Sun Planet Research Articles

Passive Control Feasibility of Collinear Equilibrium Points with Solar Balloons

A = solar balloon’s surface area, m E = Young’s modulus of the skin, Pa h = auxiliary variable, see Eq. (13) i, ĵ, k = unit vectors of rotating frame K = second-order tensor, see Eq. (5) k = gain ‘ = sun–planet distance (with ‘ ≜ 1 AU), astronomical unit m = mass, kg O = center of mass p = internal pressure, Pa R = solar balloon’s radius, m r = absolute position vector, r krk T = spacecraft equilibrium temperature, K T O; x; y; z = rotating reference frame u = vector, see Eq. (6) W = thermal power flux,W=m W = solar constant, 1350 W=m 2 = coefficient of absorptivity = lightness number = variation = coefficient of emissivity = angular coordinate, deg = planet’s dimensionless mass = skin’s Poisson ratio = dimensionless x coordinate = relative position vector, k k = skin’s tensile stress, Pa ~ = Stefan–Boltzmann constant = coefficient of linear expansion, K 1 ! = angular velocity, rad=s

Dynamic Response and Dynamic Load of Wind Turbine Planetary Gear Transmission System Under Changing Excitation

The dynamic model of planetary gear system was built up with the consideration of the running characteristics of variable speed and variable load of wind turbine transmission system. The expression of dynamic factor which described by external change load and deformation vibration was studied. Then, the response characteristics and dynamic load of planetary gear system of wind turbine have been studied with the consideration of changing external load and time-varying stiffness, mesh phase and nonlinear stiffness of bearing. The results show that: the frequency response of system reflects the low frequency component of external load. The influence of external incentives on sun gear and planet gear is very significant, and the distinguish between low frequency vibration and high frequency vibration is obvious. The flexibility of system has an obvious impact on dynamic load of bearing. The results lay a foundation for strength design and fatigue analysis of wind turbine gearbox.

Two mechanisms of natural transport in the Solar System

In this paper, two natural transport mechanisms in Solar System are considered. The first is a short-time transport, and is based on the existence of “pseudo-heteroclinic” connections between libration point orbits of pairs of Sun–planet planar circular restricted three-body problems (PCR3BP). The stable and unstable manifolds associated with the libration point orbits of different Sun–planet PCR3BP systems are computed. Then the intersections between the inner and the outer manifolds of all the consecutive planets in the Solar System are explored. The second mechanism, which is common and qualitatively well understood in two-degrees of freedom Hamiltonian systems, corresponds to a long-time transport, and is the result of the strongly chaotic motion of the minor body in the PCR3BP. In this contribution, we present an analysis of the natural transport in the Solar System based on these two mechanisms. In particular, we discuss the key properties of the natural transport, such as the possibility of transfering between two specified celestial bodies, the type of transport and the time of flight. The final objective is to provide a deeper dynamical insight into the exchange mechanisms of natural material in the Solar System.

Elastohydrodynamic Lubrication Design of Planetary Gear Transmission

Based on elastic hydrodynamic lubrication (EHL) theory, an EHL model of the meshing between the sun gear and planet gear in planetary gear transmission was established. The EHL oil film thicknesses at meshing areas and those distributions for two operation cases were calculated: one case with the sun gear as the driving gear and another case with the ring gear as the driving gear. The Lubrication with second case was worse. Through the many comparing calculations the lubrication film thickness can be significantly increased by right parameter design. Reasonable raise of lubricant viscosity can get better gear lubrication. Increased gear pressure angle can greatly increase the oil film thickness. The increase of oil film thickness can improve the lubrication of gears and prevent wearing and reduce the production cost of gears, which have great practical value.

Epicyclic Load Sharing Map — Development and validation

Under ideal conditions, every sun–planet–ring path in an epicyclic gear set transmits the same amount of torque. But, in the presence of certain manufacturing variations, equal load sharing is not achieved. In a companion paper, a physical explanation has been provided for the load sharing behavior observed in epicyclic gears. The explanation of the root cause led to the development of a load sharing formulation for 3, 4, 5, and 6 planet epicyclic systems. In this paper the same approach will be taken to develop the formulation for a seven planet epicyclic gear set. The developed expressions will then be used to develop the concept of an Epicyclic Load Sharing Map. This map describes the load sharing characteristics of every epicyclic gear set at any positional error and torque level. The developed expressions are then expanded to describe the general case when there are arbitrary errors on the position of every planet in the epicyclic gear set. Finally, the developed expressions will be validated by comparing the predicted load sharing behavior with the results from a validated system level computational model.

