The frictional behaviour of rubber is a topic of great interest and importance due to the invaluable uses of rubber in industry. The very particular behaviour of rubber also makes rubber friction a fascinating subject matter. Despite this it is still a topic not well understood. Previous studies have attempted to link the fracture mechanics of rubber crack propagation to the adhesive friction of rubber. The feasibility of such an approach to the adhesive friction of a rough rubber against a smooth surface, a configuration which can occur in various situations such as rubber seals or windscreen wipers, has been investigated. Rolling friction, described well by a fracture-like peeling process, is used to evaluate the viscoelastic dependence of sliding friction for various combinations of surfaces. A novel use of rubber is proposed as a material for particles to be used for jamming based soft robotics applications. This area of soft robotics is comparatively new and the materials that are being used at present are neither well established nor have been examined in great detail. Rubber would offer a material easily manufactured to desired shapes and dimensions with a wide range of moduli allowing modification to suit specific applications. The effect of jammed rubber particles on the response of a jammed packing to an externally applied load is examined. The evolution of inter-particle forces is studied using a rheometer configuration. Finite element techniques and modelling are employed to study the rubber in more detail.

Tyres are used in everyday life for a variety of practical and recreational tasks. Frictional behaviour of tyres on any surface is important for vehicle safety and control; this behaviour becomes more important when that surface is snow. The interaction of rubber and a snow surface is complex and a deeper understanding of both is needed in order to help develop better tyres. Outdoor full scale tyre test results were compared to results from indoor laboratory tests using a linear tribometer and a surface of compacted artificial snow; these were in excellent correlation allowing a systematic and comprehensive study of rubber friction on snow to be conducted in the laboratory. Rubber samples of varied rubber compositions and geometries were used to gain an understanding of friction on snow. Samples with varying glass transition temperature (Tg), dynamic rigidity (G*) and Payne effect (dependence of the dynamic moduli on the amplitude of the applied strain) were investigated along with samples with and without sipes. The rubber friction coefficient (μ) was measured as a function of velocity and temperature. The siped samples exhibited a higher μ than those without sipes. FE simulations, rubber friction tests for varying contact pressures and steel blade force tests were performed to evaluate contributions from ‘surface’ friction and ploughing separately. The increased μ was attributed to the ploughing force from the front edges of the ‘subblocks’ created by the sipes. Although it is well known in the industry that siped tyres grip well, this is the first time it has been explained how sipes grip effectively through a combination of ploughing and rubber snow interaction. A comprehensive study of varying rubber properties (Tg, G* and Payne effect) was conducted to better understand their impact on snow friction. The findings were evaluated using the WLF shift factor to account for the running frequency of the rubber from the snow surface roughness. G* was found to be the dominant parameter for rubber μ when considering running frequency. Increased μ values were exhibited by rubbers with a lower G*. The decreased G* makes the rubber more compliant, thus increasing the contact area between the rubber and the snow, in turn increasing μ. A better knowledge of the surface roughness of snow will aid the understanding of the interaction between rubber and snow for tyres. A method was developed to characterise the artificial snow surface utilising sectioning and imaging of chemically stabilised snow samples. From images of the snow surface before friction testing the average indentor size can be found, this is used to analyse the running frequency of the rubber. Qualitatively comparing the surfaces before and after rubber friction testing shows a decrease in surface profile aggressivity after a test; this is attributed to melting of the snow from frictional heating and snow grain fracture. Friction tests were conducted to directly compare rubber friction on snow and ice using round edged samples. Again it was found that the rubber with the decreased G* exhibited higher friction; this was seen on both snow and ice confirming G* as the dominant rubber property for both surfaces, regardless of the surface roughness change. It was found that at low temperatures ice had a higher μ than snow, while at high temperatures snow exhibited a higher μ than ice. It is hypothesised that this intriguing switch is due to the surface roughness change leading to differing contact areas both with and without melt water. This switch is not seen when a simple heat transfer model is used, confirming the effect as a surface roughness change. The use of a modified Hertz model shows that indentation is the dominant mechanism at low velocities on snow. It is hypothesised that at high velocities melt water dominates on both snow and ice while adhesion may have a more significant role on ice at low velocities. These findings provide knowledge that can be used in the design of tyres for snow and ice in the future.

