2.1 Wet-Pavement Skid Resistance
2.1.2 Classical Theories on Tire-Pavement Friction
The skid resistance phenomenon on wet pavement surfaces is so complex that to date its mechanisms are still not totally understood. It involves the combined effects of rubber friction, lubrication theory, fluid dynamics and tire mechanics. The
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classical tire-pavement friction theory may be a starting point for research in pavement skid resistance performance. Research on friction can be traced back to the 15th century, when Leonardo da Vinci developed the basic laws of friction and introduced the concept of the coefficient of friction (Leonardo and MacCurdy, 1948).
Amontons (1699) and Coulomb (1785) later contributed to the five classical laws of friction, most of which are now found to be limitative (Moore, 1975). Equation (2.1) presents a friction theory proposed by Coulomb (1785) considering the works of Amontons (1699) and Desguliers (1734).
N A
F (2.1)
where F is the friction force, A represents the component attributed to the adhesive or cohesive effect, and μN refers to the deformation effect. This relationship cannot explain the low friction on lubricated surfaces, and suffers from the variations of parameters with speed and contact pressure. However, it forms the basis of modern contact mechanism modelling.
2.1.2.1 Theories on Rubber Friction
Friction mechanisms turn out to be much more complicated if rubber is involved. The classical laws of friction does not work on elastomers and the coefficient of friction becomes a variable depending on the real contact area, normal load and velocity (Brown, 1996). The study on the relaxation of polymers by Williams et al. (1955) was useful in presenting friction data at different temperatures and speeds. Gough (1958) described the general characteristics of rubber friction and illustrated the variation of frictional force with sliding velocity. The coefficient of friction was found to peak at a certain velocity.
The adhesion and hysteresis effects were the first two components in rubber friction proposed and are based on Coulomb's laws (Moore and Geyer, 1972; 1974).
It was assumed that the measured friction force F consists of an adhesion force Fadh
and a hysteresis force Fhys when a rubber block slides on a rough surface under a
15 uniform loading (Tabor, 1959). As shown in Equation (2.2) and (2.3), adhesion force can be expressed as the product of shear strength and actual contact area, while hysteresis force is related to energy losses within the deformed rubber (Moore, 1966).
p s A f A
n
adh (2.2)
bp A f QD
n
hys (2.3)
where fadh is the adhesion coefficient = L Fadh
, A is the actual contact area, An is the nominal area, s is the interface shear strength, p is the pressure on rubber block, L is the normal load, fhys is the hysteresis coefficient =
L Fhys
, Q is the volume of rubber participating in the deformation, D is the energy dissipated per unit volume of rubber due to damping, and b is the rubber sliding distance.
The formulation of rubber friction was refined by Veith (1986), taking wear component Fwear into consideration to express the total friction force as:
wear hys
adh F F
F
F (2.4)
The adhesion component is usually dominant on smooth surfaces, while the hysteresis term normally governs friction on rough or lubricated surfaces. The wear term depends on the texture and hardness of contacting surfaces. It should be noted that all the three components are affected by the condition of interface, including the actual contact area and the presence of lubricants.
Adhesion Effect
The adhesion effect of skid resistance refers to the shear force developed at the tire-pavement interface when a tire is conformed to the shape of its contact area (Choubane et al., 2003). There exists an adhesion bonding of surface atoms between sliding members, and energy is needed to break this bonding. The dissipation of this energy presents difficulties in the development of adhesion theory for rubber (Veith,
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1986). Molecular theory and macroscopic theory are two main categories of adhesion theories (Moore and Geyer, 1972). The former typically takes the van der Waals force as the adhesion between rubber and solid, where a maximum coefficient of friction could be explained by the Eyring rate theory (Bowden and Tabor, 1964). The latter is based on phenomenological theory, assuming rubber is adhered to solid with a number of bonds in each domain, with each bond being able to sustain a finite small force (Savkoor, 1965).
It was indicated in past pavement research that the adhesion component of skid resistance is governed by pavement microtexture (Jayawickrama and Graham, 1995). Microtexture ensures physical penetration of the thin squeeze film at interface and a better tire draping effect at low vehicle speed, so that a good adhesion could develop (Moore, 1969; 1972). Previous studies also showed that the presence of water at the contact interface would reduce the adhesion effect significantly (Persson, 1998). If the surface is completely lubricated, the adhesion component may even disappear (Highway Research Board, 1972). Therefore, appropriate surface drainage provided by pavement macrotexture is also important in maintaining adhesion effect.
Hysteresis Effect
Hysteresis is the resistance due to rubber deformation when energy losses occur in rubber which is subjected to cyclic stress variation. It is a characteristic feature of visco-elastic material when "flowing" over an uneven rigid surface and conforming to the surface contours. Hysteresis theories could be classified into three types: elastic and visco-elastic theories, single and multiple element models and force and energy concepts (Moore and Geyer, 1974). Greenwood and Tabor (1958) applied elastic theory to the concepts of hysteresis and conjectured that a small fraction of input elastic energy from the deformation of elastomers must be dissipated in the form of hysteric friction. Kummer (1966) and Hegmon (1969) proposed a unified theory of friction and a relaxation theory of hysteresis respectively, based on either
17 semi-empirical analogy or energy concept. It is noted that skid resistance obtained from these works are extremely insensitive to speed, especially at lower sliding speeds. The theory developed by Yandell (1971), using a complex network of spring and dashpot elements, permitted large deformations and any value of Poisson's ratio, rigidity and damping factor. The contribution of hysteric effect due to microtexture and macrotexture can be identified by the superposition principle.
