Sun Planet Research Articles

Dynamical Structures Associated with High-Order and Secondary Resonances in the Spin–Orbit Problem

In our solar system, spin–orbit resonances are common under Sun–planet, planet–satellite, and binary asteroid configurations. In this work, high-order and secondary spin–orbit resonances are investigated by taking numerical and analytical approaches. Poincaré sections as well as two types of dynamical maps are produced, showing that there are complicated structures in the phase space. To understand numerical structures, we adopt the theory of perturbative treatments to formulate resonant Hamiltonian for describing spin–orbit resonances. The results show that there is an excellent agreement between analytical and numerical structures. It is concluded that the main V-shape structure arising in the parameter space (θ̇,α) is sculpted by the synchronous primary resonance, those minute structures inside the V-shape region are dominated by secondary resonances and those structures outside the V-shape region are governed by high-order resonances. Finally, the analytical approach is applied to binary asteroid systems (65803) Didymos and (4383) Suruga to reveal their phase-space structures.

Biostructure of Corona Virus Infection Cycle Protein & Genome Bioanalysis & Generalised Route of Bio-Vaccine & DNA Vaccine: A Review with Bioactive Compounds to Tackle Covid-19

Possibly Corona virus is a Space Virus. Another Possibility behind spreading of Corona virus maybe it was present in Earth Biosphere in inactive form from many years before Covid -19 pandemic. Spreading of Corona Virus was made possible by 5G & 6G Technology. Extensive Space Research by which Radio signals have to be sent to Superclusters of Stars Galaxies such as IC Galaxy & NGC Galaxy of Corona Austalis & Corona Bolaris to search Alien Life & New Stars cum Galaxy Cluster is another reason for corona virus to come on/at Earth Biosphere. As such super clusters are high energy clusters. ISM related important gaseous component which are called coronal are analogy with the solar corona. Sun Planet is thought to be surrounded by a local bubble with a radius of 100 pc containing coronal Atmosphere that produces in huge amount which contains High Temperature Sensitive Microbes which are called Galactic Corona. Worldly Known that space agencies and space centres in India, worldwide & Globally are working on SETI & Planetary Science as some Scientists or group of Scientist are working on Sun Planet as All those Laboratories in India Worldwide Globally send Radio Signal to Sun Planet & others planets & of/to their galaxies as said above such as Messier Galaxy IC Galaxy NGC galaxy & targeted space microbes from those planets & galaxies from space to make Space Microbes Library by which Became Discharge cum Spout by Reasons to worldwide Globally. However, they forgot it will harm to themselves too. In the Present Review we are Providing GENEREALISED BIO-NANO-ECO-BIO VACCINE ROUTE FOR COVID 19 In vitro. Also in this review we are Providing Generalised Chart of Corona DNA Vaccine to Develop it in Future.

On the co-orbital asteroids in the solar system: medium-term timescale analysis of the quasi-coplanar objects

The focus of this work is the current distribution of asteroids in co-orbital motion with Venus, Earth and Jupiter, under a quasi-coplanar configuration and for a medium-term timescale of the order of 900 years. A co-orbital trajectory is a heliocentric orbit trapped in a 1:1 mean-motion resonance with a given planet. As such, to model it this work considers the Restricted Three-Body Problem in the planar circular case with the help of averaging techniques. The domain of each co-orbital regime, that is, the quasi-satellite motion, the horseshoe motion and the tadpole motion, can be neatly defined by means of an integrable model and a simple two-dimensional map, that is invariant with respect to the mass parameter of the planet, and turns out to be a remarkable tool to investigate the distribution of the co-orbitals objects of interest. The study is based on the data corresponding to the ephemerides computed by the JPL Horizons system for asteroids with a sufficient low orbital inclination with respect to the Sun–planet orbital plane. These objects are cataloged according to their current dynamics, together with the transitions that occur in the given time frame from a given type of co-orbital motion to another. The results provide a general catalog of co-orbital asteroids in the solar system, the first one to our knowledge, and an efficient mean to study transitions.

