Rotational Dynamics Research Articles

Three-dimensional configuration tip rotor dynamics analysis

Abstract In order to analyze and study the dynamic characteristics of the 3D blade tip rotor, an aeroelastic dynamic model for a complex 3D blade tip rotor is established based on mechanics principles. The theory of medium deformation beam or large deformation beam is adopted as the blade structural dynamic model, and the quasi-steady and unsteady aerodynamic models (ONERA model) are adopted as the aerodynamic model. The rotor dynamics, aeroelastic stability and rotor loads of three-dimensional blade tip and rectangular blade tip are compared by examples. The analysis shows that both the forward and backward sweep angles have a certain effect on the rotor blade frequency, but the downward dihedral angle has little effect. The 3D tip configuration has the greatest influence on torsion mode frequency, followed by lagging mode frequency, which has little impact on flapping frequency. Reasonable design of forward and backward sweep angles and downward dihedral angles of 3D tip configuration can effectively reduce rotor loads, increase damping margin for aeroelastic stability, and improve stability.

Temperature-Dependent Rotational Dynamics of a Polar Probe in Non-Polar Aprotic Solvents: Interplay of Solvent Viscosity and Size Effect.

Rotational dynamics of 3-(benzo[d]thiazol-2-yl)-7-(diethylamino)-2H-chromen-2-one (3BT7D2H-one) probe in non-polar aprotic 1,4 dioxane, toluene and cyclohexane solvents of different and comparable viscosity are studied with varying temperature using steady-state and fluorescence depolarization technique. The experimental reorientation time is compared with the hydrodynamic Stoke's-Einstein-Debye(SED). The experimentally measured rotational reorientation times are higher in 1,4 dioxane attributed to its solvent viscosity. In cyclohexane, the solute rotational dynamics behavior shows a transition from sub-slip to SED slip boundary conditions with varying temperatures. Solvent viscosity, size, and subtle changes in the molecular shape of solute play an important role in the rotational dynamics of polar probes in non-polar aprotic solvents.

Effective extensional-torsional elasticity and dynamics of helical filaments under distributed loads

We study slender, helical elastic rods subject to distributed forces and moments. Focussing on the case when the helix axis remains straight, we employ the method of multiple scales to systematically derive an ‘equivalent-rod’ theory from the Kirchhoff rod equations: the helical filament is described as a naturally-straight rod (aligned with the helix axis) for which the extensional and torsional deformations are coupled. Importantly, our analysis is asymptotically exact in the limit of a ‘highly-coiled’ filament (i.e., when the helical wavelength is much smaller than the characteristic lengthscale over which the filament bends due to external loading) and is able to account for large, unsteady displacements. In addition, our analysis yields explicit conditions on the external loading that must be satisfied for a straight helix axis. In the small-deformation limit, we exactly recover the coupled wave equations used to describe the free vibrations of helical coil springs, thereby justifying previous equivalent-rod approximations in which linearised stiffness coefficients are assumed to apply locally and dynamically. We then illustrate our theory with two loading scenarios: (I) a heavy helical rod deforming under its own weight; and (II) the dynamics of axial rotation (twirling) in viscous fluid, which may be considered as a simple model for a bacteria flagellar filament. In both scenarios, we demonstrate excellent agreement with solutions of the full Kirchhoff rod equations, even beyond the formal limit of validity of the ‘highly-coiled’ assumption. More broadly, our analysis provides a framework to develop reduced models of helical rods in a wide variety of physical and biological settings, and yields analytical insight into their elastic instabilities. In particular, our analysis indicates that tensile instabilities are a generic phenomenon when helical rods are subject to a combination of distributed forces and moments.

