Article

An analytical model of dissipated viscous and hysteretic energy due to interaction forces in a pneumatic tire: Theory and experiments

Article

An analytical model of dissipated viscous and hysteretic energy due to interaction forces in a pneumatic tire: Theory and experiments

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... In the model, the amount of heat generated by deformation (SEL) is estimated through experimental tests carried out deforming cyclically the tyre in three directions (radial, longitudinal and lateral) [11]. Estimated energies do not exactly coincide with the ones dissipated in the actual operative conditions, as the deformation mechanism is different; it is however possible to identify a correlation between them on the basis of coefficients estimated from real data telemetry. ...
... Note the absence of the generative term and the presence of the term identifying the exchange with the outside air, characterized by hforc coefficient. (11) in which ܽ is the generic coefficient, relative to the energy balance equation of the node ݅, that multiplies the ݆-th node temperature, while ܾ is the generic coefficient not multiplying nodes temperatures. ...
... where Tsurf,avg is the mean temperature value of the entire surface layer. The above-mentioned equations are therefore developed in order to write a complete set of normal-form equations (11), as follows: ...
Chapter
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.
... Interpolating all the results obtained by means of the test plan, an analytic function has been identified [17]; it expresses the SEL as a function of the parameters (amplitude of the interaction force components and applying frequency) on which it depends. ...
... Then, considering that in steady state conditions the variations of the inflation pressure are small and that camber angle does not have a great influence on the size of the contact area, for simplicity, these dependencies have been neglected. As a result, it is possible to 1 A eff = f (F z ) · groove factor (17) As said, in order to avoid excessive computational loads, the number of nodes in contact has been considered constant during a simulation. So for its determination the average normal load acting on the single wheel has been considered. ...
Article
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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.
... Nowadays, it is still challenging to characterize the viscoelastic material considering its particularities, such as time-varying properties and energy dissipation. Even with good results, the finite element method can be time-consuming, and the high computational cost motivates the investigation of alternative modeling methods, for example, the article of Brancati et al. (2011) develops an analytical model of dissipated energy based on a hysteresis model. ...
Article
Reducing tire rolling resistance and energy loss is a topic of interest to the tire industry. Understanding and modeling these phenomena are essential to approach this problem and propose robust solutions. This work suggests a reduced-order model based on the Bouc-Wen model to simulate internal variables from viscoelastic constitutive laws. Furthermore, sensitivity analysis is performed on the Bouc-Wen parameters to evaluate their influence on the system response and capture the full range of possible values that improve the predictive ability of the reduced-order model. This task is accomplished by calculating the Sobol's indices estimated from a Polynomial-Chaos expansion. Once the range of feasible model solutions is established, the reduced-order model is calibrated through Bayesian inference. Finally, the uncertainties are propagated, and the reduced-order model is validated using data of viscoelastic internal variables from the finite element approximation of a steady-rolling tire. Satisfactory results are obtained, as the reduced-order model can simulate vis-coelastic internal variables with a reduced computational cost for some branches of interest. Its responses are in agreement with the experimental data.
... In the model, the amount of heat generated by deformation (SEL) is estimated through experimental tests carried out deforming cyclically the tyre in three directions (radial, longitudinal and lateral) [11]. Estimated energies do not exactly coincide with the ones dissipated in the actual operative conditions, as the deformation mechanism is different; it is however possible to identify a correlation between them on the basis of coefficients estimated from real data telemetry. ...
Conference Paper
Full-text available
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.
... The availability of a reliable tyre model for Software or Hardware in the Loop (SIL or HIL) vehicle dynamics could help to reduce the use of costly experiments and prototypes[6],[22],[23]. In this paper a numerical model is presented and the results of normal interaction are shown; in particular, using the finite segment method, it has been possible to include in the tyre simulations various aspects: @BULLET The structural effects: in fact the model takes into account the stiffnesses[5],[24](extensional, flexural and torsional) of belt and sidewalls and the dissipations of energy due to the visco-elastic[25],[26] ...
Article
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.
