Stochastic Kinematics of Fibre Control in Staple Fibre Drafting: A Theoretical Multiphysics Framework and the Fibre Control Index

The mechanical drafting of staple fibre assemblies represents the most kinematically critical and theoretically least resolved operation in staple fibre spinning. Despite more than a century of empirical study and progressive machine evolution, no universal deterministic model exists that can predict the precise temporal and spatial trajectory of individual staple fibres within the dynamic drafting zone. The present work advances a rigorous theoretical examination of the multiphysics nature of fibre control, synthesising principles from discrete granular mechanics, contact tribology, stochastic dynamical systems, non-Newtonian fibre rheology, and finite element analysis into a coherent conceptual framework. Central to this framework is the formalisation of the Fibre Control Index (FCI) — a dimensionless instantaneous process metric defined as the ratio of mechanically governed fibres to the total fibre population at any given moment — proposed as a complementary, proactive in-process descriptor intended to augment, not replace, conventional post-process quality metrics such as mass unevenness coefficient of variation (CV_m%) and yarn imperfection counts (thick places, thin places, and neps). Theoretical analysis reveals that fibre control breakdown is governed by the complex and largely unresolved interaction of six physical domains: contact mechanics, dynamic friction, fibre elasticity, stochastic biological variability, inertial fluid dynamics, and triboelectric charging. The floating fibre problem — characterised as the irreversible stochastic transition from deterministic roller-controlled fibre motion to turbulent friction-matrix-dependent drift — is identified as the fundamental root-cause mechanism underpinning the complete spectrum of yarn structural defects, including thick and thin places, neps, hairiness anomalies, and catastrophic end-breakages. The avalanche effect, arising from the cascade acceleration of insufficiently restrained fibres, is modelled as a granular instability analogous to turbulent flow onset. A hybrid Discrete Element Method–Finite Element Analysis digital twin framework is proposed as the principal computational pathway to achieving real-time FCI estimation. Practical implications for process engineers operating within the boundary conditions of ring spinning, air-jet spinning, and rotor spinning systems are discussed within the scope of the theoretical framework presented herein. This work proposes the FCI as a candidate in-process metric for investigation in future spinning process control research.