Modal characteristics analysis of a variable-speed pump-turbine rotor system: a perspective of resonance

Abstract The safety and stability of the rotor system is crucial to the pump-turbine unit. The present paper analyzed the modal characteristics of a variable-speed pump-turbine rotor system based on the rotor dynamics theory and FEM method. The results show that the bending mode of the rotor system exhibits the forms of forward whirling (FW) and backward whirling (BW). The added mass effect will reduce the natural frequency of the rotor system, and it is more obvious for the torsional mode Torsional 1. In addition, the critical speed analysis shows that both the critical speed of the dry mode and wet mode of the rotor system is greater than 700rpm, which proves the safety of the unit. The results of the analysis can be used as a reference for the optimized design of similar variable-speed pump-turbine rotor system, which is conducive to the improvement of the reliability and life of the rotor system.

A thermal flexible rotor dynamic modelling for rapid prediction of thermo-elastic coupling vibration characteristics in non-uniform temperature fields

The flexible rotors within aero-engines operate in complex thermal environments, where temperature influences both the vibration frequency and amplitude. This study establishes a simple thermal flexible rotor dynamics model to rapidly and precisely predict thermo-elastic coupling vibration characteristics within a non-uniform temperature field. The thermal potential energy of the thermal rotor element is derived for any temperature field, and the motion equation is obtained using the Euler-Lagrange equation. Specifically, the generalized vector of an arbitrary point and cross-sectional non-uniform thermal stress of the thermal rotor element are considered in the thermal potential energy. The model's frequency error is less than 1% under identical boundary conditions. Numerical findings indicate that thermal stress, temperature-dependent material properties, and the coupling effect collectively reduce the natural frequency (NF), with thermal stress having a more pronounced impact under axial constraint. Additionally, thermal stress and material decrease the amplitude across a broad range of rotation speeds, contrasting with thermal bending. This model will play a key role in the iterative calculation of thermo-elastic coupling vibration control due to its accuracy and simplicity.

Rapid Interpretation of Protein Backbone Rotation Dynamics Directly from Spin Relaxation Data.

Besides their structure, dynamics is pivotal for protein functions, particularly for intrinsically disordered proteins (IDPs) that do not fold into a fixed 3D structure. However, the detection of protein dynamics is difficult for IDPs and other disordered biomolecules. NMR spin relaxation rates are sensitive to the rapid rotations of chemical bonds, but their interpretation is arduous for IDPs or molecular assemblies with a complex dynamic landscape. Here we demonstrate numerically that the dynamics of a wide range of proteins, from short peptides to partially disordered proteins and peptides in micelles, can be characterized by calculating the total effective correlation times of protein backbone N-H bond rotations, τeff, from experimentally measured transverse 15N spin relaxation rates, R2, using a linear relation. Our results enable the determination of magnetic-field-independent and intuitively understandable parameters describing protein dynamics at different regions of the sequence directly from experiments. A practical advance of the approach is demonstrated by analyzing partially disordered proteins in which rotations of disordered regions occur with timescales of 1-2 ns, independent of their size, suggesting that rotations of disordered and folded regions are uncoupled in these proteins.

Research on flow-induced radiated noise of twin-screw pumps based on the Lighthill acoustic analogue theory

Abstract To optimize the control of twin-screw pumps (TSP), it is essential to ensure performance while simultaneously preventing noise levels from exceeding specified limits. In order to investigate the flow characteristics and the mechanism of flow-induced radiated noise under various operating conditions, a coupled numerical simulation approach using Computational Fluid Dynamics (CFD) and Computational Acoustics (CA) was employed, and the findings were validated through experiments. The study reveals that the highest sound pressure levels of radiated noise occur near the rotor outlet surface, and the dynamic-static interference at the rotor-boundary interface is the primary cause of flow-induced noise in TSP. The flow-induced noise in TSP exhibits dipole characteristics, with the overall sound pressure level gradually increasing and then sharply rising with the increase in rotational speed (or flow rate). It stabilizes near the design operating point and continues to increase steadily with further increases in rotational speed (or flow rate). Modal testing using a dual-distributed measurement technique highlights significant interference effects between the rotor inlet and the dynamic rotor for the first two Blade Passing Frequencies (BPF) in TSP. The results of this study provide a theoretical foundation for the low-vibration and low-noise design and operation of TSP.

