Calendering of Pseudoplastic and Viscoplastic Sheets of Finite Thickness

The lubrication approximation theory (LAT) is used to provide numerical results for calendering sheets with a desired final thickness. The Herschel-Bulkley model of viscoplasticity is used, which reduces with appropriate modifications to the Bingham, the power-law and the Newtonian models. For a desired final sheet thickness, the results give the required thickness of the entering sheet as a function of the dimensionless power-law index (in the case of pseudoplasticity) and the dimensionless yield stress (in the case of viscoplasticity). The corresponding pressure-gradient and pressure distributions are also given. The integrated quantities of engineering interest are calculated. These include the maximum pressure, the roll-separating force, and the power input to the rolls. Both pseudoplasticity and viscoplasticity lead to thicker sheets than the Newtonian model for large entry thickness ratios, while they lead to thinner sheets for small entry thickness ratios. In the case of viscoplastic sheets, the interesting yielded/unyielded regions appear as a function of the dimensionless yield stress. All engineering quantities, given in a dimensionless form, increase substantially with the departure from the Newtonian values. A test case for calendering a plastic sheet with a yield stress is given as an example of implementing the present results.