Fourier Transform and Spectral Analysis in Yarn Mass Variation and Periodic Fault Detection

Yarn mass variation is one of the most critical quality parameters in the spinning industry, directly impacting fabric aesthetics, tensile performance, and downstream process efficiency. Among the root causes of mass variation, periodic faults originating from defective drafting components—cots, aprons, and rollers—represent a class of highly diagnosable yet often overlooked anomalies. This article presents a comprehensive, mathematically rigorous treatment of Fourier Transform (FT) and Spectral Analysis as applied to yarn mass variation signals measured by capacitive evenness testers. The theoretical derivation of the Discrete Fourier Transform (DFT) is developed alongside the physical interpretation of frequency-domain peaks as signatures of rotating machine elements. The relationships between cut length, sampling resolution, and fault detectability are systematically explored using the Nyquist–Shannon sampling theorem. Worked case studies—spanning a single front-line spinning cot at 250 RPM, dual front/back cot scenarios, and a complete mill-wide component matrix—demonstrate how individual fault frequencies are computed and matched to spectrometric peaks. The concept of minimum CV% is introduced as the theoretical noise floor against which periodic disturbances must be discriminated. A component-frequency lookup table covering draw frame, speed frame, and ring frame cots is provided as a practical diagnostic tool. Limitations of the technique—periodicity assumptions, stationarity constraints, noise sensitivity, and resolution dependencies—are discussed with recommended mitigations. The article concludes with practical guidance for spinning mill technologists on integrating Fourier-based diagnostics into their quality-control workflow, enabling proactive maintenance and measurable improvements in yarn evenness indices.