Calendering of metal/polymer composites: An analytical formulation

This paper mathematically studies calendering with a tangent hyperbolic model to simulate non-Newtonian polymers. The constitutive equations based on Lubrication Approximation Theory (LAT) are first non-dimensionalized and then simplified. The simplified equations describing the flow inside the calender are solved (a) analytically using the perturbation method and (b) numerically using MatLab built-in routine “BVP4c” method. The first case, obtains an analytical expression for velocity, pressure gradient, and final sheet thickness with the help of the perturbation method, while “BVP4c and Runge-Kutta methods are used to calculate the velocity, pressure, pressure gradient, and mechanical quantities numerically. The power-law index and Weissenberg number influence on pressure, pressure gradient, and velocity profiles of fluid being calendered are shown with graphs. The pressure inside the calender decreases as the power-law index and Weissenberg number increase. The force function and final sheet thickness decreases as the power-law index and Weissenberg number increases.

Section: Introductionmentioning

confidence: 99%

Mathematical simulation of the calendering process for non-Newtonian polymers

Javed

Nasir

Ali

et al. 2022

“…Hannachi and Mitsoulis 27 worked on coextruded multilayer calendering based on LAT and tabulated quantitative results with different operating conditions and fluid arrangements. Calcagno et al 28 analyzed calendering polymer composites across a metal strip for Newtonian and power law models. Apart from some experimental results in multi-layer calendering, no mathematical development has been found in the literature.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of two-layered isothermal calendering of viscoplastic and Newtonian fluids with different viscosity ratios

Ilyas

Zahid

Mushtaq

2022

Co-extruded multi-layer plastic sheets and polymer structures formed by calendering process or by cold rolling are widely used in the packaging industry and thin-film transistor manufacturing. The different materials are extruded from separate extruders into the single sheet die which delivers a multi-layer sheet with uniform layer thickness at die exit. This multi-layer sheet is then stretched between counter-rotating rolls to obtain final uniform multi-layer sheet. There are many factors which can influence this process. In this article, calendering a single layer Newtonian or Non-Newtonian material has been extended to analyze a two-layer calendering process for an incompressible Viscoplastic and Newtonian fluids as upper and lower layers with different viscosity ratios. To simplify the equations of motion, the lubrication approximation theory is used. The expressions of non-dimensional pressure gradient, pressure and velocity distribution of both layers are obtained analytically by using proper no slip boundary conditions and dimensionless variables. The dimensionless detachment point is approximated by Regula-Falsi (false position) method. The important engineering factors including detachment point, calendered sheet thickness, roll separation force, power input by rolls, torque on each roll, and adiabatic temperature are all computed. In addition, how the viscosity ratios and viscoplastic casson parameter affect these factors have been investigated. Moreover all established results in literature for single layer calendering Newtonian fluids are also validated at casson parameter β tending towards infinity.

“…They discussed how the Phan-Thien-Tanner parameter affects the calendering quantities, pressure and velocity. Calcagno et al 15 presented the calendering mechanism using Newtonian and power law fluid models. They compared their calculated pressure with experimental pressure sensor data.…”

Section: Introductionmentioning

confidence: 99%

Numerical approach for the calendering process using Carreau-Yasuda fluid model

Javed

Ali

Arshad

et al. 2021

This paper presents a numerical study of the calendering mechanism. The calendered material is represented using the Carreau-Yasuda fluid model. The governing flow equations in the calendering process are made first dimensionless then the lubrication approximation theory (LAT) is used to simplify them. The simplified flow equations are transformed into stream function and then are numerically solved. A numerical method is constructed with Matlab’s built-in-bvp4c routine to find the stream function and pressure gradient. We use the Runge-Kutta algorithm to calculate the pressure and mechanical quantities related to the calendering process. In this analysis the pressure distribution increases with increasing Weissenberg number, however the pressure domain length decreases as the Weissenberg number increases. The pressure inside the nip region decreases from its Newtonian value when the power law index is less than one (shear thinning), and the pressure profile increases from its Newtonian pressure when the power law index is greater than one(shear thickening). How the Carreau-Yasuda fluid model parameters influence the velocity and related calendering process quantities are also discussed via graphs.