In recent years, the interest in the design, construction and utilization of rubber tracks for agriculture and earth moving machinery has increased considerably. The development of such types of tracks was initiated by the efforts to invent a more environmentally friendly vehicle-terrain system. These tracks are also the result of the continuous effort to develop more cost-effective traction systems. A rubber-surfaced and friction-based prototype track was developed and mounted on the patented modification of a new Allis Chalmers four wheel drive tractor. The track is propelled by smooth pneumatic tyres by means of rubber-rubber friction and the tractive effort of the track is mainly generated by soil-rubber friction between the rubber surface of the track elements and terrain. The experimental track layer tractor, based on an Allis Chalmers 8070 tractor (141 kW) was tested on concrete and on cultivated sandy loam soil at 7.8%; 13% and 21% soil water content. The contact pressure and the tangential force on an instrumented track element, as well as the total torque input to one track, was simultaneously recorded during the drawbar pull-slip tests. Soil characteristics for pressure-sinkage and friction-displacement were obtained from the field tests by using an instrumented linear shear and soil sinkage device. By applying the approach based on the classical bevameter technique, analytical methods were implemented for modelling the traction performance of the prototype track system. Different possible pressure distribution profiles under the tracks were considered and compared to the recorded data. Two possible traction models were proposed, one constant pressure model, for minimal inward track deflection and the other a flexible track model with inward deflection and a higher contact pressure at both the front free-wheeling and rear driving tyres. For both models, the traction force was mainly generated by rubber-soil friction and adhesion with limited influence by soil shear. For individual track elements, close agreement between the measured and predicted contact pressure and traction force was observed based on the flexible track model. The recorded and calculated values of the coefficient of traction based on the summation of the traction force for the series of track elements were comparable to the values predicted from modelling. However, the measured values of drawbar pull coefficient were considerably lower than the predicted values, largely caused by internal track friction in addition to energy dissipated by soil compaction. The tractive efficiency for soft surface was also unacceptably low, probably due to the high internal track friction and the low travel speeds applied for the tests. The research undertaken identified and confirmed a model to be used to predict contact pressure and tangential stresses for a single track element. It was capable of predicting the tractive performance for different possible contact pressure values. / Thesis (PhD (Argricultural Engineering))--University of Pretoria, 2007. / Civil Engineering / Unrestricted

Rubber friction is an important aspect to tire engineers, material developers and pavement engineers because of its importance in the estimation of forces generated at the contact, which further helps in optimizing tire and vehicle performances, and to estimate tire wear. It mainly depends on the material properties, contact mechanics and operating condition. There are two major contributions to rubber friction, due to repeated viscoelastic deformation from undulations of surface called hysteresis and due to Vander Waals interaction of the molecules called adhesion. The study focuses on analytical modeling of friction for stationary sliding of rubber block on rough surfaces. Two novel approaches are discussed and compared. Frictional shear stress is obtained from the energy dissipated at the contact interface due to the elastic deformations of rubber block at different length scales. Contact mechanics theories based on continuity approach combined with stochastic processes to estimate the real contact area, mean penetration depth and true stresses at contact depending on operating conditions. Rubber properties are highly temperature dependent. Temperature model developed based on heat diffusion relation is integrated to consider the effects of temperature rise due to frictional heating. Model results are validated with theoretical results of literature. Simulation results of friction model is obtained for Compound A sliding on rough surface. Material properties are obtained using Dynamic Mechanical Analysis and Time temperature superposition. Influence of the friction models under different conditions are discussed. Model results are validated with experimental data from Dynamic friction tester on a 120-grit surface followed by future works. / Master of Science

This dissertation aims to contribute towards the understanding and modeling of tribological phenomena of contact, friction, and wear in viscoelastic materials with application in rubber compounds. Tribiological properties of rubber compounds are important for many applications such as tires, shoe heels and soles, wiper blades, artificial joints, O-ring seals, and so on. In all these applications, the objective is to maximize the friction coefficient to avoid slipping and reduce the wear rate to improve the life expectancy and performance of the products. The first topic in this study focuses on a novel multiscale contact theory proposed by Persson and explains the advantages of this theory over other classical contact theories. The shortcomings of this theory are also investigated, and three methods are proposed to improve Persson's original contact model by correcting the approximation of deformation in the contact area. The first method is based on the original Greenwood and Williamson (GW) contact theory, which neglects the effect of elastic coupling between asperities. The second method is based on an improved version of GW theory, which considers the elastic coupling effect of asperities in an approximate way. The third method is based on the distribution of local peaks of asperities, which is particularly suitable to determine the fraction of a skewed height profile involved in tribological processes. This method can be implemented within the framework of other proposed methods. Since the height profiles of rough surfaces studied in this dissertation are approximately normally distributed, the second correction method is applied to the original contact model to calculate the real contact area and friction coefficient. The second topic addresses the theoretical model of hysteresis friction in viscoelastic materials. The multiscale temperature rise of the rubber surface due to hysteresis friction is also modeled and the effect of flash temperature on the real contact area and friction coefficient is studied. Since the hysteresis friction is not the only mechanism involved in the rubber friction, a semi-empirical model is added to the hysteresis model to include the contribution of adhesion and other processes on the real contact area. Based on the improved multiscale contact theory, a pressure-dependent friction model is also developed for viscoelastic materials, which is in good agreement with experimental results. The third topic deals with the theory of stationary crack propagation in viscoelastic materials and the effect of crack tip flash temperature on the instability of crack propagation observed in some experimental results in the literature. Initially, a theoretical model is developed to calculate the tearing energy vs crack tip velocity