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Design of Transmission Shafts - Stress Analysis

Design of Transmission Shafts - Stress Analysis

Designing a transmission shaft requires a thorough understanding of the stresses induced by bending moments and torques, especially in systems where power is transferred through gears. These forces create force-couple systems at the centers of the shaft's cross-sections, leading to both transverse and torsional loading. Although shearing stresses from transverse loads are typically smaller than those from torques and are often overlooked, the significant normal stresses from these loads...

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Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...

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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...

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Related Experiment Video

Updated: Nov 7, 2025

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

Parametric Optimization Design Method for Friction Plates of Hydro-Viscous Clutches

Published on: July 22, 2025

Reliability-based tolerance redesign of mechanical assemblies using Jacobian-Torsor model.

Bingxiang Wang¹, Xianzhen Huang^1,2, Miaoxin Chang¹

¹School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China.

Science Progress

|April 30, 2021

Summary

This study introduces a new method for redesigning mechanical assembly tolerances, reducing costs and improving reliability. The approach optimizes process variances for better economic outcomes and enhanced product dependability.

Keywords:

Jacobian-Torsor model Lagrange multiplier method reliability tolerance optimization tolerance redesign

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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

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Area of Science:

Mechanical Engineering
Manufacturing Processes
Reliability Engineering

Background:

Traditional tolerance analysis often overlooks cost and reliability optimization.
Redesigning tolerances requires efficient models for complex mechanical assemblies.

Purpose of the Study:

To present a novel method for redesigning dimensional and geometric tolerances in mechanical assemblies.
To achieve lower costs and higher reliability through advanced tolerance optimization.

Main Methods:

Development of a parametric Jacobian-Torsor model for tolerance analysis.
Establishment of a reliability-based tolerance optimization model.
Determination of optimal process variances for tolerances, unlike fixed parameters in prior studies.

Main Results:

Analytical solution obtained using the Lambert W function and Lagrange multiplier method.
Numerical example demonstrated a 10.93% reduction in total cost.
Assembly reliability was improved by 2.12%.

Conclusions:

The proposed reliability-based tolerance optimization model is efficient.
The tolerance redesign method offers significant economic benefits and improved reliability for mechanical assemblies.