Research Article
Mathematical Modelling and Analysis of Yarn Breakage Rates in Spinning Processes
Sujai Balasubramanian*
Issue:
Volume 12, Issue 3, June 2026
Pages:
57-68
Received:
15 March 2026
Accepted:
30 June 2026
Published:
22 July 2026
Abstract: Yarn breakage in ring-spinning remains one of the most significant contributors to production downtime and quality loss in modern textile mills. This paper presents a first-principles predictive model that quantifies the end-break rate (EBR) expressed as breaks per 100 spindles per hour using a Poisson stochastic framework. The model integrates four independently computed tension components — spinning tension (Sₜ), ballooning tension (Bₜ), winding tension (Wₜ), and aerodynamic drag tension (Aₜ) — with fibre characterisation via the Spinning Consistency Index (SCI) to derive the mean link-frequency at the front-roller nip. The probability of breakage is modelled as an exponential decay function of the stress-strength ratio (mean yarn strength / total tension), scaled by the total number of fibre-bundle links traversing the nip per unit time across 1,008 spindles. Applying the model to a 30s Ne carded yarn with a SCI of 131.50 yields a predicted EBR of 5.91 breaks per 100 spl/hr. Sensitivity analysis reveals that spindle speed, top-arm load, and mean yarn strength are the most influential parameters. The model provides process engineers with a tractable, real-time diagnostic tool for root-cause analysis and parameter optimisation, thereby reducing waste, improving yield, and advancing the state of predictive quality control in ring-spinning. Limitations including the assumption of constant environmental conditions and the empirical derivation of the proportionality constant are discussed in detail.
Abstract: Yarn breakage in ring-spinning remains one of the most significant contributors to production downtime and quality loss in modern textile mills. This paper presents a first-principles predictive model that quantifies the end-break rate (EBR) expressed as breaks per 100 spindles per hour using a Poisson stochastic framework. The model integrates fou...
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Research Article
Convergence of Fourier Series of Regulated Functions in Generalized Orlicz Sequence Spaces
Rachid Conte,
Ousmane Toure,
Mamadouba Toure,
Aboubakary Diakhaby
Issue:
Volume 12, Issue 3, June 2026
Pages:
69-73
Received:
28 May 2026
Accepted:
10 June 2026
Published:
12 August 2026
DOI:
10.11648/j.ijtam.20261203.12
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Abstract: The study of Fourier coefficients in function spaces is a classical topic in harmonic analysis, with foundational results by Hardy, Littlewood, and Zygmund for Lebesgue and Orlicz spaces. This paper investigates the convergence of Fourier series of regulated functions, which are uniform limits of step functions, within the framework of generalized Orlicz sequence spaces. Regulated functions form a broad class that includes continuous, monotone, and piecewise continuous functions, making them natural candidates for studying Fourier series at points of discontinuity. The purpose of this work is to establish a continuity result for the Fourier coefficient operators acting from an Orlicz space of functions into a generalized Orlicz sequence space. The methodology relies on a modular approach using a non-decreasing sequence of N-functions, combined with a uniform Delta-2 condition and a controlled growth condition on the sequence. A classical Hausdorff-Young estimate is used to relate the decay of Fourier coefficients to the modular of the function. The main result (Theorem 4.1) states that the maps sending a regulated function to its sequences of cosine and sine Fourier coefficients are continuous linear operators under the stated hypotheses. Examples including the sawtooth wave and piecewise constant functions illustrate the theory. These results extend classical Hardy?Littlewood type theorems to a broader class of sequence spaces. The findings contribute to the theory of modular spaces and Fourier analysis, with potential applications to partial differential equations and approximation theory.
Abstract: The study of Fourier coefficients in function spaces is a classical topic in harmonic analysis, with foundational results by Hardy, Littlewood, and Zygmund for Lebesgue and Orlicz spaces. This paper investigates the convergence of Fourier series of regulated functions, which are uniform limits of step functions, within the framework of generalized ...
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