in a Kelvin-Voigt rubber model. Besides, two coupled iterative algorithms are developed to calculate the temperature field around the crack tip in addition to the tearing energy as a function of crack tip velocity. In this model, the effect of crack tip flash temperature on the tearing energy is considered to update the relation between tearing energy vs crack tip velocity, which also affects the flash temperature. A theoretical model is also developed to calculate the contribution of the hysteresis effect to the tearing energy vs crack tip velocity using the dynamic modulus master curve of a rubber compound. Then, the low-frequency fatigue test results are compared with the theoretical predictions and used in the framework of powdery rubber wear theory to calculate the stationary rubber wear rate due to fatigue crack propagation. Moreover, a sliding friction and wear test set-up, with both indoor and outdoor testing capability, is developed to validate the theoretical models. The experimental results confirm that the theoretical model can successfully predict the friction coefficient when there is no trace of thermochemical degradation on the rubber surface. Investigating the wear mechanism of rubber samples on three different surfaces reveals that the contribution of fatigue wear rate is less important than other wear mechanisms such as abrasive wear due to sharp asperities or thermochemical degradation due to a significant rise of temperature on the contact area. Finally, the correlation between friction coefficient and wear rate on different surfaces is studied, and it is found that the relation between friction and wear rate strongly depends on the dominant wear mechanism, which is determined by the surface characteristics, sliding velocity, normal load, and contact flash temperature. / PHD / The objective of this dissertation is to understand and develop models for contact, friction, and wear in rubber-like materials. Friction and wear of rubber-like materials are important in many applications such as tires, shoe heels and soles, wiper blades, artificial joints, O-ring seals, and so on. In all these applications, it is desired to maximize the friction to avoid slipping and reduce the mass loss due to abrasion to improve the life expectancy of the products. The first topic in this dissertation focuses on a novel multiscale contact theory proposed by Persson and different approaches proposed in this work to improve this theory. Then, the real contact area is calculated using an improved version of the contact model. The second topic addresses the theoretical model of rubber friction due to hysteresis energy dissipation and the effect of frictional heating on the real contact area. Since the hysteresis friction is not the only mechanism involved in the rubber friction, a semi-empirical model is also used to include the contribution of adhesion and other processes on the real contact area. Based on the improved contact theory, a pressure-dependent friction model is also developed for rubber-like materials, which is in good agreement with the experimental results. The third topic deals with the theory of stationary crack propagation in rubberlike materials and the effect of crack tip temperature rise on the instability of crack propagation observed in some experimental results in the literature. The low-frequency fatigue test results are compared with the theoretical predictions, and the results are used in the framework of powdery rubber wear theory to calculate the rubber wear rate due to slow crack propagation. A sliding friction and wear test set-up is also developed to validate the theoretical models. The theoretical model of the friction coefficient is successfully validated by experimental results. Investigating the rubber wear on different surfaces reveals that the contribution of fatigue wear rate is less important than the other wear mechanisms. The correlation between friction coefficient and wear rate on different surfaces reveals that relation between friction and wear rate strongly depends on the dominant wear mechanism, which is determined by the surface characteristics, sliding velocity, normal load, and temperature rise on the contact surface.

Styrene-Butadiene Rubber (SBR) is a form of rubber compound that is widely used in the tire industry. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. In this study, a material aging model that can predict the hyperplastic response of styrene-butadiene rubber (SBR) was mathematically developed using an integrated testing and continuum damage model framework. Coupling between the mechanical changes of SBR to the change in the chemical properties, specifically crosslink density (CLD) was also investigated. SBR dogbone shaped samples were accelerated aged in an aging oven at various temperatures and aging periods. Subsequently, hyperelastic tests were conducted to obtain the high strain response taking the 'Mullin's effect' into consideration. These responses were calibrated to different hyperelastic material models and the Arruda-Boyce model was chosen, due to its stable behavior and optimal fit. An aging evolution function was developed based on the variation in the model coefficients. This damage model is able to predict the hyperelastic response of SBR as it ages. A user material subroutine (UMAT) was also implemented in Abaqus based on the obtained aging evolution function to predict the stress response of SBR for varied applications. Additionally, to couple the chemical variations with the hyperelastic response, the rubber structure and composition was probed using Fourier-transform infrared spectroscopy (FTIR). The degradation of additives and SBR polymer chains were analyzed microscopically to explain the impact on the macroscopic properties. This study helps to correlate the change in crosslink density to ameliorate mechanical properties, such as strain at break, modulus, and stiffness. The effects of aging on the viscoelastic properties of SBR were also studied. Dynamic Mechanical Analysis (DMA) was used to characterize the viscoelastic response. Master curves of storage and loss modulus were generated using the time-temperature superposition principle (TTSP). The friction coefficient was estimated from the storage and loss modulus using a simplified form of the Persson equation [1]. CLD was also estimated from DMA data. Wear experiments were conducted on the Dynamic Friction Tester (DFT) for various aging conditions. The estimated friction coefficient was compared to the one from the experiments. Archard's law was used to correlate the frictional energy to the volume loss during wear experiments. Correlation between the wear and the viscoelastic properties of SBR is also studied. Finally, the lifetime of SBR for various aging temperatures is predicted using various models. [1] M. Ciavarella, "A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses," J. Tribol., vol. 140, no. 1, 2018, doi: 10.1115/1.4036917. / Master of Science / Elastomers or rubbers are they are generally referred to are an indispensable part of human life. They are made up of long-chain polymer units linked to one other through crosslinks. This peculiar morphology of rubbers is what gives them their unique characteristics. There are as many as 40,000 known products that use some form of rubber as the primary raw material. Apart, from this, they are also widely used in aviation and aerospace, automobiles, dampers and absorbers, civil engineering, electronics, medical, toys, clothing, sports, footwear, and so on. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. Over the last couple of years, it has also played a pivotal role in personal protective equipment (PPE) and masks worn by billions of people and frontline workers all over the globe. The fact that rubber is included in the EU's list of critical raw materials highlights its global importance. However, over the past several years, the rubber supply has dwindled. COVID-19 also caused disruptions in the supply chain of rubber. As the effects of COVID-19 are fading, there has been a spike in the demand for rubber; the primary reason being automotive tires! Even though substantial research is being conducted to try and replace rubber as a raw material with synthetic alternatives such as polyurethane, the excellent blend of damping, friction and wear characteristics, heat dissipation provided by natural rubber cannot be replicated by any of these laboratory compounds. Hence, at this time, there is an increased need to conserve and improve the longevity of rubber compounds. Styrene-Butadiene Rubber (SBR) is a form of a rubber compound that is widely used in the tire industry. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. The present study aims to model changes in the hyperelastic (large stretching) behavior of SBR using a Continuum Damage Mechanics (CDM) approach. This mathematical model is translated into ABAQUS, a finite element analysis software to study the mechanical response of components with various geometries and loading conditions. Secondly, the effects of aging on the viscoelastic behavior of SBR is studied. This helps us to estimate the cross-link density (CLD) as well as the friction coefficient of SBR as it is aged. The impact of aging on the wear and friction properties of SBR is studied experimentally. Finally, using various mechanical and chemical models the lifetime of SBR is estimated for various aging temperatures. Thus, the end goal of the study is to drive the development of new rubber compounds that will help improve the service life of rubbers and also have a positive impact on the environment.

Tire, or in its primitive form, Wheel, an important invention for the transportation sector, has evolved from a circular block of hard and durable material to one of the most complex and influential components of an automobile. It is the only means of contact between the vehicle and the road and is responsible for generating forces and moments that impact vehicle performance, stability, and control. Tire tribology is the study of interacting surfaces in relative motion which includes friction and wear. Tire friction is an essential concept for estimating the tractive effort/ traction at the tire-road interface that further helps to determine the control and stability of the vehicle. In contrary, it also results in rolling resistance and wear. Tire and vehicle engineers are henceforth interested in a robust and efficient approach towards estimation of friction and wear. Past experimental observations using tread compound samples have revealed the different factors influencing the friction at the contacting interface. In addition, different mechanisms or components resulting in frictional losses, being Hysteretic, Adhesive and Viscous, and wear being abrasive, fatigue, adhesive and corrosive were also observed. Although experimental and empirical observations have provided us with an accurate estimation of friction and wear parameters, it is very tedious and expensive approach. Recent developments in the computational power encouraged researchers and engineers towards evolution of analytical and numerical models considering the underlying physical mechanisms at the contact interface. Past research studies developed multiscale techniques for estimation of friction coefficient due to hysteretic losses from internal damping of the rubber material because of oscillation from surface undulations. Later, contact mechanics models developed using Hertzian technique or stochastic approach were considered in conjunction with frictional losses to obtain the hysteretic component of friction to consider the effect of surface roughness. Previous studies at CenTiRe focused on surface characterization techniques and estimation of friction for dry surfaces using Persson and Klüppel's approach. Comparative studies unveiled the importance of considering pressure/ normal load towards friction estimation. In addition, it was found that effect of adhesion for estimation of contact mechanics parameters must be considered. The present work focusses on obtaining a conceptual framework to model a comprehensive friction model considering the effect of surface roughness, substrate condition and asperity interaction. A finite element simulation of rubber block sliding on a rough substrate is performed using a multiscale technique for estimation of friction and contact mechanics under dry condition. The estimated contact mechanics and friction is compared with analytical models and experimental measurements obtained using Linear sliding friction tester developed in collaboration with other members of the group. In addition, a FE model is developed to measure the wear properties of rubber material based on continuum damage mechanics and further obtain the wear profile of a rubber block sliding on a rough substrate. / Doctor of Philosophy / Tribology, a recent terminology for an age-old concept of friction, wear, and lubrication. the study of interacting surfaces in relative motion which includes friction and wear. Friction is the resisting force at the contact interface leading to heat build-up and material loss at the contact interface which is known as flash temperature and wear respectively. Tire is one of the most complex and influential components of a vehicle that helps in optimizing its performance for better stability and control. Knowledge of tire friction and wear is important for tire engineering and vehicle dynamics engineers as it helps in characterizing the handling characteristics of the vehicle, characterizing the tire material compounds to understand the tire durability. Rubber is a viscoelastic material, the friction and wear in rubber is intricate as opposed to other elastic materials. Based on experimental observations in the past, friction and wear are influenced by factors like material properties, normal load/ pressure, sliding velocity, temperature, surface characteristics, and environmental conditions. In addition, the frictional losses at the contact interface are considered to compose of adhesion, hysteresis and viscous components and wear is categorized as – adhesive, abrasive, fatigue, corrosive and erosive. Recent developments in computational power encouraged researchers and engineers in developing analytical and computational models that consider the physical mechanisms occurring at the contact interface. The present research focuses on obtaining a comprehensive friction and contact mechanics model considering the effect of surface roughness at different length scales, surface condition (dry/ wet) and asperity interaction. In addition, the developed model in conjunction with a brush model is considered for estimating the tire traction characteristics such as the forces and moments. A finite element simulation of rubber block sliding on a rough substrate is performed using a multiscale technique for estimation of friction, contact mechanics and abrasion parameters under dry condition. The results thus obtained are compared with the analytical model that is developed for wet conditions. Experimental validation of the friction estimated using the analytical and numerical methods will be performed using a linear sliding friction tester developed in collaboration with other members of the group.

