Article

Experimental Investigations on Rubber Friction Coefficient Dependence on Visco-Elastic Characteristics, Track Roughness, Contact Force, and Slide Velocity

Article

Experimental Investigations on Rubber Friction Coefficient Dependence on Visco-Elastic Characteristics, Track Roughness, Contact Force, and Slide Velocity

If you want to read the PDF, try requesting it from the authors.

Abstract

The results of an experimental activity, carried out using a prototype of pin on disk machine and aimed at investigating the frictional behavior of visco-elastic materials in sliding contact with rigid asperities, are presented. The pin is a rubber specimen coming from three different passenger automotive tires, while the disk is covered with glass, marble, or 3M anti-slip tape surfaces. Tests, performed both in dry and wet conditions, highlighted that the friction coefficient is strongly influenced by the effect that surface roughness plays on friction mechanisms of adhesion and hysteresis. The results confirmed the theoretical dependence of friction on vertical load, sliding velocity, rubber characteristics, and track conditions.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... The adhesive contribution arises from the attractive binding forces between the rubber surface and the substrate (often dominated by weak Van Der Waals forces). Since the adhesive friction is a result of short duration of physical bonds between molecules at the rubber-substrate interface, it is dominant at slow sliding velocities [7,12]. On the contrary, the hysteresis effect is due to substrate roughness that exert pulsating forces onto the rubber surface causing a large dissipation of energy in the rubber bulk. ...
... In this paper, a physical-analytical model is proposed for the hysteretic contribution calculation referring to a tyre tread block volume in sliding contact with road asperities. The model is based on the energy balance between the work done by the friction force component and the energy dissipated in the material due to hysteresis, resulting in a function of stress-field distribution [12]: ...
... Substituting (12) in (8) is obtained: ...
Chapter
Full-text available
The numerical prediction of rubber friction properties is a great challenge from the modelling point of view. In many applications such as tyres, sealing systems, conveyor belts, the observed friction process arises from complex mechanisms occurring at the interface rubber/substrate [1]. During the sliding contact between two deformable bodies, the friction main contributions can be accountable in adhesive and hysteretic causes [2]. The adhesive contribution is related to the formation and breaking of the adhesive bridges in the real contact points inside the nominal contact region, instead the hysteretic contribution is related to the deformation cycles that result in energy losses due to the viscoelastic behaviour of the bodies. Due to these mechanisms, a frictional force is generated during the relative sliding between two bodies. As concerns the hysteretic contribution, previous studies [3] showed that even in the absence of adhesion in the contact region, the contact pressure is distributed in a non-symmetrical manner causing a force of resistance that opposes the motion. In this paper, a physical-analytical model is developed to calculate the friction hysteretic component of a tyre tread elementary volume in sliding contact with road asperities. In this study, the road macroscale is only considered. The shape of the asperity is modelled as the osculating sphere [4]. The model is based on the energy balance between the work done by the friction force component and the energy dissipated in the material due to hysteresis. The compound viscoelastic properties are defined in terms of storage and loss moduli by means D.M.A. experimental tests. The internal dissipated energy is evaluated considering the stress and strain field calculated by Hamilton formulation [5]. Finally, some consideration about further model improvements are made regarding the introduction of a complete road spectrum (PSD) and the material modelling by fractional derivative algorithms.
... This means that experimental methods are needed to determine this physical property [1][2][3][4][5][6][7][8][9][10]. It is also important to determine the coefficient of sliding friction when making objects of "soft" materials (elastomers, rubber, plastics, etc.) [11][12][13][14][15][16]. Experimental evaluations sometimes need to determine additional physical parameters that characterize rolling friction [17][18][19]. ...
... The methods under consideration use the approaches of vibro technique, by taking the parameters of the damped oscillations of an object on inclined plane. The main difference between the proposed methods and the existing methods [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] is that different initial conditions and several cycles of oscillations are used for the identification. The proposed methods allow to determine both the coefficients of sliding friction and coefficients of rolling friction. ...