Probabilistic Analysis of Orbital Characteristics of Rotary Systems with Centrally and Off-Center Mounted Unbalanced Disks

Rotor dynamics plays a crucial role in the performance and safety of rotating machinery, with disk position and unbalance significantly impacting system behavior. This study investigates the dynamic characteristics of two rotor configurations: a centrally mounted unbalanced disk (Rotor05un) and an off-center unbalanced disk (Rotor025un). Using numerical simulations and Monte Carlo analysis, we examined critical speeds and orbital patterns for both configurations. Probability distributions of shaft orbital positions revealed distinct patterns for each configuration. Quantile analysis revealed approximate linear trends for Rotor025un, suggesting higher system stiffness and more predictable behavior near critical speeds. Cross-sectional analyses of the orbits provided insights into the complex interactions between disk position, gyroscopic effects, and system natural frequencies. These findings provide valuable insights for rotor system design, particularly for applications with non-ideal mass distributions. The study goes beyond traditional critical speed analysis to examine orbital patterns and point on orbit occurrence from a probabilistic perspective. Based on the simulation of the orbits, an orbital is determined that allows the probability of the shaft occurring at the analyzed distance from the origin to be determined. The paper also offers insights into the complex interaction behavior of chosen rotor configurations and highlights the importance of considering disk position in predicting and optimizing rotor dynamic behavior, contributing to the development of more robust and efficient rotating machinery.

Molecular influence on nuclear-quadrupole-coupling effects in laser induced alignment.

We computationally studied the effect of nuclear-quadrupole interactions on the field-free impulsive alignment of different asymmetric-top molecules. Our analysis is focused on the influence of the hyperfine- and rotational-energy-level structures. These depend on the number of nuclear spins, the rotational constants, and the symmetry of the tensors involved in the nuclear spin and external field interactions. Comparing the prototypical large-nuclear-spin molecules iodobenzene, 1,2-diiodobenzene, 1,3-diiodobenzene, and 2,5-diiodobenzonitrile, we demonstrate that the magnitude of the hyperfine splittings compared to the rotational-energy splittings plays a crucial role in the spin-rotational dynamics after the laser pulse. Moreover, we point out that the impact of the quadrupole coupling on the rotational dynamics decreases when highly excited rotational states dominate the dynamics.

Effect of Temperature on Rotational Dynamics of 3BT7D2H-one in Acetone and Ethyl Acetate Solvents.

The rotational dynamics of 3-(benzo[d]thiazol-2-yl)-7-(diethylamino)-2H-chromen-2-one (3BT7D2H-one) in two non-polar solvents acetone and ethyl acetate have been studied with varying temperatures. The rotational dynamics follow follows the Stoke's-Einstein-Debye (SED) model in ethyl acetate solvent but shows deviation in acetone solvent when temperature is increased. Quasi-hydrodynamic models Gierer and Wirtz (GW) model and Dote-Kivelson Schwartz (DKS) is studied in a qualitatively way.

Ideal Collision Rate of Symmetric Hexapods in a Simple Shear Flow.