Elastomer seals are used in a variety of industries that require flow isolation. The characterization of the behavior of these seals remains largely unexplored and hence, this study is focused on simulating and validating the axial-compressive behavior of an annular rubber seal constrained concentrically in a pipe. The elastomer material composing the seal, was experimentally characterized for its mechanical, frictional, and viscoelastic properties and modelled using models developed by Yeoh, Thirion, and Prony respectively. A 2D axisymmetric finite-element model was developed using ANSYS 16 and used alongside the material models to simulate an axial load versus displacement curve, a contact pressure distribution, and a pipe hoop strain gradient. The results for quasi-static loading and viscoelastic effects agreed within 7% and 18% of the experimental results, respectively. It was observed that pipe geometry, rubber chemistry, frictional properties, and viscoelastic effects have significant effect on the compressive behavior of the seal. / October 2016

Die Kontaktverhältnisse zwischen Reifen und Fahrbahn bestimmen die maximal übertragbaren Beschleunigungs-, Brems- und Seitenkräfte des Fahrzeugs und sind daher für die Fahrsicherheit von großer Bedeutung. In dieser Arbeit wird ein Modell zur numerisch effizienten Simulation der hochfrequenten Dynamik einzelner Reifenprofilblöcke entwickelt. Der vorgestellte Modellansatz nutzt einerseits die Vorteile der Finite-Elemente-Methode, welche die Bauteilstruktur detailliert auflösen kann, bei der jedoch lange Rechenzeiten in Kauf genommen werden. Andererseits profitiert der vorgestellte Modellansatz von den Vorteilen stark vereinfachter Mehrkörpersysteme, welche die Berechnung der hochfrequenten Dynamik und akustischer Phänomene erlauben, jedoch strukturdynamische Effekte und das Kontaktverhalten in der Bodenaufstandsfläche des Reifens nur begrenzt abbilden können. Das hier vorgestellte Modell berücksichtigt in einem modularen Ansatz die Effekte der Strukturdynamik, der lokalen Reibwertcharakteristik, der nichtlinearen Wechselwirkungen durch den Kontakt mit der rauen Fahrbahnoberfläche und des lokalen Verschleißes. Die erforderlichen Modellparameter werden durch geeignete Experimente bestimmt. Ein Schwerpunkt der Arbeit liegt in der Untersuchung reibungsselbsterregter Profilblockschwingungen bei Variation der Modell- und Prozessparameter. Zur realistischen Betrachtung des Reifenprofilblockverhaltens erfolgt eine Erweiterung des Modells um eine Abrollkinematik, die tiefere Einblicke in die dynamischen Vorgänge in der Bodenaufstandsfläche des Reifens ermöglicht. Diese Simulationen lassen eine Zuordnung der aus der Literatur bekannten zeitlichen Abfolge von Einlaufphase, Haftphase, Gleitphase und Ausschnappphase zu. Es zeigen sich bei bestimmten Kombinationen aus Fahrzeuggeschwindigkeit und Schlupfwert ausgeprägte Stick-Slip-Schwingungen im akustisch relevanten Frequenzbereich. Das Modell erlaubt die Untersuchung des Einflusses der Profilblockgeometrie, der Materialparameter, der Fahrbahneigenschaften sowie der Betriebszustände auf den resultierenden Reibwert, auf das lokale Verschleißverhalten sowie auf das Auftreten hochfrequenter reibungsselbsterregter Schwingungen. Somit ermöglicht das Modell ein vertieftes Verständnis der Vorgänge im Reifen-Fahrbahn-Kontakt und der auftretenden Wechselwirkungen zwischen Struktur- und Kontaktmechanik. Es kann eine Basis für zukünftige Optimierungen des Profilblocks zur Verbesserung wesentlicher Reifeneigenschaften wie Kraftschlussverhalten, Verschleiß und Akustik bilden. / The contact conditions between tyre and road are responsible for the maximum acceleration, braking and side forces of a vehicle. Therefore, they have a large impact on the driving safety. Within this work a numerically efficient model for the simulation of the high-frequency dynamics of single tyre tread blocks is developed. The presented modelling approach benefits the advantage of the finite element method to resolve the component structure in detail. However, a long computation time is accepted for these finite element models. Moreover, the presented modelling approach makes use of the advantage of simplified multibody systems to calculate the high-frequency dynamics and acoustic phenomena. However, structural effects and the contact behaviour in the tyre contact patch can be covered only to a minor degree. The model treated here considers the effects of structural dynamics, the local friction characteristic, the non-linear interaction due to the contact with the rough road surface and local wear. The required model parameters are determined by appropriate experiments. One focus of this work is the investigation of self-excited tread block vibrations under variation of the model and process parameters. In order to realistically investigate the tread block behaviour the model is extended with regard to rolling kinematics which provides a deeper insight into the dynamic processes in the tyre contact patch. The corresponding simulations allow the allocation of the run-in phase, sticking phase, sliding phase and snap-out which is reported in the literature. For certain combinations of vehicle velocity and slip value pronounced stick-slip vibrations occur within the acoustically relevant frequency range. The model enables to study the influence of the tread block geometry, the material properties, the road surface characteristics and the operating conditions on the resulting tread block friction coefficient, local tread block wear and the occurrence of high-frequency self-excited vibrations. The simulation results provide a distinct understanding of the processes in the tyre/road contact and the interactions between structural mechanics and contact mechanics. They can be a basis for future tread block optimisations with respect to essential tyre properties such as traction, wear and acoustic phenomena.