... As concerns the modelling of global tyre system hysteretic dissipation due to interaction forces with road [5], an analytical model has already been developed [12,13]. In the presented study the analyses will be focused on the only hysteretic friction component due to asphalt macro roughness and consequently a single tread element will be considered. ...
Conference Paper
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Knowledge about phenomena concerning with adherence is a key factor in the automotive field and in particular in the braking/traction and stability control systems design. Moreover, the continuous drivers’ seeking of the optimal grip conditions, makes the development of a physical friction model an essential instrument for the investigation of the factors acting on indentation and adhesion mechanisms on which tyre/road interaction is based. Rubber/asphalt friction, in fact, is influenced by a great number of variables and parameters, often hard to be controlled and measured: macro and micro roughness of the bodies in contact, pressure arising at their interface, materials stiffness characteristics and their frequency and temperature dependence, relative motion direction and speed. The possibility offered by a physical model to provide a better comprehension of the cited factors allows to act on them with a wide range of aims: studying soil textures structured in order to increase drivers' safety both in dry and in wet conditions, producing more performing rubber compounds, able to optimize frictional behaviour under certain temperatures or frequencies and, in particular in race applications - for which the presented studies have been originally carried out - in order to configure optimal vehicle setup and driving strategies. A deep knowledge of the mechanisms involved with tyre/road friction is a key factor in the design of the suspension system: an optimal setting of tyre working angles, operated in order to optimize temperature, contact pressure and sliding velocity distributions, can be efficiently provided by a physical grip model able to indicate the best wheel configuration at the boundary conditions changes.
... As concerns the modelling of global tyre system hysteretic dissipation due to interaction forces with road [11], an analytical model has already been developed [18], [19]. In the presented study the analyses will be focused on the only hysteretic friction component due to asphalt macro roughness and consequently a single tread element will be considered. ...
Article
Full-text available
According to the most recent approaches, the friction coefficient arising between tyre rubber and road can be seen as constituted by three components: adhesion, deforming hysteresis and wear. This paper deals with the estimation of the hysteretic component of friction. This component is due to indentation phenomena regarding contact mechanics of deformable bodies sliding on the asperities of a rough substrate, which exert oscillating forces at the interface, leading to cyclic deformations of the rubber and then to energy "dissipation" via its internal damping. To evaluate this component, a physical model able to calculate energy dissipation of a rubber block indented by a rigid asperity in sliding contact has been built. To this aim the visco-elastic characteristics of the material have been taken into account. The road profile has been modelled as the sum of two sinusoidal waves characterizing the macro and the micro roughness scales. The results coming out from the physical model have been validated by means both of FEM models results and of experimental tests carried on a pin on disk tribometer.
... In the technical literature some mathematical models, that do not came from the analysis of the physical behavior, are available; they are constituted by empirical differential equations able to describe the system dynamic behavior with an appropriate choice of the coefficient values that, of course, have no physical meaning. One of the most utilized way to express this force is the Bouc-Wen model [7][8][9], that essentially consists of a first-order non-linear differential equation that relates the input displacement x(t) to the output restoring force z(t), as follows: ...
Article
Wire rope springs (WRS) are widely used to protect sensitive equipment from shock or vibrations but they do not have the characteristics of a seismic isolator that must have a high vertical stiffness to support the vertical load with an acceptable vertical deflection and, at the same time, a low horizontal stiffness to isolate low frequency ground horizontal acceleration of an earthquake. To take advantage of their peculiar characteristics due to the dry friction that arises among the wires, they can be adopted in parallel with a Ball Transfer Unit (BTU), able to support vertically the weight of the sensitive equipment and to allow the equipment itself to move in any horizontal direction with low friction. The WRS-BTU isolator can be considered rigid in the vertical direction and the horizontal stiffness can be properly chosen to give the isolated system a low natural frequency and a suitable re-centering force. In order to evaluate the feasibility of adopting an isolator based on WRS and BTU, a prototype was developed and tested. In this paper, the description of the seismic isolator prototype and some experimental results are presented; it is also presented a procedure to identify the restoring force by means of the Bouc-Wen model. Finally, adopting this analytical description of the restoring force, the non-linear behavior of sensitive equipment suspended on these isolators, for different operational conditions, is simulated.