Conference Paper
Full-text available
The use of soft and flexible materials in technology, transport, and everyday life is well known. Mechanical properties such as slip and rolling friction play an important role in the manufacture of such objects. It appears as objects slide along each other. High friction is desirable in some objects, although high wear will be expected, in others, it is desirable to reduce friction. The study considers the possibility of experimentally determining some important mechanical properties of soft materials (textiles, elastomers). For this purpose, the forces of interaction between objects made of the same or different materials during their mutual motion are analyzed. From the analysis two physical parameters have been chosen as the estimation of the mechanical properties for the materials: the coefficient of sliding friction and the coefficient of rolling friction. For the identification of each parameter, the corresponding experimental rigs were dynamically studied. First, the oscillatory motion of a physical pendulum along an inclined plane with large angle of inclination, when the motion is damped by a constant sliding friction force, is studied. It is shown that by changing the initial conditions it is possible to synthesize a wide range of damped oscillations, from one half-cycle to five and more cycles. By measuring the angle at the starting position of the pendulum and the angle at the subsequent stopping position (after one oscillation cycle), an analytical formula for determining the coefficient of sliding friction was obtained. Then, the rolling friction coefficient was determined from the motion of the object along an inclined plane with a small angle of inclination. The moving object is designed as a platform on wheels. Two parameters were used to identify the rolling friction coefficient: the angle of inclination of the plane and the angle between the direction of motion of the object and the horizon. In addition, it has been shown that the rolling friction coefficient can also be determined with the above-mentioned physical pendulum rig. The results obtained in the work can also be used to identify the mechanical properties of non-soft materials. The main goal of the study is to obtain a theoretical justification for three new prototypes of experimental rigs for identifying the friction parameters of materials
... In these applications, the viscoelastic behaviour of tire block, which depends on rubber temperature and frequency solicitation of bitumen asperities, plays a fundamental role in the contact mechanics modelling [10,11] for the comprehension of the limit value of the local friction coefficient. ...
... In Figure 13, as well as in Figure 7, the coefficient values at fixed indentation frequency of 200 Hz are shown. Therefore, the above analysis by using the velocity ratio of the indenter or Cp coefficient could be employed by the authors in future applications as indexes well-related with the loss factor trends towards the typical temperature range in which the tread block usually works [5,11]. ...
Chapter
Full-text available
The knowledge of tires tread viscoelastic behaviour plays a fundamental role in automotive to optimize vehicle performance and safety. These properties are usually characterized by means of Dynamic Mechanical Analysis [1] which implies the testing of compound sample that can be obtained by destroying the tire of interest or manufactured in different condition respect to the final product provided by tiremakers. Nowadays, the non-destructive analysis procedures are an attractive solution. These techniques are essentially advantageous for being employed in testing the whole tire, allowing the analysis of a great number of them without affects costs. The purpose of this work is the experimental analysis of the tire tread response, in different working condition, evaluated by a commercial dial indicator [2] considering the measured displacement values of the device. Experimental tests have been carried out on different tread compounds and, being the tire performance strictly affected by the working temperature, additional tests have been performed by heating and cooling each sample in a range of interest [3, 4]. Moreover, the effects of aging on a tire has been studied. The comparison of the testing activity results shows the reliability of the dynamic dial indicator to capture the tires tread different behaviour within the operating condition of interest. These encouraging results lead to next step of the research activity which will focus on the evaluation of properties characterizing the hysteretic behaviour of tires.
... In general, it is understood that the dry road surface would generate more friction than the wet road surface and hence tire wear will be greater on a dry road [18]. Farroni et al. [19] had also expressed that a dry road would results in a difficulty for the tire rubber to slip over the road surface which in turns leads to heat build-up in the tire. This eventually increase the tire wear and tear due to an increase of tire temperature. ...
Article
Full-text available
A tire tends to trap stones in its tread pattern when the vehicle is on a move and this might affects the tire balance due to uneven tread wear of tread portion. The study aims to simulate stone trapping performance under various tire tread patterns and road conditions as well as assessing the performance of tires with stones trapped. The stone trapping phenomena on different tire tread pattern were analyzed under dry and wet road conditions. The tire models chosen were the symmetrical tire, asymmetrical tire, and directional tire. The model of these tires, stone and a flat road surface were created using SolidWorks and Fusion360 software and the static structural simulation is performed by using finite element analysis method. Tire inflation analysis and steady state rolling analysis were conducted to evaluate three parameters: total deformation, Von-Mises stress and equivalent elastic strain of the tires. It found that all three parameters are higher when stone trapped in tire for all tread pattern types. Symmetrical tread pattern provides the least wear and tear since it has the lowest increment of maximum equivalent elastic strain in both road conditions. Stone trapping in tire grooves would impact on the lifespan of the tire.