Die Kontaktverhältnisse zwischen Reifen und Fahrbahn bestimmen die maximal übertragbaren Beschleunigungs-, Brems- und Seitenkräfte des Fahrzeugs und sind daher für die Fahrsicherheit von großer Bedeutung. In dieser Arbeit wird ein Modell zur numerisch effizienten Simulation der hochfrequenten Dynamik einzelner Reifenprofilblöcke entwickelt. Der vorgestellte Modellansatz nutzt einerseits die Vorteile der Finite-Elemente-Methode, welche die Bauteilstruktur detailliert auflösen kann, bei der jedoch lange Rechenzeiten in Kauf genommen werden. Andererseits profitiert der vorgestellte Modellansatz von den Vorteilen stark vereinfachter Mehrkörpersysteme, welche die Berechnung der hochfrequenten Dynamik und akustischer Phänomene erlauben, jedoch strukturdynamische Effekte und das Kontaktverhalten in der Bodenaufstandsfläche des Reifens nur begrenzt abbilden können. Das hier vorgestellte Modell berücksichtigt in einem modularen Ansatz die Effekte der Strukturdynamik, der lokalen Reibwertcharakteristik, der nichtlinearen Wechselwirkungen durch den Kontakt mit der rauen Fahrbahnoberfläche und des lokalen Verschleißes. Die erforderlichen Modellparameter werden durch geeignete Experimente bestimmt. Ein Schwerpunkt der Arbeit liegt in der Untersuchung reibungsselbsterregter Profilblockschwingungen bei Variation der Modell- und Prozessparameter. Zur realistischen Betrachtung des Reifenprofilblockverhaltens erfolgt eine Erweiterung des Modells um eine Abrollkinematik, die tiefere Einblicke in die dynamischen Vorgänge in der Bodenaufstandsfläche des Reifens ermöglicht. Diese Simulationen lassen eine Zuordnung der aus der Literatur bekannten zeitlichen Abfolge von Einlaufphase, Haftphase, Gleitphase und Ausschnappphase zu. Es zeigen sich bei bestimmten Kombinationen aus Fahrzeuggeschwindigkeit und Schlupfwert ausgeprägte Stick-Slip-Schwingungen im akustisch relevanten Frequenzbereich. Das Modell erlaubt die Untersuchung des Einflusses der Profilblockgeometrie, der Materialparameter, der Fahrbahneigenschaften sowie der Betriebszustände auf den resultierenden Reibwert, auf das lokale Verschleißverhalten sowie auf das Auftreten hochfrequenter reibungsselbsterregter Schwingungen. Somit ermöglicht das Modell ein vertieftes Verständnis der Vorgänge im Reifen-Fahrbahn-Kontakt und der auftretenden Wechselwirkungen zwischen Struktur- und Kontaktmechanik. Es kann eine Basis für zukünftige Optimierungen des Profilblocks zur Verbesserung wesentlicher Reifeneigenschaften wie Kraftschlussverhalten, Verschleiß und Akustik bilden.:Formelverzeichnis VII Kurzfassung X Abstract XI 1 Einleitung 1 1.1 Zielsetzung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Gliederung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Stand des Wissens 6 2.1 Mechanische Eigenschaften von Elastomeren . . . . . . . . . . . . . . . . . . 6 2.2 Elastomerreibung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Modelle zur Beschreibung von Hysteresereibung . . . . . . . . . . . 11 2.2.2 Modelle zur Beschreibung von Adhäsionsreibung . . . . . . . . . . . 12 2.2.3 Phänomenologische Beschreibung von Elastomerreibung . . . . . . 13 2.3 Verschleiß von Profilblöcken . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Entstehung von Stick-Slip-Schwingungen . . . . . . . . . . . . . . . . . . . . 28 2.5 Profilblockmodelle und -simulationen . . . . . . . . . . . . . . . . . . . . . . 31 2.6 Experimentelle Einrichtungen zur Untersuchung von Profilblöcken . . . . . 42 2.6.1 Schwerlasttribometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6.2 IDS-Tribometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.6.3 Mini-mue-road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6.4 Linear Friction Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.6.5 Prüfstand für Stollenmessungen . . . . . . . . . . . . . . . . . . . . . 48 2.6.6 Hochgeschwindigkeits-Abrollprüfstand . . . . . . . . . . . . . . . . 49 2.6.7 Hochgeschwindigkeits-Linearprüfstand . . . . . . . . . . . . . . . . 50 2.7 Experimentelle Reibwertbestimmung . . . . . . . . . . . . . . . . . . . . . . 52 3 Profilblockmodell 55 3.1 Modularer Modellansatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Modul 1: Strukturdynamik . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.1 Transformations- und Reduktionsverfahren . . . . . . . . . . . . . . 59 3.2.2 Implementierung in das Gesamtmodell . . . . . . . . . . . . . . . . . 