A novel mathematical model of transmission path effect for the research of vibration characteristics of planetary gearboxes

Model-based vibration signal analysis to interpret and understand vibration characteristics can provide prior guidance for the condition monitoring and fault diagnosis of planetary gearboxes (PGs). Transmission path effects due to the rotational motion of planet gears with respect to the accelerometer mounted on the PG housing make understanding its real dynamic behavior challenging. To overcome this challenge, a novel mathematical model of the transmission path effect is proposed to support the construction of more realistic dynamic response of PGs. This model is derived only from the geometric parameters and material properties, and it has higher applicability than traditional models. Subsequently, a phenomenological vibration model is used to simulate all vibration sources, including sun–planet and ring–planet gear meshes. On these bases, a comprehensive vibration signal model is proposed by considering all vibration sources and the corresponding transmission path effects. Moreover, the theoretical spectral structure is deduced via Fourier series analysis. Finally, the vibration characteristics of the vibration signals obtained using the proposed mathematical model are analyzed and validated through simulations and experiments in the time and frequency domains.

On the stability of satellites at unstable libration points of sun–planet–moon systems

The five libration points of a sun–planet system are stable or unstable fixed positions at which satellites or asteroids can remain fixed relative to the two orbiting bodies. A moon orbiting around the planet causes a time-dependent perturbation on the system. Here, we address the sense in which invariant structure remains. We employ a transition state theory developed previously for periodically driven systems with a rank-1 saddle in the context of chemical reactions. We find that a satellite can be parked on a so-called time-periodic transition state trajectory – which is an orbit restricted to the vicinity of the libration point L2 for infinitely long time – and investigate the stability properties of that orbit.

Nonlinear dynamic characteristics of planetary gear transmission system considering squeeze oil film

Based on the planetary gear transmission system considering the coupling effects of friction and elastohydrodynamic lubrication, a torsional dynamic model considering friction, oil film, time-varying meshing stiffness, meshing damping, and gear backlash is established. The Runge–Kutta numerical method is used to solve the vibration equation of the system. The bifurcation diagram and largest Lyapunov exponent are used to analyze the dynamic characteristics of the system under different bifurcation parameters such as the excitation frequency, lubricant viscosity, sun–planet backlash, and planet–ring backlash. The numerical results demonstrate that with the increase of excitation frequency, the system exhibits rich nonlinear dynamic characteristics such as short-period motion, long-period motion, and chaotic motion. With the increase of lubricant viscosity, the chaotic motion of the system is suppressed at low excitation frequency and the periodic motion of the system increases at high excitation frequency. With the increase of sun–planet backlash, the chaotic motion of the system increases at low excitation frequency, and the bifurcation characteristics become complicated at high excitation frequency and enters chaotic motion in advance. With the increase of ring–planet backlash, the system delays into chaotic motion at low excitation frequency and bifurcates from single-period motion to multi-period motion in advance at high excitation frequency.

Effect of roughness on meshing power loss of planetary gear set considering elasto-hydrodynamic lubrication

Meshing power loss is one of the most important parts in power loss calculation of planetary gear set. However, most of the conventional methods assumed the friction coefficient between gears as a constant value in the meshing power loss calculation, and most importantly, the influence of gear tooth surface geometry is usually ignored, for example, roughness. Therefore, a new meshing power loss calculation model for planetary gear set that considers tooth surface roughness is proposed on the basis of elasto-hydrodynamic lubrication method. With the proposed model, a planetary gear set dynamic model that considers friction force between gears is first established to study the time-varying meshing forces, sliding speeds, and curvature radii of the gear pairs. Then, an elasto-hydrodynamic lubrication model of the gear pair contact interface is constructed to investigate and modify the friction force distribution in the gear meshing process of the dynamic model iteratively until the meshing forces converge to stable values. Furthermore, the relationship between the tooth surface roughness and film thickness is studied in the elasto-hydrodynamic lubrication model. After that, the meshing power loss is calculated based on the obtained meshing forces, friction coefficients, sliding speeds, and so on. The results show that there is a sudden growth of the meshing power loss at the end of the meshing cycle, which has a good agreement with the meshing force impact. And, it is found that tooth surface roughness has a direct influence on the meshing power loss of sun–planet gear pair, which yields an increasing tendency as the surface roughness growing.

