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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...
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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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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...
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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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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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Three-dimensional runout characterisation for rotationally symmetric components.

Christopher G Tompkins1, Luke D Todhunter2, Harald Gottmann3

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Summary
This summary is machine-generated.

This study introduces a new 3D standard for measuring runout in rotationally symmetric parts. The method uses minimal surface data and virtual instrumentation for accurate characterization, ensuring compatibility with existing standards.

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Area of Science:

  • Manufacturing Engineering
  • Metrology
  • Mechanical Engineering

Background:

  • Precision manufacturing of rotationally symmetric components is crucial for device functionality and cost-efficiency.
  • Manufacturing errors, termed 'runout', affect the shape along the axis of rotation.
  • Existing methods for runout characterization may lack comprehensive 3D surface deformation analysis.

Purpose of the Study:

  • To propose an updated standard for characterizing three-dimensional (3D) runout in rotationally symmetric machined parts.
  • To enable accurate 3D surface deformation analysis using minimal surface information and virtual instrumentation.
  • To ensure compatibility with existing metrology standards for widespread adoption.

Main Methods:

  • Development of a novel 3D runout characterization method based on four standard profile measurements.
  • Utilization of virtual instrumentation for evaluating the proposed runout measurement technique.
  • Creation of a technique to quantify virtual instrument errors, decoupled from the instrument's inherent inaccuracies.

Main Results:

  • A proposed 3D runout vector generation method from minimal surface data.
  • Successful evaluation of virtual instrumentation efficacy using a developed error quantification technique.
  • Demonstration of a method compatible with existing standards for runout measurement.

Conclusions:

  • The proposed 3D runout characterization method offers an accurate and compatible approach for assessing surface deformation.
  • The developed virtual instrument evaluation technique provides a reliable measure of system performance.
  • This work contributes to advancing metrology standards for precision-engineered components.