Modeling of Shape Defects (Crossbow and Wavy Edges) in Thin Webs Due to Cross-Direction Length Profile

Presented by Boliang Meng, Texas A&M University

Most prior work on web flatness and shape control has emphasized process variables such as friction, roll geometry, and force, often supported by inline flatness measurements. Although useful for mitigation and monitoring, these approaches typically do not directly link the web’s Cross-Direction (CD) length profile to the resulting three-dimensional shape. This work introduces a unified, geometry-first modeling framework that uses length nonuniformity across the web width (CD) as the primary driver of web shape distortions and predicts the out-of-plane shape for thin webs up to 0.01 inch thick, in regimes where bending dominates over membrane stretching. Two types of CD length profiles are considered in this work: (i) longer web center profiles when compared to web edges that generate crossbow (bow-shaped curvature) and (ii) shorter center profiles that generate wavy edges (periodic edge undulations). The proposed framework provides a mechanistic explanation based on the length profile for crossbow and wavy-edge defects and relates the span length and length-ratio parameters to the severity of the defect for diagnosis and operating guidance. By separating upstream length variations from their geometric consequences, this work offers a practical basis for predicting, diagnosing, and controlling CD-length-driven shape defects in thin-web R2R manufacturing.