An investigation on dynamic characteristics of herringbone planetary gear system with torsional flexibility between the left and right teeth of the sun gear

Herringbone planetary gear system (HPGS) has high power density and complex structure. The torsional flexibility of the left and right teeth of the sun gear is closely related to the dynamic characteristics of the HPGS. In this research, considering the coordination conditions of both sides torsional stiffness and axial slide of the sun gear, a new dynamic model of the HPGS considering the meshing phase difference between left and right teeth of the sun gear is developed based on the lumped-parameter method, and the influence mechanism of torsional stiffness and axial sliding is studied. Moreover, the dynamic parameters and dynamic characteristics of the HPGS are analyzed in the case of varying torsoinal stiffness and axial slide. The results show that the torsional stiffness of left and right teeth and the axial slide of sun gear have significant impacts on the dynamic parameters and dynamic mesh force response. With the increase of the torsional flexibility (the decrease the torsional stiffness), the sun gear and planet gear meshing stiffness and the maximum tooth surface load are both increased on the left side (input side) and decreased on the right side, but the main peak values and peak frequencies of dynamic response on both sides of the s-p meshing pairs decrease significantly. In addition, when the sun gear slides toward the output side axially, meshing stiffness and dynamic mesh force response main peak values decreased on the left side (input side) and increased on the right side, but the main resonance peaks frequencies keep the same.

Halo orbit of regularized circular restricted three-body problem with radiation pressure and oblateness

In this paper, computation of the halo orbit for the KS-regularized photogravitational circular restricted three-body problem is carried out. This work extends the idea of Srivastava et al. (Astrophys. Space Sci. 362: 49, 2017) which only concentrated on the (i) regularization of the 3D-governing equations of motion, and (ii) validation of the modeling for small out-of-plane amplitude ( $$A_z =110000$$ km) assuming the third-order analytical approximation as an initial guess with and without differential correction. This motivated us to compute the halo orbits for the large out-of-plane amplitudes and to study their stability analysis for the regularized motion. The stability indices are described as a function of out-of-plane amplitude, mass reduction factor and oblateness coefficient. Three different Sun–planet systems: the Sun–Earth, Sun–Mars and the Sun–Jupiter are chosen in this study. Stable halo orbits do not exist around the $$L_{1}$$ point, however, around the $$L_{2}$$ point stable halo orbits are found for the considered systems.

Crack Fault Classification for Planetary Gearbox Based on Feature Selection Technique and K-means Clustering Method

During the condition monitoring of a planetary gearbox, features are extracted from raw data for a fault diagnosis. However, different features have different sensitivity for identifying different fault types, and thus, the selection of a sensitive feature subset from an entire feature set and retaining as much of the class discriminatory information as possible has a directly effect on the accuracy of the classification results. In this paper, an improved hybrid feature selection technique (IHFST) that combines a distance evaluation technique (DET), Pearson’s correlation analysis, and an ad hoc technique is proposed. In IHFST, a temporary feature subset without irrelevant features is first selected according to the distance evaluation criterion of DET, and the Pearson’s correlation analysis and ad hoc technique are then employed to find and remove redundant features in the temporary feature subset, respectively, and hence, a sensitive feature subset without irrelevant or redundant features is selected from the entire feature set. Further, the k-means clustering method is applied to classify the different kinds of health conditions. The effectiveness of the proposed method was validated through several experiments carried out on a planetary gearbox with incipient cracks seeded in the tooth root of the sun gear, planet gear, and ring gear. The results show that the proposed method can successfully distinguish the different health conditions of a planetary gearbox, and achieves a better classification performance than other methods. This study proposes a sensitive feature subset selection method that achieves an obvious improvement in terms of the accuracy of the fault classification.

