Synchronous Rotation Research Articles

Europa's hemispheric color dichotomy as a constraint on non-synchronous rotation

Europa's surface reflectance exhibits a pronounced hemispheric dichotomy, which is hypothesized to form due to enhanced irradiation of the trailing hemisphere by energetic particles entrained in the jovian magnetosphere. We propose that this pattern can only persist if the timescale for discoloration is much shorter than that of Europa's rotation relative to the synchronous state, and provide a means for constraining the rotation rate using the observed color pattern. By decomposing the longitudinal ultraviolet and visible color variations from Voyager data into sine and cosine terms, we find no detectable signature of non-synchronous rotation (NSR). This same conclusion is reached with two observational models of discoloration: one representing an actively discoloring surface, and the other assuming that the present-day exogenic discoloration on the surface is in steady-state. Magnitudes of the expected signature are presented as functions of the age of the crater Pwyll, which is used to constrain the timescale of discoloration. Furthermore, we develop a physical model of discoloration to validate the geometric models, producing consistent results. The failure to identify a signature of NSR using Europa's hemispheric color dichotomy magnifies the outstanding problem of the origin of the stress to explain Europa's pervasive tectonic features.

Physical modelling of the circumstellar material in the early-type active binary HH Carinae

ABSTRACT High-resolution spectra ($R\sim 48\, 000$) of the massive binary system HH Carinae have been analysed. Precise absolute parameters were derived from a simultaneous solution of the radial velocities and the light curves. The primary component is found to be an O9-type main-sequence star with a temperature of 33 500 K, while the secondary component is a B0-type giant/subgiant star with a temperature of 27 500 K. An analysis of the spectroscopic and photometric data has shown that the primary component rotates at a speed of vrot1 = 220 km s−1, which is three times faster than the synchronous rotation, while the secondary component synchronously rotates with the orbit at a speed of vrot2 = 150 km s−1. The distance to the system and the velocity of the centre of mass are determined as d = 4.6 ± 0.8 kpc and Vγ = –16 km s−1, respectively. The distance of the system is in agreement with the most probable Gaia distance of $4.9^{+0.9}_{-0.7}$ kpc and the distance in the latest data release (DR3) of 4.4 ± 0.3. Emission structures at the Hα region were modelled using the code shellspec where the derived absolute parameters of the components have been considered. Because the components are massive stars, mass loss as a result of stellar winds is expected. Produced models confirm that the components do indeed have strong stellar winds and there is mass transfer from the secondary to the primary. Stellar winds and the gas stream between the components have been modelled as a hot shell around the system, with a temperature of ∼22 000 K. Models also indicate that the interaction between the wind and the gas stream causes the formation of a high-temperature (100 000 K) impact region.

Obliquity, Precession, and Fracture Mechanics: Implications of Europa's Global Cycloid Population

AbstractWe catalog the global inventory of Europa's cycloids, arcuate fractures whose paths have been linked to diurnal tidal stress, and use the locations and orientations of their cusps to further test the formation mechanism of cycloids and constrain Europa's rotation state. We find that the global distribution of cycloids is better explained by a precessing spin pole than longitude translation due to nonsynchronous rotation, which is consistent with studies of Europa's strike‐slip faults and linear fractures. We also find that a small obliquity can reproduce the orientations of most cycloid cusps at their current locations, outperforming a model using stress from eccentricity alone. Matching cycloid locations and cusp orientations under these conditions implies a variable failure threshold and that most cusps form at stresses that are 50%–90% of the local peak tidal stress, suggesting that periodic deformation is causing failure through fatigue. The fact that cycloids are not observed in some regions, despite the low failure stresses implied by some cusp orientations, suggests an additional control on cusp formation that was not included in our simplified model. We hypothesize that the larger amplitude of tidal stress in some regions leads to fatigue‐induced failure after fewer tidal cycles, leading to a build‐up of cycloids in those regions. Why more linear fractures do not seem limited in location or density is still unknown. More physically informed constraints on how ice fails under low, periodic deformation and across generations of fractures would be helpful in interpreting Europa's cycloids.

