Lubrication, hydrodynamic

The most important engineering application of laminar flow at low Reynolds Number is hydrodynamic lubrication that is discussed next. Other applications, such as flow in capillaries of small diameter, are less important in engineering, and therefore, consideration of this type of flow is postponed to the end of this chapter. 

Bearing surfaces of one type or another restrain the motion of a part relative to that of its neighbor in practically every mechanism. The journal bearing (Fig. 5.11) is commonly used to support a rotating shaft against a radial force, and was first analyzed by Reynolds in 1886. 

In the design of a journal bearing, the minimum film thickness (h) is of major interest since the load capacity of the bearing is the value of W corresponding to the minimum allowable value of (/z). Quantities to be considered in performing a dimensional analysis for (/z) are listed in Table 5.4. Quantities to be considered in performing a dimensional analysis for (/) are listed in Table 5.5. 

The last nondimensional quantity [p(Ne)yP] is a Reynolds Number. When R is evaluated for practical bearings, it is found to be small compared with imity. This suggests that inertia effects will be negligible compared with viscous effects, and that p need not have been included in the dimensional analysis. This is verified by experiment. Thus, Eq. (5.8) may be written  

It is further found that i has a small influence on /z as long as Hd is greater than one, which is usually the case. Thus He may be omitted from Eq. (5.9). Also, die and pNIP may be combined into one nondimensional group as follows  

Depending on the thickness of the lubricating layer, we distinguish between two different lubrication regimes. In hydrodynamic lubrication the lubrication layer is thicker than the maximum height of the surface asperities resulting in a complete separation of the friction partners. In boundary lubrication the lubrication layer is typically only a few molecular layers thick and therefore thinner than the surface roughness. In many practical applications we are between the two extremes, which is referred to as mixed lubrication. 

Since in hydrodynamic lubrication the friction force is completely determined by the viscous friction of the lubricant, the coefficient of friction can be calculated from hydrodynamics using the Navier-Stokes equations. This had already been done in 1886 when Reynolds published his classical theory of hydrodynamic lubrication [494], The friction force Fp between two parallel plates of area A separated by the distance d is given by  

For a fixed geometry, the friction force depends solely on the viscosity of the lubricant. We could try to decrease the viscosity of the lubricant to reduce friction. There is, however, a limit to this The lubrication film thickness must always be kept higher than the surfaces asperities. Otherwise the surfaces will come into direct contact, resulting in much higher friction. Therefore, it is common to use an oil with a viscosity that is just high enough to maintain a continuous lubrication layer. 

In practical applications, the increase of viscous friction with speed is often lower than expected from Eq. (11.9). The explanation is that friction leads to an increased temperature of the lubricant which reduces the viscosity. For most lubricants the temperature dependence of the viscosity is given by 

Ea is the effective activation energy. This leads to an inherent stability of hydrodynamic lubrication, as a thinning of the lubricant at higher temperatures reduces the friction and therefore avoids further heating. 

In such a system, the coefficient of friction depends on the fluid dynamics, in particular on the viscosity r of the lubricant. For this reason, hydrodynamic lubrication is also called fluid lubrication. A well-known example of hydrodynamic lubrication is the effect of aquaplaning. When a car is driven at high speed on a wet road, the water forced between the surfaces of the tires cannot escape and separates the car from the road traction is lost. The build-up of the lubrication film either can be solely due to the relative movement of the bearing surfaces or can be achieved by active pumping of the lubricant (for a textbook, see Ref [954]) 

For typical lubrication situations with a density of the lubricant of p = 10 kg m , a sliding velocity Vo = Im s, a viscosity of the lubricant of t) = 1 Pa s, and a gap width ho = 10 [xm, we obtain a Reynolds number Re = pvoL/r] 0.01 (Eq. (6.42)). This means, we can safely assume laminar flow. For constant Vq also, the explicit time dependence vanishes, d /dX k, 0, and we have creeping flow. If we exclude a side leakage in y-direction and due to symmetry we can assume that Vy = 0. In addition, the flow velocity of lubricant in z-direction is negligible. As a result, the Navier-Stokes equation for creeping flow (Eq. (6.10)) reduces to 

The second equation tells us that P is only a function of x. The change of the flow velocity in z-direction is much stronger than thechange of flow velocity inx-direction. Thus, (P-v jdyP d Vxjdz and the first equation simplifies to 

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Sihcone oils are good hydrodynamic lubricants but have generally poor frictional lubricating properties (352—354). The latter can be improved by incorporating chlorophenyl groups into the polymer side chains (355). For steel on steel, the coefficient of friction is about 0.3—0.5. The load-bearing capacity of PDMS (Almen-Wieland machine) is only 50—150 kg, compared with - 1000 kg for polychlorophenyLmethylsiloxane and up to 2000 kg for mineral oil. 