An ideal collision rate (ICR) is defined as the average rate of contact between two particles that translate and rotate with the imposed fluid flow in the absence of interparticle interactions. ICR in a simple shear flow provides an estimate of the collision rate in a flowing dilute particle suspension, and its value is known only for traditional convex shapes such as spheres and cylinders. In this work, we compute the ICR for a family of symmetric hexapods (shown in Figure 1) that are particles composed of three orthogonal cylinders with coinciding centers (forming six arms) with at least two cylinders having the same length. We employed the finite-element method to obtain the rotational dynamics of hexapods and Monte Carlo simulations to calculate their ICR. Our results indicate that the ICR for hexapods is not directly proportional to the volume of the particle, in contrast to what is observed for convex shapes such as spheres and cylinders. For hexapods of the same size, the ICR could be similar for particles with order-of-magnitude differences in their volumes and it could also vary by an order of magnitude for particles with similar volumes. Specifically for hexapods termed branched fibers, which have one longer cylinder, the ICR changes by an order of magnitude even when the shorter cylinders are significantly smaller than the longer cylinder. This change is attributed to the increase in the tumbling frequency of the particle due to hydrodynamic forces acting on the shorter arms, in addition to the increased probability of collision afforded by them. Using asymptotic theory for high-aspect ratio cylinders, we showed that the tumbling period of hexapods was proportional to an algebraic power of the ratio of its arm lengths and has a weaker logarithm relationship with the aspect ratio of its arms. The collision cross-section provided the relative cross-streamline particle separations for the most likely binary collisions in the suspensions, and its value was sensitive to the arm lengths, as well. The collision rate of hexapods also could not be estimated within an order of magnitude from existing geometric models, such as the ICR of a circumscribing convex shape, ICR for one of the individual cylinders of the hexapod, or using the particle volume times the shear rate. Our work indicates that collision rate for non-convex particles in shear flows critically depends on the shape of the particle due to nontrivial changes in the particle's orientational dynamics, and the ICR calculation serves as a more reliable method for estimating their true collision rates in the suspension.

Site Disorder Drives Cyanide Dynamics and Fast Ion Transport in Li6PS5CN.

Halide argyrodite solid-state electrolytes of the general formula Li6PS5 X exhibit complex static and dynamic disorder that plays a crucial role in ion transport processes. Here, we unravel the rich interplay between site disorder and dynamics in the plastic crystal argyrodite Li6PS5CN and the impact on ion diffusion processes through a suite of experimental and computational methodologies, including temperature-dependent synchrotron powder X-ray diffraction, AC electrochemical impedance spectroscopy, 7Li solid-state NMR, and machine learning-assisted molecular dynamics simulations. Sulfide and (pseudo)halide site disorder between the two anion sublattices unilaterally improves long-range lithium diffusion irrespective of the (pseudo)halide identity, which demonstrates the importance of site disorder in dictating bulk ionic conductivity in the argyrodite family. Furthermore, we find that anion site disorder modulates the presence and time scales of cyanide rotational dynamics. Ordered configurations of anions enable fast, quasi-free rotations of cyanides that occur on time scales of 1011 Hz at T = 300 K. In contrast, we find that cyanide dynamics are slow or frozen in Li6PS5CN when site disorder between the cyanide and sulfide sublattices is present at T = 300 K. We rationalize the observed differences in cyanide dynamics in the context of elastic dipole interactions between neighboring cyanide anions and local strain induced by the configurations of site disorder that may impact the energetic landscape for cyanide rotational dynamics. Through this study, we find that anion disorder plays a decisive role in dictating the extent and time scales of both lithium ion and cyanide dynamics in Li6PS5CN.

Molecular-Scale Interactions in the Choline Chloride-Ethylene Glycol Deep Eutectic Solvent System: The Importance of Chromophore Charge in Mediating Rotational Dynamics.

We report on the rotational diffusion dynamics of three chromophores (disodium fluorescein, oxazine 725, and perylene) in a series of choline chloride-ethylene glycol (ChCl:EG) deep eutectic solvent (DES) systems. We observe behavior independent of DES bulk viscosity for the cationic and neutral probes and behavior that is consistent with stick-limit interactions for the modified Debye-Stokes-Einstein model for the anionic probe. This finding indicates that the anionic species is integral to the interactions between DES constituent species that are responsible for local organization, consistent with previous MD simulations that showed higher interaction energies associated with both the hydrogen bond donor (EG) and hydrogen bond acceptor (Ch+) interactions with Cl- in ChCl:EG mixtures. The reorientation data reported here also indicate a region around 15 mol % ChCl where the stoichiometric relationship between the species gives rise to changes in the details of intermolecular interactions.

