Safety Analysis and Optimization of Travelling Webs Subjected to Fracture and Instability

Abstract

AbstractThe problems of safety analysis and optimization of a moving elastic web travelling between two rollers at a constant axial velocity are considered in this study. A model of a thin elastic plate subjected to bending and in-plane tension (distributed membrane forces) is used. Transverse buckling of the web and its brittle and fatigue fracture caused by fatigue crack growth under cyclic in-plane tension (loading) are studied. Safe ranges of velocities of an axially moving web are investigated analytically under the constraints of longevity and instability. The expressions for critical buckling velocity and the number of cycles before the fracture (longevity of the web) as a function of in-plane tension and other problem parameters are used for formulation and investigation of the following optimization problem. Finding the optimal in-plane tension to maximize the performance function of paper production is required. This problem is solved analytically and the obtained results are presented as formulae and numerical tables.KeywordsFracture ToughnessStress Intensity FactorFatigue Crack GrowthPerformance FunctionLinear Elastic Fracture MechanicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.