Numerical simulation analysis of die ring spinning process

Aiming at the technical challenge of spinning forming used for ultra long tubular parts, a new spinning technology based on floating die and synchronous rotation of both ends of the spinning blank was put forward. That is die ring spinning, which is divided into die ring forward spinning and die ring backward spinning. The die ring spinning utilizes to improve the stress condition of deformed metal parts and enhances the fluidity of crystal phase structure along the slip surface. It can not only eliminate the phenomenon of material bulging before spinning wheels, but also improve the straightness and reduce the ellipticity of pipes at the same time.

Acoustic black-hole bombs and scalar clouds in a photon-fluid model

Massive bosonic fields in the background of a Kerr black hole can either trigger superradiant instabilities (black-hole bombs) or form equilibrium configurations corresponding to pure bound states, known as stationary scalar clouds. Here, similar phenomena are shown to emerge in the fluctuation dynamics of a rotating photon-fluid model. In the presence of suitable vortex flows, the density fluctuations are governed by the massive Klein-Gordon equation on a ($2+1$) curved spacetime, possessing an ergoregion and an event horizon. We report on superradiant instabilities originating from quasibound phonon states trapped by the vortex background and, remarkably, on the existence of stationary modes in synchronous rotation with the horizon. These represent the acoustic counterpart of astrophysical scalar clouds. Our system offers a promising platform for analogue gravity experiments on superradiant instabilities of massive bosons and black-hole-field equilibrium configurations.

Formation and dynamics of water clouds on temperate sub-Neptunes: the example of K2-18b

Context. Hubble Space Telescope (HST) spectroscopic transit observations of the temperate sub-Neptune K2-18b were interpreted as the presence of water vapour with potential water clouds. 1D modelling studies also predict the formation of water clouds in K2-18b’s atmosphere in some conditions. However, such models cannot predict the cloud cover, which is driven by atmospheric dynamics and thermal contrasts, and thus neither can they predict the real impact of clouds on spectra. Aims. The main goal of this study is to understand the formation, distribution, and observational consequences of water clouds on K2-18b and other temperate sub-Neptunes. Methods. We simulated the atmospheric dynamics, water cloud formation, and spectra of K2-18b for a H2-dominated atmosphere using a 3D general circulation model. We analysed the impact of atmospheric composition (with metallicity from 1× solar to 1000× solar), concentration of cloud condensation nuclei, and planetary rotation rate. Results. Assuming that K2-18b has a synchronous rotation, we show that the atmospheric circulation in the upper atmosphere essentially corresponds to a symmetric day-to-night circulation with very efficient heat redistribution. This regime preferentially leads to cloud formation at the sub-stellar point or at the terminator. Clouds form at metallicity ≥100× solar with relatively large particles (radius = 30–450 μm). At 100–300× solar metallicity, the cloud fraction at the terminators is small with a limited impact on transit spectra. At 1000× solar metallicity, very thick clouds form at the terminator, greatly flattening the transit spectrum. The cloud distribution appears very sensitive to the concentration of cloud condensation nuclei and to the planetary rotation rate, although the impact on transit spectra is modest in the near-infrared. Fitting HST transit data with our simulated spectra suggests a metallicity of ~100–300× solar, which is consistent with the mass-metallicity trend of giant planets in the Solar System. In addition, we found that the cloud fraction at the terminator can be highly variable in some conditions, leading to a potential variability in transit spectra that is correlated with spectral windows. This effect could be common on cloudy exoplanets and could be detectable with multiple transit observations. Finally, the complex cloud dynamics revealed in this study highlight the inherent 3D nature of clouds shaped by couplings between microphysics, radiation, and atmospheric circulation.