... In these applications, the viscoelastic properties determination of tire block, which depends on rubber temperature and frequency solicitation of bitumen asperities, is essential for contact mechanics modelling and the prediction of the limit value of the local friction coefficient [1]- [4]. ...
Chapter
Full-text available
The evaluation of the viscoelastic properties is a key topic for the analysis of the dynamic mechanical behaviour of polymers. In vehicle dynamics field, the knowledge of the viscoelasticity of tread compound is fundamental for tire-road contact mechanics modelling and friction coefficient prediction for the improvement of vehicle performance and safety, i.e. motorsport field. These properties are usually characterised by means of Dynamic Mechanical Analysis, which implies testing a compound sample obtained by destroying the tire of interest or a slab manufactured in different conditions respect to the final product provided by tiremakers. In this scenario, the non-destructive procedures are an advantageous solution for the analysis of the tread viscoelasticity, without affecting the tire integrity, allowing a great number of tests in the shortest possible time. For this reason, the authors propose an innovative instrument, called VESevo, for viscoelasticity evaluation by means of non-destructive and user-friendly technique. The purpose of the following work is the preliminary analysis of the dynamic response of the tires tested employing the VESevo in order to determine viscoelastic behaviour indexes for mechanical properties evaluation.
Article
Full-text available
Elastic wheels contain the chassis of airplanes, automobiles and other vehicles. Their tires interact with a solid supporting surface – roads and airfields. As a result of this interaction, only static friction, only sliding friction or a combination of them, depending on the mode of the wheel movement, can be present in the contact patch. The geometric dimensions and relative position of the different friction areas determine the stable, unstable or boundary movement of the elastic wheel. Purpose of work: calculation and measurement of geometric characteristics of static and sliding friction areas in the wheel-to-road contact. Determined that: the slip area appears on the longitudinal axis of the contact patch, at a distance from the center of the contact patch equal to 1/4 of the length of the contact patch, then it increases due to a decrease in the static friction area; the center of the static friction area in the contact patch moves toward the current moment by an amount proportional to the moment; the maximum displacement of the center of the static friction area corresponds to the moment maximum in terms of adhesion, and is 1/3 of the length of the contact patch.
Article
Full-text available
Surface roughness evaluation is very important for many fundamental problems such as friction, contact deformation, heat and electric current conduction, tightness of contact joints and positional accuracy. For this reason, surface roughness has been the subject of experimental and theoretical investigations for many decades. The real sur face geometry is so complicated that a finite number of parameters cannot provide a full description. I f the number of parameters used is increased, a more accurate description can be obtained. This is one of the reasons for introducing new parameters for surface evaluation. Surface roughness parameters are normally categorized into three groups according to its functionality. These groups are defined as amplitude parameters, spacing parameters, and hybrid parameters. This paper illustrates the definitions and the mathematical formulas for about 59 of the roughness parameters. This collection of surface roughness parameter was used in a new software computer vision package called SutfVision developed by the authors. In the package, these definitions were extended to calculate the 30 surface topography of different specimens.
Article
Full-text available
Among load cases concerning vehicle suspension strength and durability, the misuse case is very special because of large obstacles. In this paper, an extension of the flexible belt model RMOD-K 7 concerning misuse situations is discussed. In normal rolling conditions, contact occurs between tire and road surface. To handle misuse deformations, the contact between the inner surface of the tire and the rim has to be dealt with. Results of the validation process are shown, leading to normal forces up to 70 [kN]. The model can be used together with mbs full vehicle models. One example is the determination of the critical test velocity, which generates the maximum of suspension stresses and can be found using RMOD-K 7.
Chapter
Full-text available
DSC furnishes information on temperature and heat flow rates (or respectively, heat). Whether it is suited to solve the respective problem depends on the efficiency of the instrument. The characteristic data of the DSC which describe the instrument unambiguously must therefore be known. They allow a decision to be taken as to whether the DSC will be suitable for the intended use, and they also make a comparison with other DSCs possible.