Celestial Mechanics: The Non-Stability of The Newtonian Model

Multiple researchers and the three-body problem highlight a potential instability in the Classic model of the Solar System, indicating a possible fundamental instability in the system's dynamics. Therefore, we consider that the Classical model does not reflect reality, and we propose an alternative model that we call: Theory of Dynamic Interactions, providing a brief exposition of the studies carried out by Advanced Dynamics, until defining a Rotational Dynamics of Interactions, applicable to bodies subjected to multiple pairs of successive non-coaxial forces.

Modeling and control of perturbation torques and mass distribution impact on a tethered system for a 12U CubeSat in sun-synchronous orbit

Tethered CubeSat systems are characterized by momentum exchange and gravity gradient stabilization, and encounter stability challenges, especially with shorter tethers in highly inclined and eccentric orbits. This study investigates the libration dynamics of a 12U CubeSat in its stowed configuration, which separates into two satellites connected via tether, throughout its deployment, station-keeping, and retrieval phases. Two deployed configurations, symmetrical 6U-6U, and asymmetrical 8U-4U connected by a non-conductive tether with a maximum length of 100m are analyzed. The study accounts for perturbations including Earth’s oblateness, atmospheric drag, solar radiation pressure, and lunisolar gravitation, modeling the tether as a rigid, extendable rod and the satellites as lumped masses. The translational and rotational dynamics are decoupled, assuming the system’s center of mass follows an unperturbed Keplerian Sun-synchronous orbit at altitudes between 400 and 600km. A tension control strategy based on Lyapunov’s direct method and supplemented by external actuation torques is explored. Results show high orbit eccentricity significantly affects the maximum in-plane libration angle. The 6U-6U system experiences smaller disturbance torques but greater tether tension variations than the 8U-4U system. Both configurations exhibit larger in-plane oscillations compared to near-zero out-of-plane oscillations, nonetheless, eclipse passages exacerbate the out-of-plane libration of the 8U-4U system. Relative stability is maintained during deployment, however, retrieval is chaotic, with notable oscillations in libration angles and tether tension. The tension control strategy effectively dampens oscillations during retrieval but loses effectiveness as tether tension approaches zero at retrieval’s conclusion. External actuation torques, ranging from 1-2mNm for deployment to 15mNm for retrieval, complement tension control.

A comprehensive review on crack detection schemes and modelling techniques in high-speed rotor systems

ABSTRACT The combination of a rotor and bearings plays a pivotal role in various industrial applications, including gas turbines, compressors, turbochargers, aircraft engines, and wind generators. Ensuring the structural integrity of the rotor-bearing assembly during static and dynamic conditions is most important, as any failure could lead to unpredictable losses. Due to their continuous operation, high-speed rotors are more susceptible to faults such as misalignment, bow, eccentricity, and cracks. Among these faults, cracks are the most predominant fault that affects the system’s reliability. Despite significant advancements in rotor dynamics, cracks still threaten the integrity and performance of the rotor-bearing assembly. This review paper aims to thoroughly review the challenges and issues associated with crack formation in high-speed rotor systems. Various crack detection methods are also explored using vibration signals obtained from the rotor-bearing unit and their associated processing techniques. This study also gives an extensive overview of different crack modelling and analysis techniques. Furthermore, a novel rotor-bearing model is modelled using the finite element method, and the numerical results obtained from this model are validated with the existing literature model. This review paper will serve as a valuable resource for researchers that offers insights into the latest advancements and emphasises the importance of crack detection for ensuring the reliability of high-speed rotor systems.

Characterizing Rotational Dynamics and Heterogeneity via Single-Molecule Intensity Measurements.

