Manual High Pressure Rheology for Quantitative Elastohydrodynamics (Tribology and Interface Engineering)

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Above a critical value of S the hydrodynamic regime with thin film is established and the surfaces are completely separated by a continuous and uniform film. At high speeds, and high S values, a hydrodynamic regime with thick film is established and the viscous shearing is increased. The pressurized lubricant film modifies strip surface roughness. Wilson and Mizuno and Hasegawa have shown that in strip compression tests the establishment of a hydrodynamic regime modifies the surface texture of the deformed material by two mechanisms. With low viscosity lubricants this texture modification is due to the differential deformation of individual crystalline grains.

This mechanism is more easily observed during formation of quasi-isotropic materials with coarse grains, like in cold rolling of hot rolled strips.

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With more viscous lubricants the texture modification is due to the indentation caused by the pressurized film, associated to the differential deformation of the grains. In this case, the modification is more pronounced than in the first mechanism, and the mean roughness Ra can be related to the film thickness in the work zone h 1 , as follows: In that region the strip becomes rigid again. The film thickness is slightly reduced and the pressure in the film drops to the ambient pressure. The passage from the work zone to the exit zone occurs at a position x 2 anterior to the line that links the centers of the rolls CL.

Equation 3 presented by Reynolds Cameron, for the tridimensional case is obtained if assumed that: Considering these hypotheses, Eq. Considering that axis x is opposite to the rolling direction in the inlet zone, Eq. When the lubricant flows under high pressures and temperatures, dynamic viscosity can be considered as of both variables Bair and McCabe, and assumed as shown in Eq.

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With a first approximation to simplify the calculus of h 1 , it was assumed that the viscosity in the entrance zone is dependent only on the pressure variation. This is a suspicious assumption since the heat generation by viscous shearing in that zone could not be negligible Dow et al. With this assumption, Eq. At the entrance of the work zone, strip becomes plastic and pressure equals to the yield stress of the strip material. Boundary conditions for Eq. With h 1 it can be written Eq. The boundary conditions that will be applied to Eq.

In the work zone the expression that relates the pressure with the film thickness, as a function of the position along this region, is determined by the slab method, first defined by Sachs. In this work, the work zone is represented as shown in Fig. Equation 17 presents the forces equilibrium in the work zone with backward slip, i.

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In this method the loads acting on one slab are balanced Fig. In this work it was assumed that the strip material presents a hardening behavior expressed by Eq. The boundary conditions necessary to the solution of Eq. Laboratory rolling tests were carried out in a duo-reversible rolling mill with the following characteristics: The material of the workpieces was a commercial aluminum alloy AA with the following properties: Three lubricants were used and their properties are shown in Table 1.

Those lubricants were chosen to analyze the influence of the viscosity on the lubrication regimes. Two area reduction per rolling pass were used, the first equal to Two different speed ranges were tested: These speeds are common in industrial practice to cold rolling of aluminum strips. To analyze how rolling conditions influenced surface texture of the rolled strips, it was measured the mean surface roughness Ra.

The measurements were done in the rolling direction and in the transversal direction, in three zones along the workpiece, each one with three measurements in three regions in a total of 54 measurements per workpiece. A computational program with the equations of this model was written to simulate the rolling tests with the parameters shown in Table 2. Figures 4 and 5 show the variation of the pressure and film thickness in the inlet zone, as a function of the iteration number used to solve the Eq.

It can be observed that the pressure is largely increased near the border inlet zone-work zone, and as a consequence, the lubricant is pressurized and dragged to the work zone forming a continuous film. The film thickness is reduced from the initial thickness some tenths of millimeters to h 1 some thousandths of millimeters. Figure 6 shows the variation of the film thickness in the entrance of the work zone h 1 as a function of lubricant viscosity.


Large values of h 1 are associated to the establishment of a continuous film, stable and thick enough to separate the surfaces, and reduce the friction. As observed in Fig. With speed increase, the viscous drag effect is enhanced and more lubricant is carried to the entrance of the work zone, the viscous shearing is also enhanced with more heat being generated and dissipated in the film, reducing lubricant viscosity and consequently its thickness, unstabilizing and breaking out the film.

With more viscous lubricants, less sensible to viscous shearing and temperature increase, proper lubrication conditions are achieved establishing a thick, uniform and continuous film. It can also be observed as a result of this study that the area reduction does not affect significantly h 1 which is more sensible to variations in lubricant viscosity and rolling speed. Figures 7 and 8 show the variation of pressure and film thickness as function of the position along the work zone x. The aspect of the curves is different in each case. Therefore, it can be concluded that despite the small film thickness observed in Fig.

Figure 8 shows the results with the oil MJF-5 more viscous and at a greater speed. It can be observed a similar pressure profile, but with a less pronounced decrease of the pressure near the entrance of the work zone. This behavior is also explained by the theory of Tselikov, since in this case, as observed in Fig. Thus, associated to a viscous lubricant less sensitive to pressure and temperature variations, a continuous and thick film will be formed and kept along this work zone.

Figures 9 and 10 show experimental results of the surface roughness Ra of rolled products and raw material. It can be observed that surface roughness is reduced as the rolling speed increases, regardless of the area reduction.

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This reduction is more intense when it is analyzed the effect of lubricant viscosity on the roughness. These results are apparently opposite to the theory stated by Wilson , who relates the surface texture to the hydrodynamic lubrication. This conclusion could be explained considering that rolling tests carried out in this work presented a lubrication regime in the transition region between mixed and hydrodynamic lubrication Fig.

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Rolling tests with more viscous lubricants and high speeds should present products with high roughness due to the deformation caused by the indentation of the surface by the viscous pressurized lubricant and by the differential deformation of individual grains in the surface.

The surface texture of the raw material shows grooves parallel to the rolling direction that are characteristic of the previous hot rolling. The analysis involves the simultaneous solution of Reynolds, elasticity and energy equations along with the computation of lubricant properties and surface temperatures. The temperature modified Doolittle-Tait equations are used to calculate viscosity and density as functions of fluid pressure and temperature, while Carreau model is used to describe the lubricant rheology.

The surface roughness is assumed to be sinusoidal and it is present on the nearly stationary surface in near-pure sliding EHL conjunction. The linear P-V oil is found to yield much lower traction coefficients and slightly thicker EHL films as compared to the synthetic oil for a given set of dimensionless speed and load parameters.

Besides, the increase in traction coefficient attributed to surface roughness is much lower for the former case.