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Deformation in a Circular Shaft

Deformation in a Circular Shaft

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

Thin-Walled Hollow Shafts

Thin-Walled Hollow Shafts

In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...

Transmission Shafts: Problem Solving

Transmission Shafts: Problem Solving

Designing a solid shaft that transmits power from a motor to a machine tool involves a series of calculations to ensure the shaft can withstand the stresses applied by bending moments and torques. First, calculate the torque exerted on the gear, considering the power transmitted by the shaft and its rotational speed. Following this, compute the tangential forces acting on the gears, which directly relate to the torque and the gear radius.
Next, use bending moment diagrams for the shaft to...

Residual Stresses in Circular Shafts

Residual Stresses in Circular Shafts

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 shaft's...

Plastic Deformation in Circular Shafts

Plastic Deformation in Circular Shafts

When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...

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Related Experiment Video

Updated: Jun 27, 2026

Neutron Radiography and Computed Tomography of Biological Systems at the Oak Ridge National Laboratory's High Flux Isotope Reactor

Neutron Radiography and Computed Tomography of Biological Systems at the Oak Ridge National Laboratory's High Flux Isotope Reactor

Published on: May 7, 2021

NeRF-Based Three-Dimensional Reconstruction for Large-Diameter Rescue Shafts.

Hairong Gu^1,2, Jiaxi Wang¹, Chenggang Chen^1,3

¹National Engineering Research Center of Highway Maintenance Technology, Chang'an University, Xi'an 710064, China.

Sensors (Basel, Switzerland)

|June 26, 2026

Summary

This study introduces a Neural Radiance Fields (NeRF) method for 3D reconstruction of large-diameter rescue shafts, enabling accurate deformation assessment for mining safety. The NeRF approach offers improved geometric accuracy and visual quality in challenging conditions.

Keywords:

3D reconstruction NR-SNR large-diameter rescue shafts neural radiance fields (NeRF)

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Last Updated: Jun 27, 2026

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Published on: May 7, 2021

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Area of Science:

Geospatial Engineering
Computer Vision
Mining Safety Engineering

Background:

Large-diameter rescue shafts are critical for mining emergency response.
Structural deformation of these shafts impacts rescue capsule safety.
Accurate 3D reconstruction and deformation assessment are essential for maintaining shaft integrity.

Purpose of the Study:

To develop and evaluate a Neural Radiance Fields (NeRF)-based workflow for 3D reconstruction of large-diameter rescue shafts.
To assess the structural deformation of these shafts using the developed NeRF scheme.
To improve the efficiency and accuracy of rescue shaft monitoring and safety evaluations.

Main Methods:

Integration of no reference signal-to-noise-ratio (NR-SNR) image filtering, Structure from Motion (SfM) for camera pose estimation, and Nerfacto for NeRF reconstruction.
Exporting the reconstructed radiance field into a dense point cloud for analysis.
Utilizing circular-section fitting and various error metrics for deformation assessment.

Main Results:

A practical trade-off was found by retaining approximately 35% of high-quality images, balancing computational load and geometric information.
The NeRF-based scheme demonstrated favorable geometric measurement applicability and visual reconstruction quality in weak-texture and low-illumination environments.
The NeRF-derived point cloud proved more suitable for circular-section fitting and deformation assessment compared to conventional Multi-View Stereo (MVS) and 3D Gaussian Splatting (3DGS) methods.

Conclusions:

The proposed NeRF-based workflow shows significant potential for accurate inner-wall reconstruction of rescue shafts.
This method enables effective engineering-oriented deformation evaluation, crucial for mining safety.
Direct implicit surface recovery methods face challenges with hollow cylindrical scenes, highlighting the advantages of the NeRF approach.