Rigid Rotation Research Articles

A centroid measurement method of large components for active compliant assembly

In the active compliant assembly system of large components, the centroid parameter is an important factor affecting the dynamic model of the attitude adjustment mechanism. This paper proposes a novel automatic centroid measurement method. Firstly, the contact force calculation method between large components during active compliant assembly was described, and the impact of the centroid of large components on the accuracy of the contact force calculation was analyzed. Secondly, based on the principles of torque balance and rigid body rotation, a novel centroid calculation model considering lateral forces is established, and RANSAC is used to optimize the centroid solution. Then, numerical simulation methods were used to analyze the impact of random errors and weighing strategies on the centroid measurement accuracy, and suggestions were given to improve the centroid measurement accuracy. Finally, a compliant assembly system for large component was built in the laboratory, and centroid measurement and accuracy verification experiments were conducted. The experimental results show that the proposed method can significantly improve the accuracy of centroid measurement and can effectively reduce the contact force calculation error during the compliant assembly process of large components.

ANALYSIS OF ASYMMETRIC PLASTIC BENDING DEFORMATION OF WELDED TUBE SHEETS AND DERIVATION OF A DAMAGE LAW FOR J SHAPE-C SHAPE -O SHAPE FORMING

The J shape-C shape -O shape (JCO) forming method of sheets for large-diameter longitudinally welded pipes has been widely used to manufacture oil and gas pipelines. The quality of welded pipes formed through the JCO process is directly affected by the accurate control of asymmetric bending springback and damage during the procedure. A finite element model (FEM) for JCO asymmetric bending was constructed to investigate the characteristics of asymmetric plastic bending deformation and the distribution laws of damage in JCO forming. This model was based on a nonlinear mixed hardening Lemaitre damage model coupled with the Quasi-Plastic-Elastic (QPE) model. Then, residual stress, forming shape, and damage degree of crimping, first bending, second bending, and third bending were analyzed. Moreover, the accuracy of the model was experimentally verified. Results demonstrate that, the asymmetric bending deformation process can be divided into five stages, including rigid body rotation phase, full elastic deformation phase, elastic–plastic uncladded deformation phase, elastic–plastic cladded phase, and springback phase. In the first bending, the stress centerline significantly misaligns with the mold centerline. Asymmetry is not evident in the second and third bending stages. Furthermore, the peak residual stress and peak damage can be effectively reduced by a larger punch radius, while the peak damage can be reduced by a larger die span. This study lays a foundation for optimizing the technical parameters of JCO forming. Keywords: JCO forming, asymmetric bending, finite element, QPE model, deformation characteristics

FINITE SHEAR STRAIN BASED ON IMAGE ANALYSIS FOR RECTANGULAR SECTION SHAFT WITH LARGE ASPECT RATIO

This paper describes the shearing strain distribution obtained by using image analysis proposed in this study when large torsion is applied to a rectangular cross-section shaft. As is well known, the shearing strain distribution for rectangular cross-section shaft have already been investigated by Saint-Venant. However, since this theory is based on the assumption that torsional angle is relatively small, it is not necessarily rational under large torsion. Therefore, in our previous study, using the image analysis based on the Natural Strain theory, where the commutative law of strain is applicable and the rigid body rotation can be removed accurately from shearing strain component, the shearing strain distributions have been investigated for the rubber shaft having square cross section. In the present paper, these distributions are investigated for a rectangular cross section with a large aspect ratio rather than a square shape. In particular, these distributions on the long side in rectangular cross-section are compared with those on the short sides. Consequently, the difference between the distribution of shearing strain obtained by the image analysis in this study and measurements based on Saint-Venant's theory increases as torsional deformation increases and this tendency is observed particularly on the short side.

