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Related Concept Videos

Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

1.0K
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...
1.0K
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

644
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...
644
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

519
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...
519
Transformation of Plane Stress01:18

Transformation of Plane Stress

813
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...
813
Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

810
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
810
Stresses in a Shaft01:18

Stresses in a Shaft

1.0K
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...
1.0K

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Studying Large Amplitude Oscillatory Shear Response of Soft Materials
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Error correction for rotationally asymmetric surface deviation testing based on rotational shears.

Weibo Wang, Pengfei Liu, Yaolong Xing

    Applied Optics
    |September 24, 2016
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    Summary
    This summary is machine-generated.

    This study introduces a new method for accurately testing rotational surface deviations. It corrects errors and improves efficiency, achieving high precision with fewer measurements.

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    Area of Science:

    • Optical metrology
    • Surface metrology
    • Precision engineering

    Background:

    • Accurate measurement of rotationally asymmetric surface deviations is crucial for optical component manufacturing.
    • Traditional methods like multiangle averaging can neglect certain angular errors, impacting precision.

    Purpose of the Study:

    • To develop a practical and accurate method for absolute testing of rotationally asymmetric surface deviation.
    • To improve upon existing methods by compensating for neglected errors and enhancing efficiency.

    Main Methods:

    • Rotation averaging combined with additional compensation and azimuthal error correction.
    • Least-squares fitting of Zernike polynomials using additional rotation measurements.
    • Least-squares estimation to correct azimuthal errors from rotation inaccuracy.
    • Estimation of relative alignment using overlapping measurement areas.

    Main Results:

    • Successfully reconstructed and compensated for angular errors (kNθ) missed by traditional methods.
    • Eliminated azimuthal errors caused by rotation inaccuracy.
    • Enabled estimation of unknown relative measurement alignment.
    • Achieved high accuracy in surface deviation testing with fewer rotation measurements.

    Conclusions:

    • The proposed method offers a balance between measurement efficiency and accuracy.
    • It provides a practical solution for absolute testing of complex surface deviations.
    • Demonstrated high precision, even with a reduced number of rotation measurements.