Article
Full-text available
In this contribution, a simple rubber friction law is presented. The model can be used for tire and vehicle dynamics calculations [19]. The friction law is tested by comparing numerical results to the full rubber friction theory [6] and to experimental data. A two-dimensional tire model is introduced. The model combines the rubber friction law with a simple mass-spring description of the tire body. The tire model is very flexible and can be applied to different maneuvers. It can be used for calculating μ-slip curves, the self-aligning torque, braking and cornering, or combined motion (e.g., braking during cornering). The theory predictions are compared to measured data from indoor tire testing on sandpaper substrate. Simulations of antilock braking systems (ABS) using two different control algorithms are also presented.
Conference Paper
Full-text available
In this paper the results of an experimental activity carried out with the aim to investigate on the frictional behaviour of visco-elastic materials in sliding contact with road asperities is presented. Experiments are carried out using a prototype of pin on disk machine whose pin is constituted by a specimen of rubber coming from a commercial tyre while the disk may be in glass, marble or abrasive paper. Tests are performed both in dry and wet conditions. Roughness of the disk materials is evaluated by a tester and by a laser scan device. Temperature in proximity of the contact patch is measured by pyrometer pointed on the disk surface in the pin trailing edge, while room temperature is measured by a thermocouple. Sliding velocity is imposed by an inverter controlled motor driving the disk and measured by an incremental encoder. Vertical load is imposed applying calibrated weights on the pin and friction coefficients are measured acquiring the longitudinal forces signal by means of a load cell. As regards to the road roughness, the experimental results show a marked dependence with road Ra index. Dry and wet tests performed on different micro-roughness profiles (i.e. glass and marble) highlighted that friction coefficient in dry conditions is greater on smoother surfaces, while an opposite tendency is shown in wet conditions. Although affected by uncertainties the results confirm the dependence of friction on temperature, vertical load and track conditions.
Conference Paper
Full-text available
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.
Article
Full-text available
Three dimensional (3D) laser profilometry (LP) and pulsed thermography (PT) were used in the inspection of Pentelic marble. Quarry Pentelic marble samples, after processed with different roughness treatments (i.e. 60, 80, 100, 220, 400 and 600 mesh), were evaluated in the laboratory. Furthermore, different surface cleaning treatments were applied to a Pentelic marble surface in situ and then representative samples were collected and evaluated in the laboratory by the means of these two non-destructive techniques. Quantitative analysis of all samples was performed. The surface roughness parameter Rq at a specific length scale was estimated by the use of the LP scanning approach. Furthermore, 3D micro-topography plots from the laser scans were attained. PT, through the formation of temperature—time plots that display the intensity of pixels as a function of time on the obtained thermal images, was able to distinguish the influence of the applied roughness treatments. Results indicate that these two non-contact and non-destructive techniques can be used for the assessment of surface roughness.
Article
Full-text available
We have measured the surface topography and calculated the surface roughness power spectrum for an asphalt road surface. For the same surface we have measured the friction for a tire tread compound for velocities 10(-6) m s(-1) < v < 10(-3) m s(-1) at three different temperatures (at -8 °C, 20 °C and 48 °C). The friction data was shifted using the bulk viscoelasticity shift factor a(T) to form a master curve. We have measured the effective rubber viscoelastic modulus at large strain and calculated the rubber friction coefficient (and contact area) during stationary sliding and compared it to the measured friction coefficient. We find that for the low velocities and for the relatively smooth road surface we consider, the contribution to friction from the area of real contact is very important, and we interpret this contribution as being due to shearing of a very thin confined rubber smear film.
Article
Full-text available
A new technique for the determination of the thermal diffusivity of a tyre compound is proposed. The diffusivity is defined as the ratio between the thermal conductivity and the product of the specific heat and density. This technique is based on infrared measurement and successive analysis of the tyre cooling. Tyre samples were heated up by a laser at constant power rate and the heating and the next cooling of the tyres were registered versus time by mean of thermocouples and infrared cameras. Determination of the thermal diffusivity was thus estimated by mean of home-made model. The research activity was carried out in the laboratories of the department of Mechanics and Energetics of the University of Naples Federico II, in cooperation with the Combustion Institute of the CNR in Naples.