Thread turn milling simulation

The study shows that the high-performance thread turn-milling process with a synchronous rotation of the helical milling cutter and the workpiece is not widely adopted since there are no reliable methods to estimate the organic thread formation errors. The thread is machined as an envelope curve along the elementary surfaces of each cut shifted along the workpiece axis by a fraction of the thread pitch inversely proportional to the number of the cutter teeth. Domestic and international researchers tried to analytically estimate the thread formation errors at the part face. Such an approach failed to produce acceptable results since thread turn-milling is a three-dimensional process. We analyzed the thread formation errors in 3D using COMPAS 3D CAD system and developed a simulation model. We modelled a reference 3D thread machined on the workpiece; a 3D resulting thread; a single cutter tooth path in the plane perpendicular to the workpiece axis; 3D cut by a single cutter tooth. We also simulated the entire process and made a 3D model of the machining errors by subtracting the reference part geometry from the 3D thread model, and estimated the errors. The results were checked for consistency (max deviations) and acceptability for each dimension. The undercut dimensions were obtained by subtracting the 3D part model from the 3D reference model. Conversely, the overcut dimensions were obtained by subtracting the 3D reference model from the 3D part model.

Direct Power Control Strategy for Three-phase Vienna Rectifier

Firstly, through a detailed analysis of the working principle of the voltage-type Vienna rectifier, the mathematical model of the rectifier power control is established according to the mathematical model of the Vienna rectifier based on the equivalent switch function in the d-q two-phase synchronous rotation coordinate system. Secondly, according to the mathematical model of power control, using the principle of direct power control (DPC), the outer loop of the DC bus voltage PI control of the Vienna rectifier is described in detail, the dual loop structure of the direct power control inner loop and the overall system structure. Finally, the control strategy was verified by Simulink simulation. The results show that the Vienna rectifier based on direct power control has good steady state and dynamic performances, and verify the correctness and feasibility of the control strategy.

Tidal Dissipation in Dual-body, Highly Eccentric, and Nonsynchronously Rotating Systems: Applications to Pluto–Charon and the Exoplanet TRAPPIST-1e

Abstract Using the Andrade-derived Sundberg–Cooper rheology, we apply several improvements to the secular tidal evolution of TRAPPIST-1e and the early history of Pluto–Charon under the simplifying assumption of homogeneous bodies. By including higher-order eccentricity terms (up to and including e 20), we find divergences from the traditionally used e 2 truncation starting around e = 0.1. Order-of-magnitude differences begin to occur for e > 0.6. Critically, higher-order eccentricity terms activate additional spin–orbit resonances. Worlds experiencing nonsynchronous rotation can fall into and out of these resonances, altering their long-term evolution. Nonzero obliquity generally does not generate significantly higher heating; however, it can considerably alter orbital and rotational evolution. Much like eccentricity, obliquity can activate new tidal modes and resonances. Tracking the dual-body dissipation within Pluto and Charon leads to faster evolution and dramatically different orbital outcomes. Based on our findings, we recommend future tidal studies on worlds with e ≥ 0.3 to take into account additional eccentricity terms beyond e 2. This threshold should be lowered to e > 0.1 if nonsynchronous rotation or nonzero obliquity is under consideration. Due to the poor convergence of the eccentricity functions, studies on worlds that may experience very high eccentricity (e ≥ 0.6) should include terms with high powers of eccentricity. We provide these equations up to e 10 for arbitrary obliquity and nonsynchronous rotation. Finally, the assumption that short-period, solid-body exoplanets with e ≳ 0.1 are tidally locked in their 1:1 spin–orbit resonance should be reconsidered. Higher-order spin–orbit resonances can exist even at these relatively modest eccentricities, while previous studies have found such resonances can significantly alter stellar-driven climate.