72 3.3 Modul 2: Lokale Reibwertcharakteristik . . . . . . . . . . . . . . . . . . . . . 72 3.3.1 Einflussgrößen auf den Reibwert . . . . . . . . . . . . . . . . . . . . 72 3.3.2 Numerische Behandlung der Reibwertberechnung . . . . . . . . . . 73 3.4 Modul 3: Nichtlineare Kontaktsteifigkeit . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Lokale Kontaktbetrachtungen . . . . . . . . . . . . . . . . . . . . . . 76 3.4.2 Kontaktalgorithmus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5 Modul 4: Lokaler Verschleiß . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.5.1 Vorgehen zur Verschleißmodellierung . . . . . . . . . . . . . . . . . 81 3.5.2 Implementierung in das Gesamtmodell . . . . . . . . . . . . . . . . . 82 4 Parameterbestimmung 84 4.1 Strukturdynamische Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.1.1 Bestimmung des Elastizitätsmoduls und der Dämpfung . . . . . . . 84 4.1.2 Optimierung der Modenanzahl . . . . . . . . . . . . . . . . . . . . . 88 4.2 Bestimmung der Reibcharakteristik . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 Bestimmung der nichtlinearen Kontaktsteifigkeit . . . . . . . . . . . . . . . 92 4.4 Bestimmung der Verschleißparameter . . . . . . . . . . . . . . . . . . . . . . 94 5 Simulationen 100 5.1 Betrachtung eines gleitenden Profilblocks . . . . . . . . . . . . . . . . . . . . 100 5.1.1 Simulationen bei hoher Gleitgeschwindigkeit ohne Verschleiß . . . . 100 5.1.2 Simulationen bei hoher Gleitgeschwindigkeit mit Verschleiß . . . . 103 5.1.3 Profilblockverhalten bei niedriger Gleitgeschwindigkeit . . . . . . . 106 5.1.4 Simulationen mit Normalkraftvorgabe . . . . . . . . . . . . . . . . . 114 5.1.5 Vergleich Experiment-Simulation . . . . . . . . . . . . . . . . . . . . 117 5.1.6 Variation der Profilblockgeometrie . . . . . . . . . . . . . . . . . . . 119 5.2 Betrachtung eines abrollenden Profilblocks . . . . . . . . . . . . . . . . . . . 124 5.2.1 Abrollkinematik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.2.2 Einfluss der Fahrzeuggeschwindigkeit . . . . . . . . . . . . . . . . . 130 5.2.3 Einfluss des Schlupfwerts . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.4 Einfluss des Kontaktdrucks . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.5 Kontaktkraftbetrachtungen . . . . . . . . . . . . . . . . . . . . . . . . 135 6 Zusammenfassung 139 Literatur 143 / The contact conditions between tyre and road are responsible for the maximum acceleration, braking and side forces of a vehicle. Therefore, they have a large impact on the driving safety. Within this work a numerically efficient model for the simulation of the high-frequency dynamics of single tyre tread blocks is developed. The presented modelling approach benefits the advantage of the finite element method to resolve the component structure in detail. However, a long computation time is accepted for these finite element models. Moreover, the presented modelling approach makes use of the advantage of simplified multibody systems to calculate the high-frequency dynamics and acoustic phenomena. However, structural effects and the contact behaviour in the tyre contact patch can be covered only to a minor degree. The model treated here considers the effects of structural dynamics, the local friction characteristic, the non-linear interaction due to the contact with the rough road surface and local wear. The required model parameters are determined by appropriate experiments. One focus of this work is the investigation of self-excited tread block vibrations under variation of the model and process parameters. In order to realistically investigate the tread block behaviour the model is extended with regard to rolling kinematics which provides a deeper insight into the dynamic processes in the tyre contact patch. The corresponding simulations allow the allocation of the run-in phase, sticking phase, sliding phase and snap-out which is reported in the literature. For certain combinations of vehicle velocity and slip value pronounced stick-slip vibrations occur within the acoustically relevant frequency range. The model enables to study the influence of the tread block geometry, the material properties, the road surface characteristics and the operating conditions on the resulting tread block friction coefficient, local tread block wear and the occurrence of high-frequency self-excited vibrations. The simulation results provide a distinct understanding of the processes in the tyre/road contact and the interactions between structural mechanics and contact mechanics. They can be a basis for future tread block optimisations with respect to essential tyre properties such as traction, wear and acoustic phenomena.:Formelverzeichnis VII Kurzfassung X Abstract XI 1 Einleitung 1 1.1 Zielsetzung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Gliederung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Stand des Wissens 6 2.1 Mechanische Eigenschaften von Elastomeren . . . . . . . . . . . . . . . . . . 