... The isolator is characterized by a hysteretic non-linear behavior. In this case, specific hysteresis model able to describe its behaviour must be adopted [3]. ...
Conference Paper
Full-text available
This paper describes an experimental investigation conducted on WRS-BTU seismic isolators that are constituted by a wire rope spring coupled with a ball transfer unit. The device can be considered rigid along the vertical direction while the horizontal stiffness can be independently chosen to shift the natural period away from the period range having the most of earthquake energy. Two kinds of tests were carried out: The first ones regard the isolator characterization; then, to evaluate the isolation efficiency, a small laboratory structure was equipped with four isolators and several tests on a shake-table were performed.
... where F BW is the restoring force, d(t) is the time history of the isolator deformation (assumed equal to the table displacement), k, k w , σ BW , ρ BW and n are the Bouc-Wen model parameters that determine the shape of the hysteretic cycle (Table 2) [22]. ...
Article
This paper concerns the modelling and the control design of a hydraulic actuator employed to carry out shear tests on seismic isolators. The testing machine requires a controller that can ensure the tracking of the target displacement in presence of the unknown restoring force of the isolation devices. To this aim, a model inversion based control, coupled with a feedback contribution, has been designed and implemented. A non-linear model has been derived and adopted for the feedforward synthesis through the inverse dynamics resolution. As a consequence, the feedback control has the function to compensate for the tracking error due to model uncertainties and the unknown isolator reaction force. The choice of a mixed approach allows to design a control action that results minimally invasive on the stability characteristics: it is possible to obtain good tracking results without the increasing of the feedback control gain. The effectiveness of the designed control has been firstly evaluated by means of simulations and, successively, executing experimental tests on the test rig with and without the specimen under test.
... Though numerous examples for calculations of rolling resistance are available in the literature, the models used are often over-simplified (e.g. [37,38]) and/or based on modelling approaches which do not readily allow identification of connections to the structural dynamics of the tyre [39][40][41]. Accordingly, the tyre manufacturers seem to have problems to make use of the theoretical knowledge in their everyday engineering work. ...
Article
From November 2012 all passenger car tyres, light truck tyres and heavy duty vehicle tyres sold on the aftermarket in the European Union must have a label classifying the external rolling noise, the fuel efficiency, and the wet grip. This regulation puts a focus on optimisation of the tyre de- sign with respect to all these parameters at once. Up to today these three parameters have been treated rather independently. There is little to no detailed information available on the relationship between rolling noise generation, rolling resistance, and grip of car tyres besides empirical data based on measurements. Today, simulation models that can simulate all these effects at once have just started to emerge. This paper gives a brief presentation of the past and the most resent develop- ment of numerical tyre/road interaction models with focus on external noise, rolling resistance, and grip. Today, the simulation models can be used to gain fundamental knowledge about the tyre/road interaction process and the resulting noise, rolling resistance, and grip. Models for combined opti- misation of rolling resistance and noise emissions exists, and are just about to be used in preliminary investigations. Models that in addition give results for grip are still under development.
... Though numerous examples for calculations of rolling resistance are available in the literature, the models used are often over-simplified (e.g. [37,38]) and/or based on modelling approaches which do not readily allow identification of connections to the structural dynamics of the tyre [39][40][41]. Accordingly, the tyre manufacturers seem to have problems to make use of the theoretical knowledge in their everyday engineering work. ...
