Research And Simulation of The Sheet Leveling Machine Manufacturing Capabilities

One of the main tasks to determine the technological settings of the sheet leveling machine (leveler) is to identify the maximum roll overlap. In the well-known works on the study of sheet metal-roll leveling, the overlaps are set on the basis of experimental data, that is applicable for the leveling sheets from material with the 800 MPa yield strength. But for materials with a higher yield strength additional research is required. The purpose of this work is to establish criteria affecting the maximum allowable overlap for the working rolls by the leveler and to determine the dependencies for the most rational working rolls adjustment. When solving the set tasks, developed by the authors, a numerical analytical mathematical model of the leveling process was used as an objective function, that allows to determine the energy-power characteristics and the sheet curvature after leveling, depending on the individual settings of the leveler rolls. Within the framework of studies, an algorithm of a mathematical model was developed that allows to determine the leveler technological settings necessary for correcting the longitudinal curvature and comes down to determining the aligning coordinates for each of the movable rolls depending on the known characteristics of the metal being processed, the leveler geometric parameters, and the permissible value of the sheet residual curvature after leveling. In consequence of studying the influence of the working rolls setup on the sheet metal-roll quality during leveling on a multi-roll leveling machine, the laws for the rational rolls positioning were established. The linear and sinusoidal laws were identified as optimal ones. Boundary factors were also established as affecting the maximum overlap of the rolls. These factors included the condition of the pickup and the condition of the rolls strength. Using the example of implementing the developed finite element model of the sheet leveling process at the leveler of NKMZ (Ukraine), it was found that the pickup condition has a dominant influence when leveling sheets with a thickness of less than 6 mm, and with larger thicknesses the condition of the rolls strength is prevailing. With a decrease in the yield strength of the material or the width of the sheets, this ratio will be redistributed towards the pickup condition.

Corotating or Codeforming Models for Thermoforming: Free Forming

Our previous work [J Pol Eng, 32, 245 (2012)] explores the role of viscoelasticity for the simplest relevant problem in thermoforming, the manufacture of cones. In this previous work, we use a differential model employing the corotational derivative [the corotational Maxwell model (CM)] for which we find an analytical solution for the sheet deformation as a function of time. This previous work also identifies the ordinary nonlinear differential equation corresponding to the upper convected Maxwell model (UCM), for which she finds no analytical solution. In this paper, we explore the role of convected derivative by solving this UCM equation numerically by finite difference. We extend the previous work to include sag by incorporating a finite initial sheet curvature. We treat free forming step in thermoforming and find that the convected derivative makes the free forming time unreasonably sensitive to the initial curvature. Whereas, for the CM model, we get a free forming time that is independent of initial sheet curvature, so long as the sheet is nearly flat to begin with. We cast our results into dimensionless plots of thermoforming times versus disk radius of curvature.