Although Yandell (1971) indicated that both microtexture and macrotexture affects hysteresis friction, it is generally believed that its magnitude is determined by the pavement macrotexture (Jayawickrama and Graham, 1995). The contribution of hysteresis to the total pavement friction is usually small. However, its contribution may become significant when pavement is slippery, due to either lubrication, round microtexture or high speed (Schulze and Beckman, 1965; Highway Research Board, 1972). It was also found that when a tire starts to skid, the adhesion component begins to decrease and the share of hysteresis effect increases relatively (Choubane et al., 2003).
Wear Effect
The wear component of friction results from the work being done to make material loss from one or both surfaces of the sliding pair (Veith, 1986). Three distinct mechanisms have been identified for rubber wear (Moore, 1972): (a) abrasive wear - abrasion and tearing of sliding elastomers caused by sharp texture on base surface; (b) fatigue wear - the failure of elastomers surface under cyclic strain and stress from the repeated deformation on blunt but rough base surface; (c) roll formation - the tearing of rolled fragment when highly elastic materials slide on smooth surfaces. The fatigue wear is relatively less severe than the other two, although all the three forms of wear generally co-exist simultaneously.
The extent of passenger car tire wear was measured on a series of pavements in Transportation and Road Research Laboratory (Lowne, 1970). It was concluded
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that microtexture is the governing pavement surface characteristic for tire wear, while macrotexture plays a secondary role. Wear rate increases with an increase in speed or temperature, and is especially high when rubber melting occurs. Wear rate decreases when the amount of water at the interface grows, which was thought by Stachowiak and Batchelor (2005) to be the consequence of hydrodynamic lubricating effect.
2.1.2.2 Lubrication at Contact Interface
Most modern pavement surfaces can provide sufficient skid resistance when they are dry. However, frictional performance decreases dramatically during wet weather, especially when the vehicle is traveling at high travel speeds (Wu and Nagi, 1995). Water film acts as a lubricant between tire and pavement surface and affects skid resistance. This phenomenon can be explained by lubrication theories. The modern lubrication theories were developed from Reynolds' hydrodynamic theory of lubrication for incompressible fluid (Reynolds, 1886). There are two basic methods to derive Reynolds' theory. One is to use the continuity and Navier-Stokes equations, and the other is to apply the principles of mass conservation and the laws of viscous flow (Pinkus and Sterlicht, 1961; Cameron, 1976; Gross et al., 1980; Hamrock, 1994).
There are no general closed-form solutions for these equations and typically, numerical methods are required (Bhushan, 2002).
The generalized Reynolds' equation consists of three components, namely the wedge term, the stretch term and the squeeze film term. The wedge term is the most significant of these three due to the film thickness variations and the possibilities of absence of the other two terms (Moore, 1975). Hydrodynamic lubrication, subjected to the surface roughness, contributes to four different forms of load supports, namely directional effect, macro-elasto-hydrodynamic effect, cavitation effect and viscosity effect. If the deformation of surrounding solids has a significant influence on the development process of hydrodynamic lubrication, elasto-hydrodynamic lubrication is said to occur. In this situation, two additional effects should be accounted for in the
19 classical theory, namely the influence of high pressure on the viscosity of fluid and the substantial local deformation of fluid geometry. Iterative procedure (see Figure 2.1) is often used in the study of elasto-hydrodynamic problems.
In a simple tire traction model developed by Veith (1983), three types of lubricated friction modes were proposed, namely boundary layer lubrication, elasto- hydrodynamic lubrication and mixed lubrication. Boundary layer lubrication mode occurs at low velocity, when tire and pavement are in relatively intimate contact with a molecular thick water film between them. Elasto-hydrodynamic lubrication occurs at high velocity, when an elastic indentation of the tire tread develops due to water accumulating at the leading edge of contact interface and an upward hydrodynamic pressure is generated. Mixed lubrication mode occurs at intermediate velocity. It is a transition between the previous two situations. A part of contact interface (usually the front part) is in the state of elasto-hydrodynamic lubrication while the other part is in boundary lubrication mode. Mixed lubrication mode is the most common situation in practice and it is closely related to the three-zone model discussed below.
2.1.2.3 Three-Zone Model
In order to describe the wet friction phenomenon in tire-pavement interaction, a three-zone model was proposed by Gough (1959) for a lock-wheel skidding on wet pavements. This model was further developed by Moore (1966) for a rolling wheel.
The concepts of three-zone model are demonstrated in Figure 2.2.
Zone A: Squeeze-Film Zone
When a vehicle is traveling at a relatively high speed on a pavement surface covered by a thick water film, the front of tire contact area would be deformed by a water wedge. This situation corresponds to the elasto-hydrodynamic lubrication mode.
The friction force developed at this zone is mainly determined from the bulk properties of lubricant, such as the viscosity and velocity gradient of water. If the
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hydrodynamic uplift force grows to be the same as the vertical load, hydroplaning is said to have occurred (Browne, 1975).
Zone B: Transition Zone
It is also known as draping zone, as it begins when tire elements start to drape over the major asperities of pavement surface and still make contact with some minor asperities. Mixed lubrication mode exists in this zone, and it is a transition between Zone A and Zone C. Partial hydroplaning may still happen, even though the vehicle speed is not as high as that in total hydroplaning (Balmer and Gallaway, 1983).
Zone C: Traction Zone
This region is usually at the tail end of contact interface, where tire elements can attain an equilibrium position on pavement surface after draping. Boundary layer lubrication dominates in this situation, providing a well-developed friction capability by an intimate contact between tire tread and pavement surface. Both properties of contacting solids and characteristics of lubricant are important for the friction force development in this zone.
At a very low speed, only Zone C exists on a wet pavement and it governs the skid resistance performance. With an increase in vehicle speed, the areas of Zone A and Zone B get larger while that of Zone C is reduced. Upon hydroplaning, there is no contact, i.e. Zone C has completely disappeared.