Conference Paper
From November 2012 all passenger car tyres, light truck tyres and heavy duty vehicle tyres sold on the aftermarket in the European Union must have a label classifying the external rolling noise, the fuel efficiency, and the wet grip. This regulation puts a focus on optimisation of the tyre de- sign with respect to all these parameters at once. Up to today these three parameters have been treated rather independently. There is little to no detailed information available on the relationship between rolling noise generation, rolling resistance, and grip of car tyres besides empirical data based on measurements. Today, simulation models that can simulate all these effects at once have just started to emerge. This paper gives a brief presentation of the past and the most resent develop- ment of numerical tyre/road interaction models with focus on external noise, rolling resistance, and grip. Today, the simulation models can be used to gain fundamental knowledge about the tyre/road interaction process and the resulting noise, rolling resistance, and grip. Models for combined opti- misation of rolling resistance and noise emissions exists, and are just about to be used in preliminary investigations. Models that in addition give results for grip are still under development.
... ntama, kaip mechanin padangos gumos deformacija atsiradusi dl padangą veikiančių vertikalių arba horizontalių jgų, pvz., važiuojant nelygiu keliu padanga kontakto su nelygumais vietoje deformuojasi, kitas atvejis – tai padangos medžiagos deformacija, t. y. tam tikro gumos kiekio atsiskyrimas arba persiskirstymas į kitą vietą (padangos dvjimasis ) (Brancati et. al. 2011) (1 pav. a ir b). Stabdymo pdsako pobūdis, nusidvjimo laipsnis ir protektoriaus rašto piešinio intensyvumas kelio dangoje priklauso oro slgio padangoje, automobilio pakrovimo, kelio dangos tipo, jos lygumo, meteorologinių sąlygų, temperatūros. Stabdymo metu padangai slystant (riedant) sausa asfaltbetonio danga protektorius briaunos defo ...
Conference Paper
Full-text available
Santrauka. Straipsnyje pateikiama su nagrinėjama tematika susijusių mokslinių straipsnių apžvalga. Atliekama padangos ir kelio sąveikos lėtėjimo režime analizė, taip pat atliekama stabdymo pėdsako formavimosi teorinė analizė ir jos susidarymo charakteristikos. Pateikiami automobilio judėjimo dinamikos pagal stabdymo pėdsakų charakteristikas teoriniai nustatymo požymiai. Taip pat analizuojamas automobilio lėtėjimo procesas ir lėtėjimo pagreičio kaitos įtaka automobilio stabdymo ke-lio ir važiavimo greičio prieš eismo įvykį nustatymui. Nagrinėjama automobilio padangų pėdsako kelio dangoje formavimosi priklausomybė nuo automobilio padangos ir kelio sąveikos lėtėjimo parametrų intensyvaus lėtėjimo režime. Atliekama auto-mobilio važiavimo greičio ir stabdymo kelio nustatymo priklausomybė pagal automobilio ratų paliktų, stabdymo pėdsakų il-gį. Įvadas Techniniu požiūriu vienas iš labiausiai naudojamų transporto priemonės valdymo būdų vengiant pavojingos arba avarinės situacijos yra stabdymas. Stabdymo metu svarbus automobilio lėtėjimo pagreitis, kurio reikšmė priklauso nuo kelio dangos, jos lygumo ir būklės. Stab-dymo metu transporto priemonės padangos kelio dangoje palieka stabdymo pėdsakus. Stabdymo pėdsakų analizė reikalinga norint nustatyti ne tik pačiam pėdsakui būdin-guosius požymius, bet ir remiantis jais nustatyti eismo įvykio kilimo mechanizmą, transporto priemonės judėji-mo dinamikos, prieš eismo įvykį ir jo metu, parametrus.
... ntama, kaip mechanin padangos gumos deformacija atsiradusi dl padangą veikiančių vertikalių arba horizontalių jgų, pvz., važiuojant nelygiu keliu padanga kontakto su nelygumais vietoje deformuojasi, kitas atvejis – tai padangos medžiagos deformacija, t. y. tam tikro gumos kiekio atsiskyrimas arba persiskirstymas į kitą vietą (padangos dvjimasis ) (Brancati et. al. 2011) (1 pav. a ir b). Stabdymo pdsako pobūdis, nusidvjimo laipsnis ir protektoriaus rašto piešinio intensyvumas kelio dangoje priklauso oro slgio padangoje, automobilio pakrovimo, kelio dangos tipo, jos lygumo, meteorologinių sąlygų, temperatūros. Stabdymo metu padangai slystant (riedant) sausa asfaltbetonio danga protektorius briaunos defo ...