Phase Shift of Planetary Waves and Wave–Jet Resonance on Tidally Locked Planets

Abstract Recent studies found that atmospheric superrotation (i.e., west-to-east winds over the equator) on tidally locked planets can modify the phase of planetary waves. But a clear relationship between the superrotation and the magnitude of the phase shift was not examined. In this study, we re-investigate this problem using a 2D linear shallow-water model with a specified uniform zonal flow. We find that the degree of the phase shift is a monotonic but nonlinear function of the strength of the mean flow and the phase shift has two limits of -π and +π. The existence of these limits can be explained using the energy balance of the whole system. We further show that a resonance between the Rossby wave and the mean flow occurs when the speed of an eastward jet approaches to the westward phase speed of the Rossby wave, or a resonance between the Kelvin wave and the mean flow happens when the speed of a westward jet approaches to the eastward phase speed of the Kelvin wave. The resonance mechanism is the same as that found in the previous studies on Earth and hot Jupiters. Moreover, in the spin-up period of a 3D global atmospheric general circulation simulation for tidally locked rocky planet, we also find these two phenomena: phase shift and wave–jet resonance. This study improves the understanding of wave–mean-flow interactions on tidally locked planets.

Rotational Dynamics of the Inner Satellites of Jupiter

The article considers the attitude stability of synchronous rotation and the most significant relativistic effects in the rotational dynamics of the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14). It is established that the plane synchronous rotation of all inner satellites of Jupiter for the most probable values of the parameters of their shapes is stable with respect to tilting the axis of rotation. For the first time, the most significant secular, periodic, and mixed terms of the geodetic rotation of the inner satellites of Jupiter in the Euler angles relative to their own coordinate systems and in the angles of their rotation with respect to the fixed equator of the Earth and the vernal equinox (for the J2000.0 epoch) are determined. It is shown that there are objects in the Solar System with significant geodetic rotation caused primarily by their proximity to the perturbing central body rather than its mass. In particular, the value of the geodetic precession of the inner satellites of Jupiter (for which Jupiter is a less massive perturbing central body than the Sun) is 105 times greater than that of Jupiter rotating around its more massive central body (the Sun) and comparable with their precession in Newton approximation.

The orbit of asteroid (317) Roxane’s satellite Olympias from Gemini, Keck, VLT and the SOR, and (22) Kalliope’s Linus from the SOR

A definitive orbit is derived for asteroid (317) Roxane’s satellite Olympias [S/2009 (317)1] by combining the 2009 discovery images from Gemini North (Merline et al. 2009) with images from Keck and the VLT obtained in 2012, as well as images from its 2016-2017 apparition from the Starfire Optical Range. The orbit is retrograde with respect to the ecliptic but in the same sense as Roxane’s spin. Olympias has a period of P=11.9440±0.0005 days, a semi-major axis of a=245±3 km, and an orbital pole at RA=97∘, Dec=−71∘, or ecliptic coordinates λ=245∘, β=−85∘, close to the south ecliptic pole. This satellite orbital pole is only 3∘ from Roxane’s orbital pole (but in a retrograde sense) and restricts all observations of Olympias from Earth to within 4∘ of the satellite’s orbital plane. By fitting the brightness ratios between Roxane (rotational period of 8.16961±0.00005 h) and Olympias as a Fourier series, we find a rotational period for Olympias of 8.2587±0.0001 h, making this an asynchronous wide binary. From the brightness ratios, and with the average infrared modeling diameter found in the literature of 19.16±0.39 km (error of the mean), we estimate triaxial ellipsoid radii of 14.5×8.5×7.2 km for Roxane and 3.6×2.5×2.0 km for Olympias. We can then apportion the mass between the two objects and find a density for both (assumed to be the same) of 2.16±0.18 g/cm3. There are only a few E-type binaries known and this is the first direct determination of E-type density from a binary. We suggest that the system was formed by the Escaping Ejecta Binary (EEB) mechanism of Durda et al. (2004a), probably forming closer together, and then undergoing the complex evolution steps described by Jacobson et al. (2014) involving synchronization, BYORP orbit expansion, loss of tidal lock, and then YORP spinup. Roxane and Olympias may be the only known EEB system to date.From the same 2016-2017 apparition the orbit of Linus around asteroid (22) Kalliope is derived from the SOR. This well-observed bright satellite is found to have a circular orbit with a period of P=3.5956±0.0004 days, in good agreement with the latest elements of Vachier et al. (2012) of P=3.5957±0.0001 days, and a semi-major axis of a=1099±6 km, somewhat greater than their a=1082±11 km for a slightly eccentric orbit (e=0.007±0.010). With a diameter for Kalliope of 161±6 km (Hanuš et al. 2017), we derive a density for Kalliope of 3.72±0.25 g/cm3 from our one apparition study, the same as Hanuš et al. (2017) but greater than the 3.24±0.16 of Vachier et al. (2012).