Article
Full-text available
A new analytical–physical tyre model for which the paternity has to be ascribed to Professor Giuseppe Capone was developed at the Department of Mechanical Engineering for Energetics at Naples University ‘Federico II’ with the support of the Bridgestone Technical Centre Europe. The whole model allows to obtain the road–tyre interactions so it can be used in vehicle dynamic simulations. The model has been named Ph.An.Ty.M.H.A., acronym of ‘PHysical ANalytical TYre Model for Handling Analysis’ and it includes the normal, longitudinal and lateral tyre–road interaction. Considering that Ph.An.Ty.M.H.A. is an analytical ‘deductive’ model, it is necessary to develop it starting just from the normal interaction, described in this paper, and then the other ones will be described in future papers. In fact, the normal interaction, i.e. the relationship between the normal load and the normal deflection, influences the tangential (longitudinal plus lateral) one, which determines the vehicle handling behaviour. The parameters used in this model are physical and geometrical so they can be measured on the real tyre. This property allows to better understand the tyre–road interaction mechanism. The tyre behaviour is modelled by analytical expressions based on equilibrium conditions and geometrical relations. To reproduce the experimental normal interaction and the pressure distribution, once the tyre geometrical quantities are known, it is necessary to identify some parameters, related to the tyre structure, by a comparison with the experimental data. Moreover, the predictive ability of the whole model, combined with a vehicle model, is very careful in analysing the vehicle handling [J.C. Dixon, Tyres, Suspensions and Handling, Cambridge University Press, Cambridge, 1991].
Article
Scitation is the online home of leading journals and conference proceedings from AIP Publishing and AIP Member Societies
Article
This paper deals with the frictional behaviour of a tyre tread elementary volume in sliding contact with road asperities. Friction is supposed as composed by two main components: adhesion and deforming hysteresis. The target, fixed in collaboration with a motorsport racing team and with a tyre manufacturing company, is to provide an estimation of local grip for on-line analyses and real time simulations and to evaluate and predict adhesive and hysteretic frictional contributions arising at the interface between tyre tread and road. A way to approximate asperities, based on rugosimetric analyses on macro and micro scale, has been introduced. The adhesive component of friction has been estimated by means of a new approach based on two different models found in literature, whose parameters have been identified thanks to a wide experimental campaign previously carried out. The hysteretic component of friction has been estimated by means of an energy balance taking into account rubber viscoelastic behaviour, characterized by means of proper DMA tests, and internal stress / strain distribution due to indentation with road. Model results are finally shown and discussed and the validation experimental procedure is described. The correct reproduction of friction phenomenology and the model prediction capabilities are highlighted making particular reference to grip variability due to changes in working conditions.
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.
Article
A theory of the adhesional friction of rubber is developed by considering adhesion as a time-dependent process in which a tangential force helps to overcome an energy barrier of the work of adhesion. The frictional phenomenon, as a consequence of such adhesion, would arise primarily from the deformation of the rubber aggregates in contact with a smooth, hard surface constituting the “top layer”. The existence and importance of such a highly-deformed layer has been shown by Schallamach1 in his studies on surface conditions. The true area of contact is considered to increase with time of adhesion as is generally observed in quasi-static behaviour of viscoelastic materials. The deformational characteristics describing the time temperature dependence of mechanical properties would then be reflected in the frictional behaviour. A simple phenomenological approach is taken here instead of a complicated one with the theory of rate processes applied to basic molecular activity. The variation of the frictional force with viscoelastic properties is in fair agreement with the experimentally-obtained results of Grosch2. The static coefficient of friction equals the dynamic coefficient at extremely low speeds. The analysis is confined to steady-state conditions and the influence of frictional heating is considered negligible.
Article
We analyze the periodic contact between an elastic half-space and two types of rough substrates: (i) a perfect isotropically rough rigid substrate (2D isotropic roughness), and (ii) a perfect anisotropically rough rigid substrate, i.e. a substrate with roughness in only one direction (1D roughness). The analysis is carried out with the aid of proprietary codes, that we have developed (both in real and Fourier space) to deal with this type of contacts. Of course, 1D contacts differ from 2D isotropic contacts. However, our results and theoretical arguments suggest a possible criterion to make 2D contacts equivalent to 1D ones from the point of view of contact area and separation calculations. The rule consists in replacing the 2D power spectral density (PSD) of the isotropic surface into an equivalent 1D PSD. Interestingly the transformation rule does not depend on the statistical properties of the surface roughness, hence seems to have a universal character for isotropic surfaces.