Conference Paper
Full-text available
Santrauka. Straipsnyje pateikiama su nagrinėjama tematika susijusių mokslinių straipsnių apžvalga. Atliekama padangos ir kelio sąveikos lėtėjimo režime analizė, taip pat atliekama stabdymo pėdsako formavimosi teorinė analizė ir jos susidarymo charakteristikos. Pateikiami automobilio judėjimo dinamikos pagal stabdymo pėdsakų charakteristikas teoriniai nustatymo požymiai. Taip pat analizuojamas automobilio lėtėjimo procesas ir lėtėjimo pagreičio kaitos įtaka automobilio stabdymo ke-lio ir važiavimo greičio prieš eismo įvykį nustatymui. Nagrinėjama automobilio padangų pėdsako kelio dangoje formavimosi priklausomybė nuo automobilio padangos ir kelio sąveikos lėtėjimo parametrų intensyvaus lėtėjimo režime. Atliekama auto-mobilio važiavimo greičio ir stabdymo kelio nustatymo priklausomybė pagal automobilio ratų paliktų, stabdymo pėdsakų il-gį. Įvadas Techniniu požiūriu vienas iš labiausiai naudojamų transporto priemonės valdymo būdų vengiant pavojingos arba avarinės situacijos yra stabdymas. Stabdymo metu svarbus automobilio lėtėjimo pagreitis, kurio reikšmė priklauso nuo kelio dangos, jos lygumo ir būklės. Stab-dymo metu transporto priemonės padangos kelio dangoje palieka stabdymo pėdsakus. Stabdymo pėdsakų analizė reikalinga norint nustatyti ne tik pačiam pėdsakui būdin-guosius požymius, bet ir remiantis jais nustatyti eismo įvykio kilimo mechanizmą, transporto priemonės judėji-mo dinamikos, prieš eismo įvykį ir jo metu, parametrus.
... 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 (SEL) is evaluated [15]. ...
Conference Paper
Full-text available
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.
... To circumvent this difficulty, the data = ( , ,̇) is separated into two datasets using -means clustering in this section: one corresponds to the viscous part = ( , ,̇) and another to hysteretic part ℎ = ( , ,̇). For harmonic excitation, another possible way to separate viscous and hysteretic mechanisms is referred to the rate-dependency property [42], that is, energy dissipation in a cycle/period varies with frequency as in Eq. (8) for viscous damping, while remains constant for hysteretic damping if the displacement amplitude is fixed. ...
Article
Damping is one of the most complicated phenomena in structural analysis and design. In principle, damping arises with energy dissipation in the vibration and therefore, friction, plasticity and viscosity etc are common sources of damping. Though various damping models have been proposed, they are only applicable to some certain damping phenomena and there is no unified way to model an arbitrary damping system. To the end, this paper presents a data-driven framework for modeling of general damping systems. There are three key ingredients in establishing this framework. At first, pre-defined dictionaries of basis functions are built to describe the hysteretic and viscous behaviors of a general damping model. Secondly, the k-means clustering technique is applied to separate the two datasets corresponding to respective hysteretic and viscous parts of the damping model from the measured data. Thirdly, a two-stage regression procedure is invoked where the viscous and hysteretic parts of the damping model are identified sequentially from the readily separated two datasets. Such identification proceeds by means of linear least-squares regression and sparse regularization. As a consequence, if a new damping system whose hysteretic and viscous behaviors are totally reflected in the dictionary, the underlying model equation can be directly and quickly recovered through the proposed data-driven approach. Numerical examples as well as an experimental test are studied to demonstrate the effectiveness and efficiency of the proposed data-driven modeling approach for general damping systems.
... The hysteretic force can be derived from the Bouc Wen model. The analytical expression of the hysteretic force has been presented in [14,15] and it is here reported: ...