Dynamic heterogeneity in glassy systems has typically been characterized at the single-molecule level by extracting rotational relaxation time scales from linear dichroism (LD) collected via two orthogonally polarized channels. However, in such measurements, localization precision is diminished due to photons lost relative to collection in a single detection channel. This poses challenges in characterizing rotational and translational dynamics simultaneously, as translational measurements require high localization precision. In this paper, we present a method for extracting rotational dynamics of glassy systems at the single-molecule level from intensity fluctuations of fluorescent probe molecules in a wide-field configuration without the use of a polarizing optical component. Through numerical analysis, we show that LD and intensity measurements probing rotational dynamics report similar, approximately second-order rotational correlation decays even at low signal to noise. Thus, within the assumptions of small, isotropic rotations, LD and intensity autocorrelation analysis should provide identical information on the time scale and heterogeneity of rotational dynamics. We then present experimental results that validate this numerical result, with direct comparison of LD and intensity-based approaches across probe molecules in both polymeric and small-molecule glass formers as well as across optical configurations. Our results demonstrate moderate correlation on a per-probe basis between rotational time scales obtained from both approaches, with deviations consistent with those expected in a dynamically heterogeneous system. We envision that this easily accessible strategy will be of use across disciplines for characterizing single-molecule rotational dynamics in limited signal situations and/or when high-precision localization is required.

Conformational Control of Donor-Acceptor Molecules Using Non-covalent Interactions.

Controlling the architecture of organic molecules is an important aspect in tuning the functional properties of components in organic electronics. For purely organic thermally activated delayed fluorescence (TADF) molecules, design is focused upon orthogonality orientated donor and acceptor units. In these systems, the rotational dynamics around the donor and acceptor bond has been shown to be critical for activating TADF; however, too much conformational freedom can increase the non-radiative rate, leading to a large energy dispersion of the emitting states and conformers, which do not exhibit TADF. To date, control of the motion around the D-A bond has focused upon steric hindrance. In this work, we computationally investigate eight proposed donor-acceptor molecules, exhibiting a B-N bond between the donor and acceptor. We compare the effect of steric hindrance and noncovalent interactions, achieved using oxygen (sulfur) boron heteroatom interactions, in exerting fine conformational control of the excited state dynamics. This work reveals the potential for judiciously chosen noncovalent interactions to strongly influence the functional properties of TADF emitters, including the accessible conformers and the energy dispersion associated with the charge transfer states.

The elliptope and bounds in the rotational dynamics of rigid bodies

The elliptope and bounds in the rotational dynamics of rigid bodies

Vibrational and stability analysis of planar double pendulum dynamics near resonance

AbstractThe focus of this paper is to examine the motion of a novel double pendulum (DP) system with two degrees of freedom (DOF). This system operates under specific constraints to follow a Lissajous curve, with its pivot point moving along this path in a plane. The nonlinear differential equations governing this system are derived using Lagrange's equations. Their analytical solutions (AS) are subsequently calculated using the multiple-scales method (MSM), which provides higher-order approximations. These solutions are considered new, as the traditional MSM has been applied to this novel system for the first time. Additionally, the accuracy of these solutions is validated through numerical results obtained using the fourth-order Runge–Kutta method. The solvability conditions and characteristic exponents are determined based on resonance cases. The Routh–Hurwitz criteria (RHC) are employed to assess the stability of the fixed points corresponding to the steady-state solutions. They are also used to demonstrate the frequency response curves. The nonlinear stability analysis is performed by examining the stability and instability ranges. Resonance curves and time history plots are presented to analyze the behavior of the system for specific parameter values. The investigation delves into a comprehensive analysis of bifurcation diagrams (BDs) and Lyapunov exponent spectra (LEs), aiming to uncover the various types of motion present within the system. Systematic examination of these charts reveals critical insights into transitions between stable, quasi-stable, and chaotic dynamical behaviors. This work has practical applications in various fields, such as robotics, pump compressors, rotor dynamics, and transportation devices. It can be used to study the vibrational motion of these systems.