FINITE SHEAR STRAIN BASED ON IMAGE ANALYSIS FOR RECTANGULAR SECTION SHAFT WITH LARGE ASPECT RATIO

This paper describes the shearing strain distribution obtained by using image analysis proposed in this study when large torsion is applied to a rectangular cross-section shaft. As is well known, the shearing strain distribution for rectangular cross-section shaft have already been investigated by Saint-Venant. However, since this theory is based on the assumption that torsional angle is relatively small, it is not necessarily rational under large torsion. Therefore, in our previous study, using the image analysis based on the Natural Strain theory, where the commutative law of strain is applicable and the rigid body rotation can be removed accurately from shearing strain component, the shearing strain distributions have been investigated for the rubber shaft having square cross section. In the present paper, these distributions are investigated for a rectangular cross section with a large aspect ratio rather than a square shape. In particular, these distributions on the long side in rectangular cross-section are compared with those on the short sides. Consequently, the difference between the distribution of shearing strain obtained by the image analysis in this study and measurements based on Saint-Venant's theory increases as torsional deformation increases and this tendency is observed particularly on the short side.

On Analytical Corrections for Restraints in Absolute Binding Free Energy Calculations.

Double decoupling absolute binding free energy simulations require an intermediate state at which the ligand is held solely by restraints in a position and orientation resembling the bound state. One possible choice consists of one distance, two angle, and three dihedral angle restraints. Here, I demonstrate that in practically all cases the analytical correction derived under the rigid rotator harmonic oscillator approximation is sufficient to account for the free energy of the restraints.

Moderate magnitude clockwise rotation of the Yunlong Basin: Implications for synchronous Eocene rotation of the southeastern Tibetan Plateau

The clockwise rotation and southeastward extrusion of the southeastern Tibetan Plateau have played important roles in accommodating the uplift and deformation of the plateau. Numerous paleomagnetic studies have suggested post−late Eocene clockwise rotation of the southeastern Tibetan Plateau along the eastern Himalaya syntaxis, whereas few researchers have addressed the specific Eocene deformation, leading to ambiguous interpretations of the tectonic evolution in the region. Herein, we conducted a paleomagnetic study of the Yunlong Formation in the Yunlong Basin, which is Late Cretaceous to early Paleocene in age. In total, 386 oriented samples were collected. Rock magnetic, scanning electron microscopy (SEM), and energy-dispersive spectroscopy (EDS) analyses revealed detrital carriers, such as hematite and some magnetite. In thermal demagnetization processes, 332 characteristic remanent magnetizations were isolated, which yielded positive reversals and tilt tests, providing a site-mean direction of declination (Ds) = 56.0° ± 2.6°, inclination (Is) = 34.3° ± 3.8°, α95 = 2.7°, k = 91.0, and N = 31 after tilt correction. Magnetostratigraphic analysis was performed, and a depositional age of 79−61 Ma for the section was obtained, which is consistent with the previous paleontological and detrital zircon ages. Compared with the Eurasia reference pole of the period, the data revealed a 45.2° ± 5.1° clockwise rotation of the Yunlong area since 79−61 Ma. The integrated regional paleomagnetic results suggest the occurrence of ∼20° of clockwise rotation of the Lanping-Simao terrane during the Eocene, which is similar (in terms of magnitude and time of occurrence) to that of the Gonjo Basin in the eastern Qiangtang terrane. Integrated with other lines of geologic evidence, we propose a new deformation model in which the entire southeastern Tibetan Plateau experienced ∼20° of rigid clockwise rotation during the Eocene, followed by subsequent oroclinal bending.

Rotation numbers and bounded deviations for quasi-periodic monotone recurrence relations

It is known that monotone recurrence relations are defined by finding equilibria of generalized Frenkel-Kontorova models. In this paper, we intend to study quasi-periodic monotone recurrence relations. By introducing a countable set consisting of integers with bounded distances and improving a method of Angenent used for studying periodic monotone recurrence relations, we derive a criterion for the existence of solutions with bounded deviations from the rigid rotation. With the help of the criterion, a range of parameters is provided to guarantee the quasi-periodic standard map has orbits with bounded deviations from the rigid rotation corresponding to each given rotation number.

