A Thermal Hydrodynamic Lubrication Analysis for Entrained Film Thickness in Cold Strip Rolling

1990 ◽  
Vol 112 (1) ◽  
pp. 128-134 ◽  
Author(s):  
K. Yuan ◽  
B. C. Chern
Keyword(s):  
Film Thickness ◽  
Reynolds Equation ◽  
Hydrodynamic Lubrication ◽  
Equation Model ◽  
Temperature Dependent ◽  
Strip Rolling ◽  
Temperature Dependent Viscosity ◽  
Approximate Models ◽  
Dependent Viscosity ◽  
Cold Strip Rolling

A thermal hydrodynamic lubrication analysis which takes account of temperature-dependent viscosity variation along as well as across the film thickness is developed for the entrained film thickness in cold strip rolling using generalized Reynolds equation (Dowson, 1962). The results are compared with that of the two approximate models (i.e., the effective viscosity model and thermal Reynolds equation model) being widely used in metal forming lubrication literature. It is found that neither of the two approximate models is more accurate than the other and that neither can deal with the effect of surface temperature difference of the roll and strip adequately.

Hydrodynamic Model for Cold Strip Rolling

1967 ◽  
Vol 182 (1) ◽  
pp. 153-162 ◽  
Author(s):  
D. S. Bedi ◽  
M. J. Hillier
Keyword(s):  
Friction Coefficient ◽  
Film Thickness ◽  
Entropy Production ◽  
Coefficient Of Friction ◽  
Hydrodynamic Model ◽  
Reynolds Equation ◽  
Viscous Friction ◽  
Strip Rolling ◽  
Roll Pressure ◽  
Cold Strip Rolling

The theory of rolling is modified to allow calculation of a hydrodynamic film thickness and viscous friction coefficient using Reynolds equation for the lubricant. Calculations are made for the case where the fluid film covers the arc of contact. The film thickness is assumed uniform and is determined by the principle of minimum rate of entropy production. It is shown that the apparent coefficient of friction varies significantly over the arc of contact. At small reductions the roll load tends to decrease with speed of rolling, while at high reductions the load tends to increase. The point of maximum roll pressure does not coincide with the neutral plane; and under certain rolling conditions there may be no maximum in the pressure over the arc of contact.

scholarly journals Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Boundary ◽  
Galerkin Approximation ◽  
Large Data ◽  
Temperature Dependent ◽  
Weak Formulation ◽  
Temperature Dependent Viscosity ◽  
Pipeline Network ◽  
Flux Boundary Conditions ◽  
Creeping Flows ◽  
Dependent Viscosity

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

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