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Related Concept Videos

Residual Stresses in Circular Shafts01:10

Residual Stresses in Circular Shafts

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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...
210
Stress Concentrations in Circular Shafts01:18

Stress Concentrations in Circular Shafts

214
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...
214
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

222
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...
222
Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

429
Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
429
Relative Motion Analysis using Rotating Axes - Acceleration01:22

Relative Motion Analysis using Rotating Axes - Acceleration

366
Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame. The absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame.
Time differentiation is...
366
Stresses in a Shaft01:18

Stresses in a Shaft

434
The shaft PQ is subjected to a twisting force when equal and opposite torques are applied on either side. A section that cuts perpendicular to the shaft's axis at any arbitrary point R is examined to understand this. When the free-body diagram of the QR segment is analyzed, it reveals the shearing forces exerted by the PR portion onto the QR segment as the shaft experiences twisting.
Applying equilibrium conditions to the QR segment establishes that the internal shearing forces within the...
434

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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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Crack Monitoring in Rotating Shaft Using Rotational Speed Sensor-Based Torsional Stiffness Estimation with Adaptive

Young-Hun Park1, Hee-Beom Lee1, Gi-Woo Kim1

  • 1Department of Mechanical Engineering, Inha University, Incheon 22212, Republic of Korea.

Sensors (Basel, Switzerland)
|March 11, 2023
PubMed
Summary

This study introduces an adaptive extended Kalman filter (AEKF) to detect crack damage in rotating shafts by estimating stiffness reduction. The method quanties fatigue crack growth using only two sensors, enhancing structural health monitoring.

Keywords:
adaptive extended Kalman filtercrack monitoringforgetting factor updaterotating shaftrotational speed sensorstorsional stiffness estimation

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Area of Science:

  • Mechanical Engineering
  • Structural Health Monitoring
  • Signal Processing

Background:

  • Crack detection in rotating machinery is crucial for preventing catastrophic failures.
  • Traditional methods often require complex sensor setups or are less sensitive to early-stage damage.
  • Torque fluctuations can complicate the accurate assessment of shaft integrity.

Purpose of the Study:

  • To develop an alternative, cost-effective method for detecting crack damages in rotating shafts.
  • To directly estimate the reduction in torsional shaft stiffness as an indicator of crack presence and growth.
  • To implement an adaptive extended Kalman filter (AEKF) for real-time stiffness estimation.

Main Methods:

  • Derivation and implementation of a dynamic system model for a rotating shaft.
  • Design of an AEKF with a forgetting factor (λ) update for time-varying parameter estimation.
  • Utilizing two cost-effective rotational speed sensors for data acquisition.

Main Results:

  • The AEKF algorithm successfully estimated the decrease in torsional shaft stiffness caused by cracks.
  • The method quantitatively evaluated fatigue crack growth by directly tracking stiffness reduction.
  • Simulation and experimental results validated the proposed AEKF approach.

Conclusions:

  • The proposed AEKF-based method offers a robust and cost-effective solution for detecting and monitoring crack damages in rotating shafts.
  • Direct estimation of torsional stiffness provides a quantitative measure of crack severity and fatigue progression.
  • The approach is suitable for integration into existing structural health monitoring systems for rotating machinery.