Article
The influence of the electron beam modification of a dual-phase filler on the dynamic mechanical properties of styrene-butadiene rubber (SBR) is investigated in the presence and absence of trimethylol propane triacrylate or triethoxysilylpropyltetrasulfide. Electron beam modification of the filler results in reduction of the tan δ at 70°C, a parameter for rolling resistance, and an increase in the tan δ at 0°C, a parameter for wet skid resistance of SBR vulcanizates. These modified fillers give significantly better overall performance in comparison with the control dual-phase filler. This variation in properties is explained in terms of filler parameters such as the filler structure that leads to rubber occlusion and filler networking. These results are further corroborated using the master curves obtained by the time–temperature superposition principle. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 2992–3004, 2003
Article
When rubber slides on a hard, rough substrate, the surface asperities of the substrate exert oscillating forces on the rubber surface leading to energy "dissipation" via the internal friction of the rubber. I present a discussion of how the resulting friction force depends on the nature of the substrate surface roughness and on the sliding velocity. I consider in detail the case when the substrate surface has a self affine fractal structure. I also present a theory for the area of real contact, both for stationary and sliding bodies, with elastic or elastoplastic properties. The theoretical results are in good agreement with experimental observation. (C) 2001 American Institute of Physics.
Article
Summary In order to measure the wall normal stresses of viscoelastic solutions, slit dies have been designed. An advantage of using the slit dies, instead of circular tubes, is that pressure transducers can be mounted flush with solid wall, so that “pressure-hole” errors, if any, can be eliminated completely in the measurements of wall normal stresses. Although the geometry of the slit die is different from that of circular tubes, the flow through a thin slit die can, to a good approximation, be considered as one-dimensional by making the aspect ratio of a slot large enough. The slit dies designed for the present study have aspect ratios of 100, 50, 30, and 20. Three pressure transducers were flush-mounted on the long side of the rectangular slot along the longitudinal center line of the die, and measurements of wall normal stresses were made with aqueous solutions of polyacrylamide (ET 597) of various concentrations. Then, exit pressures were determined by extrapolating the straight line portion of the axial pressure distributions to the duct exit. It has been found that the exit pressure increases with solution concentration at a fixed shear rate, and it also increases with shear rate of a given concentration of solution. The exit pressure measurements were then used to completely determine the primary normal stress difference, by using the measurements of axial normal stresses reported in part I of this series.
Histoire de l'Academie Royale del Sciences avec les Mémories de Mathematique et de Physique
  • G Amontons
Amontons, G., Histoire de l'Academie Royale del Sciences avec les Mémories de Mathematique et de Physique, Académie Royale des Sciences, Paris, 1699.
The Adhesion of Solids in the Structure and Properties of Solid Surfaces
  • F P Bowden
  • D Tabor
Bowden, F. P. and Tabor, D., The Adhesion of Solids in the Structure and Properties of Solid Surfaces, The University of Chicago Press, Chicago, 1953.
Unified Theory of Rubber and Tire Friction
  • H W Kummer
Kummer, H. W., ''Unified Theory of Rubber and Tire Friction,'' Engineering Research Bulletin B-94, Pennsylvania State University, State College, PA,1966.
Ride Comfort Simulations and Steps towards Life Time Calculations: RMOD-K and ADAMS
  • Ch Oertel
  • A Fandre
Oertel, Ch. and Fandre, A., ''Ride Comfort Simulations and Steps towards Life Time Calculations: RMOD-K and ADAMS,'' Proceedings of the International ADAMS Users Conference, Berlin, Germany, 1999.
45-01/tist-45-01-01/layouts/tist-45-01-01Theory of Rubber Friction and Contact Mechanics
//titan/Production/t/tist/live_jobs/tist-45/tist-45-01/tist-45-01-01/layouts/tist-45-01-01.3d Š 1 March 2017 Š 6:27 pm Š Allen Press, Inc. Page 23 FARRONI ET AL. ON DEPENDENCE OF RUBBER FRICTION ON PHYSICAL FACTORS [16] Persson, B. N. J., ''Theory of Rubber Friction and Contact Mechanics,'' Journal of Chemical Physics, Vol. 115, 2001, p. 3840.
Mémoires de mathématiques et de physique présentésà l'Académie royale des sciences par divers savants, et lus sans ses assemblées
  • C A Coulomb
Coulomb, C. A., ''Sur une application des règles de maximis et minimisà quelques problèmes de statique relatifsà l'Architecture,'' Mémoires de mathématiques et de physique présentésà l'Académie royale des sciences par divers savants, et lus sans ses assemblées, Vol. 7, 1733, pp. 343-382.