Control of oscillations in two-rotor cyberphysical vibration units with time-varying observer

In this paper the control of oscillations in the two-rotor vibration unit is studied. It is assumed that the velocity of the oscillation of the platform cannot be accurately measured. The time-varying observer is proposed to restore it. In order to guarantee stability of the frequency and amplitude of oscillations of the vibrating parts of a two-rotor vibration unit special control algorithms based on speed-gradient methodology. Simulation results confirm stability of the synchronous rotation modes of the unbalanced rotors of the vibration unit.

Effects of Spin-Orbit Resonances and Tidal Heating on the Inner Edge of the Habitable Zone

Much attention has been given to the climate dynamics and habitable boundaries of synchronously rotating planets around low mass stars. However, other rotational states are possible, particularly when higher eccentricity orbits can be maintained in a system, including spin-orbit resonant configurations. Additionally, the oscillating strain as a planet moves from periastron to apoastron results in friction and tidal heating, which can be an important energy source. Here, we simulate the climate of ocean-covered planets near the inner edge of the habitable zone around M to solar stars with ROCKE-3D, and leverage the planetary evolution software package, VPLanet, to calculate tidal heating rates for Earth-sized planets orbiting 2600 K and 3000 K stars. This study is the first to use a 3-D General Circulation Model that implements tidal heating to investigate habitability for multiple resonant states. We find that in the absence of tidal heating, the resonant state has little impact on the inner edge, because for a given stellar flux, higher-order states tend to be warmer than synchronous rotators, but for a given temperature, have drier upper atmospheres. However, when strong tidal heating is present, the rotational component implies a strong dependence of habitable conditions on the system evolution and rotational state. Since tidal and stellar heating both decrease with orbital distance, this results in a compact orbital width separating temperate and uninhabitable climates. We summarize these results and also compare ROCKE-3D to previously published simulations of the inner edge that used a modified version of the NCAR CAM4 model.

Accretion of ornamental equatorial ridges on Pan, Atlas and Daphnis

We explore scenarios for the accretion of ornamental ridges on Saturn’s moons Pan, Atlas, and Daphnis from material in Saturn’s rings. Accretion of complex shaped ridges from ring material should be possible when the torque from accreted material does not exceed the tidal torque from Saturn that ordinarily maintains tidal lock. This gives a limit on the maximum accretion rate and the minimum duration for equatorial ridge growth. We explore the longitude distribution of ridges accreted from ring material, initially in circular orbits, onto a moon that is on a circular, inclined or eccentric orbit. Sloped and lobed ridges can be accreted if the moon tidally realigns during accretion due to its change in shape or because the disk edge surface density profile allows ring material originating at different initial semi-major axes to impact the moon at different locations on its equatorial ridge. We find that accretion from an asymmetric gap might account for a depression on Atlas’s equatorial ridge. Accretion from an asymmetric gap at orbital eccentricity similar to the Hill eccentricity, might allow accretion of multiple lobes, as seen on Pan. Two possibly connected scenarios are promising for growth of ornamental equatorial ridges. The moon migrates through the ring, narrowing its gap and facilitating accretion. The moon’s orbital eccentricity could increase due to orbital resonance with another moon, pushing it into its gap edges and facilitating accretion.