6 2.2 Elastomerreibung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Modelle zur Beschreibung von Hysteresereibung . . . . . . . . . . . 11 2.2.2 Modelle zur Beschreibung von Adhäsionsreibung . . . . . . . . . . . 12 2.2.3 Phänomenologische Beschreibung von Elastomerreibung . . . . . . 13 2.3 Verschleiß von Profilblöcken . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Entstehung von Stick-Slip-Schwingungen . . . . . . . . . . . . . . . . . . . . 28 2.5 Profilblockmodelle und -simulationen . . . . . . . . . . . . . . . . . . . . . . 31 2.6 Experimentelle Einrichtungen zur Untersuchung von Profilblöcken . . . . . 42 2.6.1 Schwerlasttribometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.6.2 IDS-Tribometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.6.3 Mini-mue-road . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6.4 Linear Friction Tester . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.6.5 Prüfstand für Stollenmessungen . . . . . . . . . . . . . . . . . . . . . 48 2.6.6 Hochgeschwindigkeits-Abrollprüfstand . . . . . . . . . . . . . . . . 49 2.6.7 Hochgeschwindigkeits-Linearprüfstand . . . . . . . . . . . . . . . . 50 2.7 Experimentelle Reibwertbestimmung . . . . . . . . . . . . . . . . . . . . . . 52 3 Profilblockmodell 55 3.1 Modularer Modellansatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.2 Modul 1: Strukturdynamik . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2.1 Transformations- und Reduktionsverfahren . . . . . . . . . . . . . . 59 3.2.2 Implementierung in das Gesamtmodell . . . . . . . . . . . . . . . . . 72 3.3 Modul 2: Lokale Reibwertcharakteristik . . . . . . . . . . . . . . . . . . . . . 72 3.3.1 Einflussgrößen auf den Reibwert . . . . . . . . . . . . . . . . . . . . 72 3.3.2 Numerische Behandlung der Reibwertberechnung . . . . . . . . . . 73 3.4 Modul 3: Nichtlineare Kontaktsteifigkeit . . . . . . . . . . . . . . . . . . . . 75 3.4.1 Lokale Kontaktbetrachtungen . . . . . . . . . . . . . . . . . . . . . . 76 3.4.2 Kontaktalgorithmus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.5 Modul 4: Lokaler Verschleiß . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.5.1 Vorgehen zur Verschleißmodellierung . . . . . . . . . . . . . . . . . 81 3.5.2 Implementierung in das Gesamtmodell . . . . . . . . . . . . . . . . . 82 4 Parameterbestimmung 84 4.1 Strukturdynamische Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.1.1 Bestimmung des Elastizitätsmoduls und der Dämpfung . . . . . . . 84 4.1.2 Optimierung der Modenanzahl . . . . . . . . . . . . . . . . . . . . . 88 4.2 Bestimmung der Reibcharakteristik . . . . . . . . . . . . . . . . . . . . . . . 90 4.3 Bestimmung der nichtlinearen Kontaktsteifigkeit . . . . . . . . . . . . . . . 92 4.4 Bestimmung der Verschleißparameter . . . . . . . . . . . . . . . . . . . . . . 94 5 Simulationen 100 5.1 Betrachtung eines gleitenden Profilblocks . . . . . . . . . . . . . . . . . . . . 100 5.1.1 Simulationen bei hoher Gleitgeschwindigkeit ohne Verschleiß . . . . 100 5.1.2 Simulationen bei hoher Gleitgeschwindigkeit mit Verschleiß . . . . 103 5.1.3 Profilblockverhalten bei niedriger Gleitgeschwindigkeit . . . . . . . 106 5.1.4 Simulationen mit Normalkraftvorgabe . . . . . . . . . . . . . . . . . 114 5.1.5 Vergleich Experiment-Simulation . . . . . . . . . . . . . . . . . . . . 117 5.1.6 Variation der Profilblockgeometrie . . . . . . . . . . . . . . . . . . . 119 5.2 Betrachtung eines abrollenden Profilblocks . . . . . . . . . . . . . . . . . . . 124 5.2.1 Abrollkinematik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.2.2 Einfluss der Fahrzeuggeschwindigkeit . . . . . . . . . . . . . . . . . 130 5.2.3 Einfluss des Schlupfwerts . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.4 Einfluss des Kontaktdrucks . . . . . . . . . . . . . . . . . . . . . . . . 133 5.2.5 Kontaktkraftbetrachtungen . . . . . . . . . . . . . . . . . . . . . . . . 135 6 Zusammenfassung 139 Literatur 143