Artificial Intelligence Optimization on Automobile Drive Axle Assembly

Drive axle assembly is one of the key components of automotive, and the design quality of drive axle assembly can affect the driving performance, fuel consumption and serve life of vehicle greatly, therefore it is very important to adopt optimization to design the final drive and planetary transmission of vehicle. To reduce size and weight of transmission, the objective function should be specified that the sum of volume of pitch cylinder of sun gear and planet gears in planetary transmission incline to minimum. The objective function with penalty terms is built by penalty strategy with addition type, so as to transform the constrained optimization into the unconstrained optimization.Then the simulated annealing algorithm based on penalty strategy is adopted to solver the optimization model.

Models for planetary eclipses of the uranian satellites

A model for computing the brightness of a satellite in the shadow of a planet is described, which takes into account the Sun–planet–satellite–sensor geometry, the satellite bi-directional reflectance function, and the refraction of sunlight in the planetary atmosphere. Synthetic light curves for eclipse ingress or egress of the five large satellites of Uranus are generated. The model luminosities can be fitted to photometric observations in order to calculate a precise distance between the centers of the satellite and the planet. Alternately, when the satellite ephemeris is accurately known the atmospheric state of the planet can be studied.

PLANETARY GEAR PARAMETRIC INSTABILITY CAUSED BY MESH STIFFNESS VARIATION

Parametric instability is investigated for planetary gears where fluctuating stiffness results from the changing contact conditions at the multiple tooth meshes. The time-varying mesh stiffnesses of the sun–planet and ring–planet meshes are modelled as rectangular waveforms with different contact ratios and mesh phasing. The operating conditions leading to parametric instability are analytically identified. Using the well-defined properties of planetary gear vibration modes, the boundaries separating stable and unstable conditions are obtained as simple expressions in terms of mesh parameters. These expressions allow one to suppress particular instabilities by adjusting the contact ratios and mesh phasing. Tooth separation from parametric instability is numerically simulated to show the strong impact of this non-linearity on the response.

A PHYSICAL EXPLANATION FOR THE EFFECTIVENESS OF PLANET PHASING TO SUPPRESS PLANETARY GEAR VIBRATION

The effectiveness of planet phasing to suppress planetary gear vibration in certain harmonics of the mesh frequency is examined based on the physical forces acting at the sun–planet and ring–planet meshes. The analysis does not rely on assumptions of the nature of the dynamic excitation (e.g., static transmission error or time-varying mesh stiffness) or on an underlying dynamic model. Instead, the inherent system symmetries imply distinct relationships between the forces at the multiple meshes. These relationships lead naturally to simple rules for when a particular harmonic of mesh frequency is suppressed in the dynamic response. An important implication is that certain expected resonances when a mesh frequency harmonic and a natural frequency coincide are suppressed. Systems with equal planet spacing and those with unequally spaced, diametrically opposed planets are considered. In both cases, a substantial number of mesh frequency harmonics are suppressed naturally without optimization of the phasing. The phenomena are demonstrated with a dynamic finite element/contact mechanics simulation.

Orbital Evolution of Retrograde Interplanetary Dust Particles and Their Distribution in the Solar System