Article
The restoring force of wire rope springs is generated by the wire ropes deformation that, at the same time, dissipates energy due to the friction forces arising between its wires during the deformation of the rope. In this paper, the dynamic behavior of a light structure isolated by means of isolators, constituted by wire rope springs and a ball transfer unit, is investigated; the adopted structure simulates objects sensitive to seismic accelerations, like works of arts or cabinets containing electromechanical devices whose functioning must be ensured during seismic events. In the first part of the paper the system dynamic characteristics are evaluated by means of an experimental modal analysis conducted on a shaking table by assigning different laws of motion to its moving platform. The frequency response has been obtained through monofrequential and multi-frequential excitations; the platform has been also moved with laws deduced from accelerograms recorded during seismic events to evaluate its insulation efficiency. The modal analysis has shown the frequency range where the proposed isolation system produces a beneficial action for the specific passive vibration control application. Experimental data have been used to validate a numerical model that can be adopted to simulate operating conditions different from those of the experimental tests; the results of several simulation are reported to highlight the influence of some parameters on the system dynamic behavior.
... This last phenomenon was theoretically [5] [6] [7] and experimentally [8] [9] investigated and involves oscillations with frequencies ranging from about 5 to 12 Hz, depending on the tyre-road interaction [10] [11] [12]. Wheel unbalance excitation covers the 0-40 Hz range; engine vibrations are characterized by a wide range of possible frequencies (about 10-500 Hz) and overlap the previous ones. ...
Article
Motorcycle driver interacts with the vehicle through the hands, feet and buttocks. Through these parts of the body, the driver perceives vibrations due to engine and road roughness. A good level of comfort would require that handlebar and foot pegs natural frequencies should not line up with the operating range frequencies. In this paper the results of experimental tests direct to investigate the handlebar dynamic response is reported; the investigation is adopted to evaluate the possibility of adopting a vibration exciter placed in correspondence of the grips that could provide an alarm signal when a danger situation occur. This type of active assistance has already been used for cars and has proved effective in the accidents prevention.
... Moreover, vehicle dynamics control systems [12], [13], [14], [15], [16], [17] are usually based on the hypothesis that the tyre is always in contact with the road and this not always verified assumption can cause their improper intervention. Also tyre friction [18], [19], [20], [21], [22], [23], [24] and thermal modelling [25] are influenced by the effects of this phenomenon. ...
Article
Full-text available
This paper deals with tyre enveloping behaviour on uneven road surface. To build realistic and reliable vehicle dynamics models it is of fundamental importance to study the influence of road obstacles and irregularities on forces and displacements involving a rolling tyre. After a brief review about early studies concerning this phenomenon, the tandem model with elliptical cams is introduced and described, highlighting its hypothesis and the parameters on which it is based, the most important of which are the cams profiles and the distance between them. The main aim of this paper is the executive project of a test rig aimed to carry out an experimental campaign for the identification of the parameters of the tandem cam model and for its validation. The idea is to experimentally acquire the path of the patch centre of a tyre rolling over an obstacle, to define the parameters of the curves employed for the cam profiles and the distance between them in the tandem model. It is important to highlight that these parameters are strictly connected to tyre properties and need tests to be investigated and identified. The design started from a test bench for motorcycles already available at DII’s Tyre Lab, introducing proper changes without compromising original test bench destination. © 2016, International Association of Engineers. All rights reserved.
... In practice, the vertical load and vertical deformation of tire exhibit a hysteresis behavior [32]. To assure the consistence of tire model with test data, this paper simulates tire hysteresis curve with Bouc-Wen model as shown in Eq. (32) [33] The tire hysteretic property test was performed as shown in Fig. 11 to identify these parameters. GA-PS (genetic algorithm and pattern search) method [34] is used to efficiently attain the optimal solution of fitting parameter. ...