An objective FE-formulation for Cosserat rods based on the spherical Bézier interpolation

A generalization of the spherical linear interpolation (or slerp) for the finite rotations to the case of more than two control variables on SO(3) is introduced to design an objective FE-formulation for the non-linear space Cosserat rod model. The interpolation uses the De Casteljau’s algorithm.In this way, the same interpolation degree can be used for the placement of the centroid curve and for the finite rotation of the cross-section. A recursive formula is obtained for the interpolation of the rotations. Similar recursive formulas are derived for the spin and the curvature vector, leading to a generalization of the Bézier basis functions on the manifold SO(3).The rod formulation so obtained is invariant under a rigid rotation (objective), in the sense that the patch-test with respect to the rigid body motion is satisfied. Furthermore, an optimal path-independence is achieved as verified by several numerical investigations.

A Pilot Study of Simulation-Free Hippocampal-Avoidance Whole Brain Radiation Therapy Using Diagnostic MRI-Based and Online Adaptive Planning

We aimed to demonstrate the clinical feasibility and safety of simulation-free hippocampal avoidance whole brain radiation therapy (HA-WBRT) in a pilot study (National Clinical Trial 05096286). Ten HA-WBRT candidates were enrolled for treatment on a commercially available computed tomography (CT)-guided linear accelerator with online adaptive capabilities. Planning structures were contoured on patient-specific diagnostic magnetic resonance imaging (MRI), which were registered to a CT of similar head shape, obtained from an atlas-based database (AB-CT). These patient-specific diagnostic MRI and AB-CT data sets were used for preplan calculation, using NRG-CC001 constraints. At first fraction, AB-CTs were used as primary data sets and deformed to patient-specific cone beam CTs (CBCT) to give patient-matched density information. Brain, ventricle, and brain stem contours were matched through rigid translation and rotation to the corresponding anatomy on CBCT. Lens, optic nerve, and brain contours were manually edited based on CBCT visualization. Preplans were then reoptimized through online adaptation to create final, simulation-free plans, which were used if they met all objectives. Workflow tasks were timed. In addition, patients underwent CT-simulation to create immobilization devices and for prospective dosimetric comparison of simulation-free and simulation-based plans. Median time from MRI importation to completion of "preplan" was 1 weekday (range, 1-4). Median on-table workflow duration was 41 minutes (range, 34-70). NRG-CC001 constraints were achieved by 90% of the simulation-free plans. One patient's simulation-free plan failed a planning target volume coverage objective (89% instead of 90% coverage); this was deemed acceptable for first-fraction delivery, with an offline replan used for subsequent fractions. Both simulation-free and simulation CT-based plans otherwise met constraints, without clinically meaningful differences. Simulation-free HA-WBRT using online adaptive radiation therapy is feasible, safe, and results in dosimetrically comparable treatment plans to simulation CT-based workflows while providing convenience and time savings for patients.

A Petrological and Microstructural Study of Ten Brachinites: A Cumulate Texture?

AbstractBrachinites are igneous, ultramafic and unbrecciated primitive achondrites mainly composed of olivine and pyroxene, with a partial melt residue or cumulate origin that is still debated. This study presents a petrological and microstructural study of 10 brachinite meteorites to identify igneous and deformation processes responsible for their formation. Detailed microstructural analyses were performed using secondary electron microscopy, electron probe microanalysis, and electron backscatter diffraction. The olivine‐spinel and two‐pyroxene closure temperatures of these brachinites ranged from 814 ± 27 to 909 ± 20°C. Olivine [001] axes coincide with the elongation of olivine grains and the crystallographic preferred orientations (CPO) of clinopyroxene [001] axes, which led us to infer lineation as olivine [001] axes parallel to X for all samples. Olivine CPO displays a strong or medium concentration of [001] axes parallel to X and [010] axes parallel to Z pointing to a B‐type fabric. Limited internal deformation of olivine grains and slip systems identified from low‐angle boundary misorientation analyses are inconsistent with the CPO and grain misorientation distributions are close to those found in untextured rocks. Olivine B‐type fabrics may therefore result not from plastic deformation but rather from rigid crystal rotation or preferential crystal growth during compaction. Olivine subgrain boundary misorientation axes imply limited activation of [001](100) and [100](001) slip systems, which could be due to primary plastic deformation during or after crystal settling. These new results reveal that brachinites developed a cumulate texture and accommodated only weak plastic deformation during early differentiation processes in the parent body.

