent elasticity, density of bonded molecular chains at a contact junction, critical velocity related to viscoelastic relaxation, and critical velocity related to the rate process of formation of molecular bonds on the solid surface. The friction-velocity relationship exhibits a remarkable fit to previously obtained experimental results for polymers such as engineering rubber, gels, and plastics (glassy polymers), and all fitting parameters are physically reasonable. The viscoelastic index "n" is also related to the "glass-to-rubber transition" of a nanometer-thick polymer layer for frictional behavior. Thus, from a practical viewpoint, this model can be used effectively for fitting the adhesive friction behavior of polymers.
Identification of tyre-road friction conditions. Active braking control systems design for vehicles advances in industrial control
- S M Savaresi
- M Tanelli
Savaresi SM and Tanelli M. Identification of tyre-road
friction conditions. Active braking control systems design
for vehicles advances in industrial control, Advances in
Industrial Control. London: Springer, 2010, pp. 159-200.
Premier me´moireme´moire sur l'eíectriciteét le magne´tismene´tisme
- Ca Coulomb
Coulomb CA. Premier me´moireme´moire sur l'eíectriciteét le magne´tismene´tisme. Hist Acad R Sci 1785; 88: 569–577.
Introduction a` la physique des polymères
- S Etienne
- L David
Etienne S and David L. Introduction a` la physique des polymères. Paris: Dunod, 2012.
Unified theory of rubber and tire friction Engineering Research Bulletin B-94
- Hw Kummer
Kummer HW. Unified theory of rubber and tire friction.
Engineering Research Bulletin B-94, The Pennsylvania
State University College, University Park, State College,
Pennsylvania, 1966.
The adhesion of solids in the structure and properties of solid surfaces
- F P Bowden
- D Tabor
Bowden FP and Tabor D. The adhesion of solids in the
structure and properties of solid surfaces. Chicago: University of Chicago Press, 1953.
Premier me´moire sur l'e´lectricite´et le mag-ne´tisme
- C A Coulomb
Coulomb CA. Premier me´moire sur l'e´lectricite´et le mag-ne´tisme. Hist Acad R Sci 1785; 88: 569-577.