Lubrication in cold rolling: Numerical simulation using multigrid techniques

In the cold rolling process a lubricant is applied on the rolls and/or the strip mate­rial. Due to the velocities of the rolls and the strip, part of the lubricant is sheared into the contact causing, amongst others, a reduction of the friction. In this thesis a physical-mathematical model is described which makes it possible to predict the quantity of lubricant between roll and strip. From this, a number of statements can be made relating to the friction between the roll and the strip. After a short description of the process, an overview is presented of previous re­ search in this field. The literature reveals that the amount of lubricant between the roll and the strip is not sufficient to neglect asperity interaction : the lubrication mechanism is of the mixed type. Furthermore, the literature reveals that, despite enormous progress in this field, the available models can certainly be improved. In the present work the complexity of the problem is initially reduced by assuming the surfaces of the strip and the roll to be perfectly smooth (the so called "smooth sur­ face problem"). For this simplified problem equations have been derived describing the lubricant flow, the deformation of the strip and the deformation of the rolls. Solving the equations analytically is impossible. Consequently, a numerical ap­proach is required. In order to allow for the simulation of surface roughness at a later stage, a dense grid must be applied. By using conventional techniques, computing time will be very long when applying such a fine grid. In order to avoid this problem so-called "Multi-grid techniques" have been used. These techniques are extensively described in this thesis. Next, the application of these techniques to the governing equations describing lubrication in cold rolling is described. In the second part of this thesis a number of simulations have been performed using both steel and aluminium. These simulations resulted, despite the simplifications, in interesting insights with respect to lubrication in cold rolling. The lubricant film thicknesses calculated using the present model results in values which are much larger than those found so far. A deviation up to some 500 % may occur. In the last part of this thesis surface roughness aspects are described and implemented in the model. The thesis is concluded with recommendations for further research