Negative moment of inertia and rotational instability of gluon plasma

Using first-principle numerical simulations of the lattice SU(3) gauge theory, we calculate the isothermal moment of inertia of the rigidly rotating gluon plasma. We find that the moment of inertia unexpectedly takes a negative value below the “supervortical temperature” Ts=1.50(10)Tc, vanishes at T=Ts, and becomes a positive quantity at higher temperatures. The negative moment of inertia indicates a thermodynamic instability of rigid rotation. We derive the condition of thermodynamic stability of the vortical plasma and show how it relates to the scale anomaly and the magnetic gluon condensate. The rotational instability of gluon plasma shares a striking similarity with the rotational instabilities of spinning Kerr and Myers-Perry black holes.

Jahn-Teller effect with rigid octahedral rotations in perovskites

Jahn-Teller effect with rigid octahedral rotations in perovskites

Method of generating speckle patterns for digital image correlation based on modified Conway's Game of Life.

The measurement accuracy of digital image correlation (DIC) is influenced by the quality of the speckle pattern. Although various models for generating random speckle patterns have been well discussed, obtaining appropriate speckle images with isotropic quality and performance could be a challenging issue in DIC. In this paper, we propose a novel (to our knowledge) method for generating speckle patterns based on modified Conway's game of life (GoL). By sequentially assembling the speckle patterns generated from the modified GoL, we produced the GoL speckle image. Then, verification and comparison experiments were conducted through pure in-plane translations. The results show that the generated speckle image which was resized with k s=6& k r=2 processing and subsequently fuzzified using a Gaussian filter, produces the best accuracy for DIC measurement. Furthermore, based on the rigid body in-plane rotation displacement tests in the physical experimental results of three different speckle images, the GoL speckle generated from our proposed method shows the smallest measurement error. This indicates that the proposed speckle patterns generating method could provide a new type of speckle pattern with better quality and accuracy.

Investigating the dispersion characteristics of symmetric and asymmetric modes in rails: A theoretical and experimental study

The propagation law of ultrasonic guided waves in waveguide structures is determined by their dispersion characteristics, and the number of guided waves in symmetric and antisymmetric modes in rails is significant, so the dispersion characteristics are very complex. In order to study the dispersion characteristics of symmetric and antisymmetric modes in rails, this paper derives the wave equation based on the SAFE method with higher order elements, and the correctness of the wavestructure calculation in the SAFE model is verified using the FE method. This paper focuses on the wavestructure state at 0 kHz and the wavestructure changes during mode crossing through and repulsive deflections, and for the first time experimentally verifies the phenomenon of wave structure exchange in rails. The main conclusions are that the dispersion curves between modes with the same symmetry show repulsive deflection, and the dispersion curves between modes with opposite symmetry show crossover; the wavestructure of the rail is mainly rigid body translation and rigid body rotation at frequencies close to 0 kHz; the guided wave at the intersection of symmetric and antisymmetric modes transforms into a fading wave that cannot be continuously propagated in rails; when the dispersion curves are close, the wavestructures between the two modes are linearly superimposed, and when the dispersion curves are deflected by repulsion, the wavestructures of the two modes are exchanged.

Velocity gradient analysis of a head-on vortex ring collision

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics representing symmetries and discretization errors. Using the velocity gradient tensor and structural features of local streamlines, we characterize the evolution of the flow with a particular focus on its transition and turbulent decay. Transition is excited by the development of the elliptic instability, which grows during the mutual interaction of the rings as they expand radially at the collision plane. The development of antiparallel secondary vortex filaments along the circumference mediates the proliferation of small-scale turbulence. During turbulent decay, the partitioning of the velocity gradients approaches an equilibrium that is dominated by shearing and agrees well with previous results for forced isotropic turbulence. We also introduce new phase spaces for the velocity gradients that reflect the interplay between shearing and rigid rotation and highlight geometric features of local streamlines. In conjunction with our other analyses, these phase spaces suggest that, while the elliptic instability is the predominant mechanism driving the initial transition, its interplay with other mechanisms, e.g. the Crow instability, becomes more important during turbulent decay. Our analysis also suggests that the geometry-based phase space may be promising for identifying the effects of the elliptic instability and other mechanisms using the structure of local streamlines. Moving forward, characterizing the organization of these mechanisms within vortices and universal features of velocity gradients may aid in modelling turbulent flows.

