Film thickness speed

Dimensionless minimum film thickness-speed parameter... 

The dimensionless groups involved in this isoviscous elastohydrodynamlc analysis are those of dimensionless film thickness, speed and load. They may be written as -... 

The results for different speeds are shown In Figure 11, whilst those for different loads are Illustrated In Figure 12. A least squares fit to these to set of results gave the following relationships between film thickness speed, and load. 

Each roU carries away some of the flow. The ratio of film thickness on the two roUs, t. 1 depends on the speed ratio, and is defined as... 

Fig. 10. Reverse-roU, metered film thickness on the appHcator roU divided by gap, tjG, as a function of the ratio of the metering roU speed, U, to apphcator roU speed, U, for various capillary numbers. (—) represents theoretical values ( ) experimental ones and (------) is the lubrication model (11).

Thin film lubrication (TFL), as the lubrication regime between elastohydrodynamic lubrication (EHL) and boundary lubrication, has been proposed from 1996 [3,4], The lubrication phenomena in such a regime are different from those in elastohydrodynamic lubrication (EHL) in which the film thickness is strongly related to the speed, viscosity of lubricant, etc., and also are different from that in boundary lubrication in which the film thickness is mainly determined by molecular dimension and characteristics of the lubricant molecules. 

If the speed is smaller than that of the failure point, the film thickness will suddenly decrease to a few molecular layers, or it is in boundary lubrication [34]. 

The film thickness varies with the rolling speed as shown in Fig. 4 in which Curve (a) is from the measured data and Curve (b) is the measured value of thickness minus the static film thickness, that is, the thickness of fluid film. The data of Curve (c) are calculated from the Hamrock-Dowson formula [44]. In the higher speed region (above 5 mm/s) of Fig. 4, the film becomes thinner as speed decreases and the speed index 4> is about 0.69 (Fig. 4, Curve b), which is very close to that in Eq (1). When the film thickness is less than 15 nm, the speed... 

Fig. 5—Variation of film thickness with speed for octamethylcy-clotetrasiloxane [56].

Because EHD film thickness is determined by the viscosity of the fluid in the contact inlet [46], it is obvious that the viscosity of OMCTS remains at the bulk value down to approximately 0.1 m/s. However, below this speed the discretization of both central and minimum film thicknesses can be observed. The central film thickness begins to deviate from the theory at about 10 nm and the interval of the discretization is approximately 2 nm. If the molecular diameter of OMCTS that is about 1 nm is taken into account, it corresponds to approximately two molecular layers. 

As shown in Fig. 6 [19], for the lubricant with higher viscosity (kinetic viscosity from 320 mm /s to 1,530 mm /s), the film is thick enough so that a clear EHL phenomenon can be observed, i.e., the relationship between the film thickness and speed is in liner style in the logarithmic coordinates. 

However, for the lubricants with lower viscosity, e.g.. Polyglycol oil 1 and 2 with the kinetic viscosity of 47 mm /s to 145 mm /s in Table 1, the transition from EHL to TFL can be seen at the speed of 8 mm/sand23 mm/s, i.e., the relationship between film thickness and speed becomes much weaker than that in EHL. The transition regime can be explained when the film reduces to several times the thickness of the molecular size, the effect of solid surface forces on the action of molecules becomes so strong that the lubricant molecules become more ordered or solid like. The thickness of such a film is related to the lubricant viscosity or molecular size. 

The shapes of film thickness along A—in Fig. 8 are given in Fig. 9. With the decrease of speed, the curve of film thickness in the central region becomes flat. The thickness of the film in a cross section of the central region is about 24 nm for the mineral oil with a viscosity of 36 mPa-s (20°C). However, for the lubricant with a viscosity of 17.4 mPa s as in Fig. 10, the curve is quite crooked when the average thickness is about 24 nm, and the curve becomes flat at a thickness of about 14 nm. These indicate that the thinner the film is, the flatter the film in the central region will be. The thickness at which the shape of the film curve becomes flat is related to the critical film thickness where EHL transfers to TFL. The thicker the critical film is, the thicker will be the average film at which the film curve turns flat. 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

The cases under the pressure of 297 MPa as shown in Fig. 37(b) are similar to that under 174 MPa, except that the films are a little thinner than that under the latter pressure. Furthermore, when speed is less than 1 mm/s, the film thickness of pure PE under a higher pressure decreases by a larger slope with the rolling speed, and there is little difference in the film thickness of UDP-containing PEs under different loads. 

The concentration of UDP also affects the friction coefficient as shown in Fig. 39. It is discovered that the friction coefficient of pure PEG also decreases gradually and reaches a somewhat reduced value due to a time effect of the film thickness [16,18]. At the speed of 2 mm/s and pressure of 174 GPa, the friction coefficient of pure PEG is the highest. That for PEG + 0.5 % UDP ranks second. Those for PEG + 0.1 % UDP and PEG+ 0.3 %UDP are almost the same and have the lowest friction coefficient among all tested oils. Therefore, there is a good concentration extent of UDP in the basic oil. If the concentration is out of such extent, the effect... 

Fig. 37—Film thickness for different rolling speed [60], Base oil PE Temperature 20°C, Pressure (a) 174 MPa, and (b) 297 MPa.

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