The orbital evolution of interplanetary dust particles (IDPs) from both retrograde and prograde Halley-type comets is numerically simulated. It is found that dust particles nearly always get trapped into one or more mean motion resonances (MMRs) with giant planets while in retrograde orbits. Of the 1000 retrograde particles simulated 116 are trapped in MMRs that last longer than 100,000 years, and the MMRs are typically exterior MMRs of the type p:1 with Jupiter where p ranges from 1 to 12. We present a simple analysis of the physical processes involved when an IDP is in a resonance. A quasistable resonance is maintained by the combined effect of the direct perturbation from the planet as well as the indirect perturbation that arises because the Sun is moving around the Sun–planet barycenter. The direct and indirect perturbations are often of comparable magnitudes, although one or the other can be dominant. Of the 1000 retrograde particles simulated, 45 of them evolved to prograde orbits while in MMRs with a giant planet. Although the overall distribution in eccentricity and inclination of 10−7 g dust particles from Halley-type comets is consistent with D. H. Humes' (1980, J. Geophys. Res.85, 5841–5852) interpretation of the Pioneer 10 and 11 data, the spatial density variation is not. Instead of the constant spatial density derived by Humes, the spatial density of Halley-type comet dust varies as r−γ with heliocentric distance r, where γ ranges from 1.5 to 1.8. Additional sources of interplanetary dust particles are needed to account for the discrepancy.

Evolution of Interplanetary Dust Particles in Mean Motion Resonances with Planets

The three-dimensional orbital evolution of interplanetary dust particles in mean motion resonances (MMRs) with planets is investigated in a restricted three-body system. Using the time variation of the Jacobi “constant” due to drag forces, we develop simple analytical expressions that describe the orbital evolution of a dust grain in MMRs with a planet. Together with the time rate of change of the Tisserand criterion, the variations in eccentricity and inclination of a dust grain in any MMR are related to each other in one single equation. When expanded to the second order in eccentricity and inclination, the equation can be split into two parts and be used to describe separately the time variation of both orbital elements of a dust grain in a MMR. Dust grains in retrograde orbits in MMRs are also discussed. Numerical simulations of various Sun–planet–dust three-body systems are performed to verify the new analytical expressions. Simulations of different types of dust grains (asteroidal, cometary) in MMRs with planets in the real Solar System are also discussed and compared with our analytical predictions.

Experimental and analytical evaluation of dynamic load vibration of a 2240-kW (3000-hp) rotorcraft transmission

A dynamic analysis of a 2240-kW (3000-hp) helicopter planetary system is presented. Results from both analytical and experimental studies show good correlation in gear-tooth loads. A parametric study indicates that the mesh damping ratio has a significant effect on maximum gear-tooth load, stress and vibration. Correlation with experimental results indicates that the sun–planet mesh damping ratio can significantly differ from the planet–ring mesh damping ratio. A numerical fast Fourier transform (FFT) procedure is applied to examine the mesh load components in the frequency domain and the magnitudes of multiple tooth-pass frequencies excited by nonsynchronous meshing of the planets. Effects of tooth-spacing errors and tooth-profile modifications with tip relief are examined. A general discussion of results and a correlation with experimental study are also presented.

Low Energy Transit Orbits in the Restricted Three-Body Problems

Low Energy Transit Orbits in the Restricted Three-Body Problems

Rotational Period of the Planet Mercury

IN a recent communication by S. J. Peale and T. Gold1 the rotational period of Mercury, determined from radar Doppler-spread measurements to be 59 ± 5 days2, has been explained in terms of a solar tidal torque effect, taking into account the large eccentricity of Mercury's orbit, and the 1/r6 dependence of the tidal friction (r being the Sun–planet distance). They conclude from a very brief discussion that after slowing down from a higher direct angular velocity, the planet will have a final period of rotation between 56 and 88 days, depending on the assumed form of the dissipation function. However, from their discussion it is by no means clear why permanent deformations would imply a period of 88 days as a final rotation state after a slowing-down process. A very nearly uniform rotational motion of 58.65 sidereal-day period, that is 2/3 of the orbital period, may indeed be a stable periodic solution. This rotational motion could have the axis of minimum moments of inertia nearly aligned with the Sun–Mercury radius vector at every perihelion passage. The orbital angular velocity at perihelion (2φ/56.6 days) is close to 2φ/58.65 days, leading to an approximate alignment of the axis of minimum moment of inertia with the radius vector in an arc around perihelion where the interaction is strongest. The axial asymmetry of Mercury's inertia ellipsoid may result in a torque that counterbalances the tidal torque, giving a stable motion with this orientation and with a period two-thirds of the orbital period. It would therefore be possible for Mercury to have a higher permanent rigidity than that permitted by Peale and Gold.