Article
Full-text available
The accurate description of contact characteristics between tire and road surface may significantly affect the vehicle motion simulation and control analysis. Based on the LuGre tire model, the pressure distribution function of loading is modified as a non-uniform distribution pattern through new method of recursion formula. The mathematical expression of modified LuGre tire model is achieved through introducing the Bouc-Wen model to reflect tire hysteresis behavior, which takes into consideration the process of dynamic effect of tire vertical loading and tire footprint length. The effectiveness of model is verified through comparison with classic magic formula (MF) and LuGre tire model. Furthermore, the stability of solution for the modified LuGre tire model in the prediction of tire force and alignment torque is demonstrated in frequency domain. Finally, a nonlinear four-DOF vehicle handling dynamics model is built. The front wheel steering angle and the rotational angular velocities of the six tire from a calibrated virtual vehicle is entered into the vehicle model system with modified LuGre tire model as input data. The responses of longitudinal velocity, lateral velocity, yaw rate and roll angle are obtained under two kinds of limit conditions. The comparison results demonstrate the correctness and effectiveness of the built model, which further prove that the modified LuGre tire model is applicable for handling performance analysis of vehicle system.
... This hysteresis energy loss affects the tyre temperature and contact characteristics (Narasimha Rao et al., 2006). Brancati et al. (2011) proposed an analytical model for calculating the hysteresis loss as in equations (1) and (2). ...
... Hysteresis is a major source of energy loss within a tire [5] [6], resulting in unavoidable internal heat generation during normal use. The dynamic mechanical properties of rubber materials, related to the materials hysteresis response, have been shown to be subject to fatigue induced change, associated with endurance limitations of the material [7,8]. ...
Article
Full-text available
The material parameters of an automotive truck tire were experimentally determined and validated for use in a thermal finite element analysis to determine the temperature distribution in the tire due to different operating conditions. Uni-axial tensile tests were performed on tire samples. The force displacement response of each was used to determine material properties by means of direct curve-fitting and iterative numerical procedures. Equivalent finite element simulation models were used to validate the properties. Hysteresis behaviour of the rubber regions were identified by dynamic mechanical analysis. Material definitions were incorporated into a finite element model to predict the steady-state heat generation and temperature distribution within a tire due to hysteresis. Experimental rolling tire temperature measurements were taken on a test bench. A comparison of the results with those obtained from the equivalent thermal models was used to validate the numerical models.
... In tyre-road interaction, the hysteresis losses have two disadvantages increasing the rolling resistance and raising the temperature of the contact area. As the tyre temperature increases the hysteresis energy loss in rubber decreased [17]. Tonkovick et al, studied the lateral displacement of tyre as function of vertical displacement, and stated that tyre hysteresis losses was observed according to the nature of tyre materials [18]. ...
Article
p class="5Abstracttext">Tyre is the contact part between the vehicle and road which provides various requirements of performance. Tyres are designed to absorb road irregularities, support vehicle load and provide braking/steering characteristics. An experimental test rig for single tyre test has been designed and constructed to evaluate the tyre performance characteristics under different operating conditions. The tyre load deflection characteristic has been examined by loading and unloading the tested tyre while resting on a hard surface at three inflation pressures. The results showed that the higher hysteresis losses were at tyre inflation pressure 20 psi. Three different percentages of CuO nanoparticles have been used to evaluate their effect on the tyre hysteresis losses. Transmission electron microscopy (TEM) has been performed for the analysis of nanoparticles size. Adding CuO nanoparticle in very small amounts with the enclosed air of the tested tyre can be useful for improving its performance significantly and decreasing the hysteresis losses. This has the potential for making use of the benefits of lower inflation pressure.</p
... A model that takes into account the viscoelastic behavior of the tire is the Maxwell model [5], [6]. Other authors studied the influence of hysteresis on both the longitudinal and vertical modeling of tires [7], [8]. There are also tire models based on the 'flexible ring theory' that characterize their frequency response [9]- [12]. ...
