How core stiffness and Poisson ratio affect energy balance roll structure formulas

Abstract

The stiffness of the core determines how much support it will offer for the initial wraps of web material, and whether this support will be maintained as internal pressures are developed. An expression is developed for calculating the effective modulus of the core for isotropic and anisotropic material. The linear solution is carried further to predict how this core modulus is reflected in local radial hardness of the roll when additional material is wound onto the core. The radial modulus parameters of a roll winding model based upon energy balance are adjusted to account for the stiffening or yielding effect of the core under given winding conditions. The effect of different Poisson ratios on core stiffness and roll formation is discussed.