Pivotal Role of Spin in Celestial Body Motion Mechanics: Prelude to a Spinning Universe

This is the final article in our series dealing with the interplay of spin and gravity that leads to the generation, and continuation of celestial body motions in the universe. In our prior studies we focused on such interactions in the elementary particles, and in the celestial bodies in the solar system. Foremost among the findings was that, along with gravity, matter at all levels exhibits axial spin. We further noted that all freestanding bodies outside our solar system, including the largest such units, the stars and galaxies also spin on their axes. Also, the axial rotation speed of planets in our solar system has a linear positive relationship to their masses, thus hinting at its fundamental and autonomous nature. We have reported that this relationship between the size of the body and its axial rotation speed extends to the stars and even the galaxies. Next, all congregations of matter spin on their axes in the counterclockwise direction; all satellites orbit their mother bodies also in the counterclockwise direction, i.e.: in our solar system, with only rare exceptions, the satellite bodies follow the mother bodies’ axial rotation. This relationship exists also in the case of the rings of planets, the asteroids and the Kuiper belt bodies, as well as the stars and their galaxies. We also noted the intricate involvements between spin and gravity in the exquisite phenomena of synchronous and negative rotations of planets and some satellites; we have explained in detail how these two phenomena occur. The closest large moons of the gas and ice giants and the earth’s moon exhibit synchronous rotation. In this paper we present evidence that these synchronously rotating satellite bodies’ axial rotation speed is closely related to the size and the axial rotation speeds of their respective mother bodies. In the satellites that follow a non-synchronous rotation (most of the planets and their satellites) the satellites’ own rotation speed usually dominates. In all these rotational/orbital motions, we believe, the axial rotation and gravity collaborate with the resultant centrifugal force, which prevents the satellite bodies from crashing into the mother bodies. We have inferred from the above observations that the axial spin is a fundamental property of matter, akin to gravity, electromagnetism, and strong and weak nuclear forces. This inherent property of matter to spin on its axis is what initiates all celestial body motions and makes such motions perpetual. The lateral motions of stars within the galaxies, are also influenced by the sizes of the stars; the larger the star, the faster it moves radially. Similarly, the larger the spiral galaxy, the faster it rotates on its axis. We extrapolate from these observations that the axial rotational speeds of galaxies affect their motion in space as well, that this is circumferential, and we predict this will also be in the counterclockwise direction. This lateral movement of the galaxies will give the appearance of the whole universe spinning on its axis.

SIMULTANEOUS MULTI-SITE PHOTOMETRY OF LEO SATELLITES TO CHARACTERISE THEIR ROTATION STATES

The photometry of space objects (SO)makes it possible to determine their state of rotation aroundthe center of mass, orientation of the rotation axis androtation speed in the most cost-effective manner. However,the methods for determining the attitude parameters fromphotometric data from a single observation site (OS) requirelong series of high-quality and high-frequencymeasurements. We propose a method for determining theorientation parameters of slowly rotating SO based onsimultaneous multi-site photometry with a high temporalresolution. Preconditions for planning and building a localphotometric network that can accomplish such a task havebeen tested via computer simulation. Synchronousobservations of the unoperated spacecraft TOPEX/Poseidonwere carried out. They were attended by the observatories ofOdessa, Lvov and Uzhgorod universities, as well as theobservation station of the State Space Agency of Ukraine inZalistsi, Khmelnytsky region, took part. Synchronousnetwork-based photometric observations from three OSsenable us to calculate time lags between correlated light-curve segments and promptly determine the direction ofrotation, as well as the spatial orientation of a SO’s spin axisand its angular spin rate. A local network of severaldistributed observation sites for synchronous monitoring ofthe rotation of various SO in LEO will make it possible todetermine the rotation parameters of also slowly rotatingobjects that do not exhibit glints within their light curves.

