Title: Reliability comparison of the shafts when stress and strength follow exponential and normal distribution subjected to twisting and bending moments

Authors: Md. Yakoob Pasha; M. Tirumala Devi; T. Sumathi Uma Maheswari

Addresses: Department of Mathematics, Kakatiya University, Warangal – 506009, Telangana, India ' Department of Mathematics, Kakatiya University, Warangal – 506009, Telangana, India ' Department of Mathematics, Kakatiya University, Warangal – 506009, Telangana, India

Abstract: Shaft is a rotating machine component that is used to transmit power from one place to another. The design of a shaft is essential, subject to its strength and stress. This paper presents the reliability analysis of the shaft according to: 1) maximum shear stress theory; 2) maximum normal stress theory, for which stress and strength follow exponential and normal distributions. Reliability is computed when changing the twisting moment, bending moment, diameter and strength of the shaft. Reliability comparison has been made when stress and strength follow exponential and normal distribution. The comparison between normal and exponential distributions for designing a shaft under twisting and bending moments offers several advantages. For stress analysis, the normal distribution helps assess shaft reliability under consistent conditions, where the material undergoes gradual bending and twisting over time. In contrast, the exponential distribution identifies reliability in sudden overloads. In terms of design optimisation, comparing these distributions enables engineers to balance shaft design between gradual degradation and sudden overload risks. When predicting lifespan, the normal distribution provides a broader understanding of long-term behaviour under sustained stress, while the exponential distribution focuses on early life or sudden failures. Using both approaches together supports more optimised and comprehensive designs.

Keywords: reliability comparison; twisting moment; bending moment; combined twisting and bending moment; exponential distribution; normal distribution; maximum shear stress theory; maximum normal stress theory; round solid shaft.

DOI: 10.1504/IJQET.2024.147903

International Journal of Quality Engineering and Technology, 2024 Vol.10 No.4, pp.351 - 365

Accepted: 13 Nov 2024
Published online: 07 Aug 2025 *

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