Angular momentum and chemical transport by azimuthal magnetorotational instability in radiative stellar interiors

Context. The transport of angular momentum and chemical elements within evolving stars remains poorly understood. Asteroseismic and spectroscopic observations of low-mass main sequence stars and red giants reveal that their radiative cores rotate orders of magnitude slower than classical predictions from stellar evolution models and that the abundances of their surface light elements are too small. Magnetohydrodynamic (MHD) turbulence is considered a primary mechanism to enhance the transport in radiative stellar interiors but its efficiency is still largely uncertain. Aims. We explore the transport of angular momentum and chemical elements due to azimuthal magnetorotational instability, one of the dominant instabilities expected in differentially rotating radiative stellar interiors. Methods. We employed 3D MHD direct numerical simulations in a spherical shell of unstratified and stably stratified flows under the Boussinesq approximation. The background differential rotation was maintained by a volumetric body force. We examined the transport of chemical elements using a passive scalar. Results. We provide evidence of magnetorotational instability for purely azimuthal magnetic fields in the parameter regime expected from local and global linear stability analyses. Without stratification and when the Reynolds number Re and the background azimuthal field strength are large enough, we observed dynamo action driven by the instability at values of the magnetic Prandtl number Pm in the range 0.6 − 1, which is the smallest ever reported in a global setup. When considering stable stratification at Pm = 1, the turbulence is transitional and becomes less homogeneous and isotropic upon increasing buoyancy effects. The transport of angular momentum occurs radially outward and is dominated by the Maxwell stresses when stratification is large enough. We find that the turbulent viscosity decreases when buoyancy effects strengthen and scales with the square root of the ratio of the reference rotation rate Ωa to the Brunt–Väisälä frequency N. The chemical turbulent diffusion coefficient scales with stratification similarly to the turbulent viscosity, but is lower in amplitude so that the transport of chemicals is slower than the one of angular momentum, in agreement with recent stellar evolution models of low-mass stars. Conclusions. We show that the transport induced by azimuthal magnetorotational instability scales somewhat slowly with stratification and may enforce rigid rotations of red giant cores on a timescale of a few thousand years. In agreement with recent stellar evolution models of low-mass stars, the instability transports chemical elements less efficiently than angular momentum.

Investigation of neighboring grain effects on load shedding in titanium alloys under cold dwell fatigue

Load shedding under cold dwell fatigue in titanium alloys has been a threat to the safety of the aero-engine since it is responsible for crack formation. The strain incompatibility between the soft-hard grain pair arises from the significant creep in the soft grain during the dwell period, which is fundamentally related to the load shedding. Such deformational heterogeneity is not only affected by the soft-hard grain itself but also by its neighboring grains, but the effect of the latter is rarely reported. In this paper, the effect of neighboring grains, including location, crystal orientation, texture, etc., on load shedding is quantitatively investigated using a three-dimensional rate-dependent crystal plasticity model by controlling the microstructural morphology of the grains. In particular, the mechanism that the dwell fatigue cracks tend to nucleate from the sample's interior rather than the free surface is revealed. Restriction of rigid body rotation from neighboring grains can further enhance load shedding. The crystal orientation of individual and group neighboring grains sitting at different locations with respect to the soft-hard grain pair is evaluated. The grain directly attached to the hard grain has the strongest influence. The statistics of load shedding are analyzed by conducting hundreds of simulations with different textures. Stronger textures are found to be able to enhance load shedding and thus deteriorate the service lifetime. The change of locations showing the highest stress during the dwell period arising from plastic deformation in neighboring grain may lead to the phenomenon of reverse load shedding. Understanding the neighboring grain effects from both the mechanistic basis and the statistical point of view is important in integrity evaluations and service life assessments of titanium components in aero-engines.