Geometric and control optimization of a two cross-flow turbine array

Cross-flow turbines, also known as vertical-axis turbines, convert the kinetic energy in moving fluid to mechanical energy using blades that rotate about an axis perpendicular to the incoming flow. In this work, the performance of a two-turbine array in a recirculating water channel was experimentally optimized across 64 unique array configurations. For each configuration, turbine performance was optimized using tip-speed ratio control, where the rotation rate for each turbine is optimized individually, and using coordinated control, where the turbines are optimized to operate at synchronous rotation rates but with a phase difference. For each configuration and control strategy, the consequences of co- and counter-rotations were also evaluated. This is the first experimental cross-flow turbine array study to simultaneously address array geometry, control, and turbine rotation direction. Based on these results, we hypothesize how array configurations and control cases influence interactions between turbines and affect the performance of the array.

Optimization study on magnetorheological fluid components and process parameters of cluster magnetorheological finishing with dynamic magnetic field for sapphire substrates

Sapphire is used as the base material of high-brightness LED devices, high-speed and high-frequency wireless communication devices, and solar photovoltaic conversion chips. Its surface quality determines the performance of the device. Magnetorheological (MR) finishing can avoid scratches and surface/subsurface damage caused by uneven abrasive particles due to the viscoelasticity of the polishing pad. When MR polishing was used to polish sapphire substrates, the adaptability of the MR fluid components and the rationality of polishing process was the key to quickly obtain high-quality workpiece surface. In this study, sapphire substrates were polished using cluster MR finishing with dynamic magnetic fields formed by multiple synchronous rotation magnetic poles. The components of the MR fluid were optimized by single-factor experiments, and the polishing process parameters were optimized through orthogonal experiment. The results showed that an ultra-smooth surface of Ra 0.27 nm could be obtained when sapphire substrate was polished 8 h by using the optimized MR fluid, which contained 120 nm silica sol with a mass fraction of 8 wt% and W3 carbonyl iron powders with a mass fraction of 16 wt%, also with the optimized process parameters as the machining gap, the workpiece speed, the magnetic pole speed and the rotation speed of the polishing disc were 1 mm, 350 r min−1, 45 r min−1 and 40 r min−1, respectively.

Study on Torsional Vibration Characteristics of Cross Shaft Universal Coupling

In this work, the ship propulsion shaft system with cruciform universal coupling is studied. First, based on the analysis of the structure and characteristics of the cross-axis universal coupling, the motion relations and expressions between the components of the universal coupling are established by using the coordinate transformation method. Second, the characteristics of the four submodels of the head mass point element, the end mass point element, the universal coupling mass point element, and other mass point elements are discussed, and the corresponding torsional vibration differential equations of the four submodels are established. On this basis, the mathematical model of the propulsion shafting system and the differential equations of torsional vibration are established by using the modularization method and lumped parameter method. Finally, the torsional vibration modes and response characteristics of the shafts are calculated and analyzed by using the system matrix method when the external load driving torques of the universal coupling, propeller, and diesel engine are considered. At the same time, the correctness of the mathematical model and calculation method is verified by the test and comparative analysis of ship propulsion shafts. It lays a theoretical foundation for further research on torsional vibration characteristics and mechanisms of the ship propulsion shafting system based on universal coupling. Introduction Universal coupling is a common connection component of mechanical shaft system transmission. It is a common mechanism that can be used to transfer motion and torque. Universal coupling has no requirement for neutrality between the two axes connected. It can be used for intersecting, parallel or staggered multiposition relations, and can still ensure the continuous rotation of the two axes connected. Compared with the belt drive and chain drive, universal coupling has the advantages of large transmission range, compact transmission, high transmission efficiency, and convenient maintenance. Therefore, it is widely used in ships, automobiles, lifting and transportation (Avrigean et al. 2015; Chang et al. 2017), engineering machinery, and other equipment. Because of the manufacturing error, assembly error, and the failure to keep synchronous rotation between the driving shaft and the driven shaft in the working process, additional inertia moment of the universal coupling is generated, which causes the vibration of the system and even leads to the fracture of the universal coupling in serious cases.