Boundary Lubrication as a Limiting State of Hydrodynamic Lubrication... 

Unlike traditional textbooks of tribology, in this book we regard boundary lubrication as a limit state of hydrodynamic lubrication when film thickness is down to molecular dimension and independent of the velocity of relative motion. The discussions are based on the existing results, some from literatures but mostly from the authors own work. The topics are mainly focused on the mechanical properties of boundary films, including rheology transitions, molecular ordering, and shear responses. Ordered molecule films, such as L-B films and SAM, are discussed, with emphasis on the frictional performance, energy dissipation and the effects from structural features. Boundary films can be modeled either as a confined substance, or an adsorbed/reacted layer on the... 

Patir, N. and Cheng, H. S., "Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication, ASME J. Lubr. Technol., Vol. lOO.No. 1,1978,pp. 12-17. 

Christensen, H., "Stochastic Models for Hydrodynamic Lubrication of Rough Surfaces, Proc. Inst. Mech. Eng., PartJ J. Eng. Tribol.,Wo. 184,1969-70,p. 1013. 

Christensen, H. and Tender, K., The Hydrodynamic Lubrication of Rough Journal Bearings, Journal of Lubrication Technology, Trans. ASME Series F, 01. 95,1973,p. 324. 

Chang, L., Deterministic Model for Line-Contact Partial Elasto-Hydrodynamic Lubrication, Tribal. Int., Vol. 28, No. 2,1995,pp. 75-84. 

Practically, aU data of friction measurements on wet tracks in the speed range of hydrodynamic lubrication exist as tire skid measurements. Figure 26.10 shows the results of a braking test on wet, finely structured concrete using a smooth tire and measuring the friction coefficient as function of... 

Hydropolymer gel has been considered as a possible candidate for an artificial articular cartilage in artificial joints because it exhibits very low friction when it is in contact with a solid. The origin of such low friction is considered to be associated with the water absorbed in the gel [83-86], some of which is squeezed out from the gel under the load and serves as a lubricant layer between the gel and solid surface, resulting in hydrodynamic lubrication [87, 88]. Although the structural information about the interfacial water is important to understand the role of water for the low frictional properties of hydrogel in contact with a solid and the molecular structure of lubricants other than water at solid/solid interfaces have been investigated theoretically [89-91] and experimentally [92-98], no experimental investigations on water structure at gel/solid interfaces have been carried out due to the lack of an effective experimental technique. 

Hydrodynamic injection, capillary electrophoresis, 4 633-634 Hydrodynamic lubrication regime, 15 210-211... 

Figure 12 illustrates the effect of D on the measured friction of a system similar to that shown in the inset of Figure 6. At large separations, the behavior is reminiscent of hydrodynamic lubrication i.e., the damping coefficient Yrheo = F/Av is approximately inversely proportional to D, and yrheo is relatively independent of the orientation of the surfaces. As D is decreased, the...

Publication gravure printing inks apparently show elastic behavior at D = 105 s the modulus of shearing G is 103 Pa. This indicates that at high shear rates D, between 105 and 106 s gravure printing inks develop normal stress effects and thus show a hydrodynamic lubricating effect. These deductions are relevant to an... 

Bhushan et al. [9] independently confirmed the lack of polishing activity due to hydrodynamic lubrication. The depth of the wafer carrier in CMP was adjusted so that samples either projected above the surface of the carrier (the normal case), were essentially coplanar with the carrier, or were recessed below the plane of the carrier. This produced wafer-pad lubrication film thicknesses of controlled dimension. For the case of a wafer recess of 75 um ( 3 X the lubrication film thickness reported in Ref. [7]), removal rate was negligibly small. 

The oxidation of olefins can result in the formation of organic hydroperoxides. These compounds readily decompose to form alcohols, carbonyl compounds, and other oxidized species. These oxidized hydrocarbons can further react to form highly cross-linked, oxygen-rich materials. Some of these species can adhere to metal surfaces to form a hard vamishlike film or coating on metal parts. This varnish can act as a site for further deposition and eventual corrosion of metal. In severe cases, varnish can interfere with the hydrodynamic lubrication of moving metal parts and efficiency of component operation. 

Diesel fuel prevents wear of high-pressure fuel pumping and injection equipment parts. If the viscosity of diesel fuel is low, its ability to form a hydrodynamic lubricating film between moving metal parts diminishes. The term lubricity is used to describe the wear-inhibiting capability of distillate fuels. 

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