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Tire models are of great importance for precise investigations of vertical vehicle dynamics, including vehicular safety and riding comfort. An adequate modelling of the tire is crucial to properly reproduce vehicle vertical behavior in simulations and to evaluate the influence of the tire in the overall performance of the suspension system. This paper introduced vehicle single-point tire models and, thereafter, investigated the influence of the excitation frequency and inflation pressure on the damping and stiffness coefficients of the proposed tires experimentally. In this manner, a test-bench was used to obtain the model parameters of a light vehicle tire and a motorcycle tire. Given the obtained results, it has been observed that both factors have a significant effect on the parameters of the proposed tire models. Moreover, a quarter car suspension model was investigated using the modelled tires to illustrate the influence of the correct characterization of the tire on the vertical suspension performance.
... The hysteresis phenomena could be analytically modelled according to some specific theories [12], [13], [14], [15] although such models require knowledge of some parameters rather difficult to estimate, to be instead experimentally identified. This work falls just in this context concerning the experimental characterization of automotive tyres with the aim to determine the parameters to adopt in physical analytical models of tyreroad interaction. ...
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In this paper an experimental test rig aimed to characterize mechanical properties of a pneumatic tyre, together with some results, is presented. The objective is to determine tyre mechanical characteristics useful to physically model its behaviour; in particular: the normal interaction characteristic, the radial stiffness, the total stiffness and the longitudinal hysteretic cycles. To this aim two different kind of tests have been executed: radial and longitudinal. In the radial test the load is statically applied to the tyre, along the vertical direction, by means of an hydraulic press and it is measured together with the consequent radial deformation, so allowing the estimation of the tyre normal interaction characteristic and of its radial stiffness. Different radial tests can be conducted for an assigned tyre varying the inflation pressure. The longitudinal tests are conducted applying, under an assigned constant vertical load, a variable horizontal strain to the tyre by means of a linear actuator, two profile rail guides and a system to transfer the horizontal motion to the contact patch of the tyre, opportunely placed on a moving steel plate placed on the two linear guide rails. During the tests the horizontal load and the resulting deformations are measured and acquired so allowing the estimation of tyre total stiffness and of its longitudinal hysteretic cycles. Longitudinal tests can be conducted varying the assigned vertical load, the horizontal displacement law in terms of frequency and amplitude, the tyre inflation pressure. All the different types of rim can be mounted on the test rig thanks to a universal quick flange.
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This paper is devoted to review of the publications on the finite element modelling of rolling tyres performed during the past two decades. Starting with the description of the scope and motivation behind this work, a brief history of the finite element modelling of tyres is given. Then, a comprehensive review on the published works on modelling techniques of the simulation of the rolling tyres is presented. The applied aspects of the subject Including the energy loss (rolling resistance) and temperature prediction, interaction between tyre and road, noise, failure, and stability are considered too. It is then followed by introducing the most applied computer codes available in the numerical and computational market. A summary on the published works with particular focus to compare different developed methods and especially the current situation of the applied aspect of the finite element modelling of rolling tyres are presented and discussed. Finally, a conclusion with some remarks is drawn.
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The experimental studies often show that the damping in various solid materials increases with frequency over a finite bandwidth, and the increase is weak if the damping is low. A frequency power law is suggested and discussed in this paper to describe this damping behaviour with special respect to the low loss resilient materials used for sound and vibration control. The dynamic modulus as a function of frequency is determined from the loss modulus through the Kramers�Kronig dispersion relations to satisfy the causality requirement. It is proved that the dynamic modulus obeys the frequency power law of the same type as the loss modulus. In addition, it is proved that the weak frequency dependences of damping properties are inevitably associated with the low loss factor. Examples of fitting the frequency power law to experimental data on some materials of acoustical purposes are presented.
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In this paper we propose a new dynamic model for friction. The model captures most of the friction behavior that has been observed experimentally. This includes the Stribeck effect, hysteresis, spring-like characteristics for stiction, and varying break-away force. Properties of the model that are relevant to control design are investigated by analysis and simulation. New control strategies, including a friction observer, are explored, and stability results are presented
A solid friction model The Aerospace Corparation
  • P A Dahl
P.A. Dahl, A solid friction model, Technical Report TOR-0158H3107, The Aerospace Corparation, el Segundo, CA, 1968.