Perceptual transitions between object rigidity and non-rigidity: Competition and cooperation among motion energy, feature tracking, and shape-based priors.

Why do moving objects appear rigid when projected retinal images are deformed non-rigidly? We used rotating rigid objects that can appear rigid or non-rigid to test whether shape features contribute to rigidity perception. When two circular rings were rigidly linked at an angle and jointly rotated at moderate speeds, observers reported that the rings wobbled and were not linked rigidly, but rigid rotation was reported at slow speeds. When gaps, paint, or vertices were added, the rings appeared rigidly rotating even at moderate speeds. At high speeds, all configurations appeared non-rigid. Salient features thus contribute to rigidity at slow and moderate speeds but not at high speeds. Simulated responses of arrays of motion-energy cells showed that motion flow vectors are predominantly orthogonal to the contours of the rings, not parallel to the rotation direction. A convolutional neural network trained to distinguish flow patterns for wobbling versus rotation gave a high probability of wobbling for the motion-energy flows. However, the convolutional neural network gave high probabilities of rotation for motion flows generated by tracking features with arrays of MT pattern-motion cells and corner detectors. In addition, circular rings can appear to spin and roll despite the absence of any sensory evidence, and this illusion is prevented by vertices, gaps, and painted segments, showing the effects of rotational symmetry and shape. Combining convolutional neural network outputs that give greater weight to motion energy at fast speeds and to feature tracking at slow speeds, with the shape-based priors for wobbling and rolling, explained rigid and non-rigid percepts across shapes and speeds (R2 = 0.95). The results demonstrate how cooperation and competition between different neuronal classes lead to specific states of visual perception and to transitions between the states.

DIC technique for experimental validation of higher order numerical models

This paper presents an adaptation to the Digital Image Correlation (DIC) technique to aid and improve standard measurement methods in experimental mechanics. The practical application is demonstrated by the validation of the Cosserat Continuum model, using small-scale masonry specimens. Numerical models, such as the Cosserat continuum, play an important role in the identification and description of the mechanical behaviour of structures. Especially when it comes to anisotropic and quasi-brittle materials like masonry, these models are needed to evaluate significant aspects like performance, safety, or the effects of various strengthening interventions. The experimental investigation to validate a numerical model is not always straightforward and several of them remain theoretical. Addressing this, the experimentation presented in this paper evaluates the Cosserat identification in shear, where along with simple shear deformation, rigid rotations, micro rotations and micro couples are also exhibited. With such complex deformations, conventional techniques, such as strain gauges, or extensometers can no longer be adopted. The adapted DIC allows the quantification of these deformation data and validates the numerical model.

A unified bond–based peridynamic model without limitation of Poisson's ratio

The issue of fixed Poisson's ratio is a critical problem plaguing bond–based peridynamic (BB–PD) models. The popular approach of introducing the bond's tangential stiffness cannot completely remove Poisson's ratio limitation, but instead leads to some additional troubles, such as negative tangential stiffness and bond force density misalignment in finite rigid body rotation problems. To address the issue of fixed Poisson's ratio thoroughly, a unified bond–based peridynamics (UPD) was originally proposed. In the proposed model, a novelty pairwise force density function has been developed, in which dilatation and distortion are distinguished, and the model assigns different stiffnesses to the two deformation components. Arbitrary and reasonable values of Poisson's ratio can be achieved by adjusting the PD parameters that control the bulk and shear moduli of the material. The theoretical range of Poisson's ratio in the proposed model is (-1, 0.5], which is consistent with those in continuum mechanics. In addition, the absence of tangential stiffness prevents the proposed model from misalignment of bond force density due to rigid body rotation. Several numerical examples, including four two–dimensional and three–dimensional deformation analyses and three quasi–static fracture analyses, were implemented to verify the accuracy and reliability of the proposed model. The results show that the proposed model can accurately simulate the elastic properties of the material and obtain the deformation with high accuracy. The numerical examples also demonstrate the fracture prediction capability of the proposed model.