The spur planetary gear torsional stiffness and its crack sensitivity under quasi-static conditions

Abstract The sun–planet and ring–planet tooth mesh stiffness variations and the resulting transmission errors are the main internal vibration generation mechanisms for planetary gear systems. This paper presents the results of torsional stiffness analysis of involute spur planetary gear systems in mesh using finite element methods. A planetary gear model with three planet gears and fixed ring gear and its subsystem models have been developed to study the subsystem and overall torsional stiffnesses. Based on the analysis of torsional mesh stiffness, predictive models for single branch sun–planet–ring and overall planetary gear torsional stiffnesses have been proposed. A crack coefficient was introduced to the sun–planet and ring–planet meshes to predict the effect and sensitivity of changes to the overall torsional mesh stiffness. The resulting mesh stiffness crack sensitivity of the overall gear system was analysed under quasi-static conditions. It was found that the carrier arm stiffness has great influence on the crack sensitivity while the overall stiffness was most sensitive to the crack on the sun–planet mesh.

Analysis of ballistic capture in Sun–planet models

Analysis of ballistic capture orbits in Sun–planet systems is conducted in this paper. This mechanism utilizes purely gravitational forces, and may occur in non-Keplerian regimes. Ballistic capture orbits are generated by proper manipulation of sets of initial conditions that satisfy a simple definition of stability. Six Sun–planet systems are considered, including the inner planets, Jupiter, and Saturn. The role of planets orbital eccentricity, their true anomaly, and mass ratios is investigated. Moreover, the influence of the post-capture orbit in terms of inclination and orientation is also assessed. Analyses are performed from qualitative and quantitative perspective. The quality of capture orbits is measured by means of the stability index, whereas the capture ratio gives information on their statistical occurrence. Some underlying principles on the selection of the dynamical model, the initial true anomaly, and inclination are obtained. These provide a reference for practical cases.

An experimental investigation of spin power losses of a planetary gear set

This experimental study investigates the contributions of the key components of load-independent (spin) power losses of planetary (epicyclic) gear sets. A dedicated test set-up is developed to operate a planetary gear set under unloaded conditions in various hardware configurations within a wide range of speed. Torque provided to the gear set is measured as the spin torque loss. A test matrix is executed specifically to measure total spin loss of the gear set as well as the contributions of its main components, namely drag loss of the sun gear, drag loss of the carrier assembly, pocketing losses at the sun–planet and ring–planet meshes, viscous planet bearing losses, and planet bearing losses due to centrifugal forces caused by the rotation of the carrier. Variations of the same gear set are tested and results from these tests are compared to estimate and rank order the contributions of these components of power loss. Impact of the rotational speed and oil temperature levels on each component is also quantified.

LOAD SHARING ANALYSIS OF PLANETARY GEAR BOX

One of the advantages of epicyclic transmissions is that the input torque is divided in a number of parallel paths. For n planet epicyclic system, each sun–planet–ring path is to transmit 1/n of the input torque. However, this is only true in the ideal case when there is equal load sharing between all the planets in the epicyclic system. Because of manufacturing errors, equal load sharing is not possible and the degree of inequality in load sharing has major role for gear system sizing, tolerancing schemes, and torque ratings. Therefore it is important to understand the fundamental cause of the unequal load sharing behavior in epicyclic gear sets. Load sharing behavior is associated with positional errors causing one or more planets to lead or lag the other planets. When the error is positive the planet with error lead the other planet while when the error is negative planet with error lags the other planet. Several manufacturing errors can introduce positional errors. Some of the common contributors are carrier pinhole position error, planet size variation, and run out of the gears. A set of precision planetary gear set is selected with the objectives of experimental and theoretical investigation of the load sharing behavior by introducing the position errors for the planets, the load shared by each planet is estimated by maximum stresses induced in each pin. The results of the experimentation are then validated with the FEM (Finite Element method) results.

Dynamic and quasi-static modeling of planetary gear set considering carrier misalignment error and varying line of action along tooth width

Misalignment error of gear pair will affect the load distribution along the tooth-width and have a great effect on dynamic characteristics. For the planetary gear set, it is complicated to model the misalignment error of carrier as, when this error is present, the planets and the carrier are tilted and contacts between sun–planet and ring–planet along tooth width are skewed. In this paper, a new lumped parameter model is set up to quasi-statically and dynamic analyze the planetary gear set with the position-dependent line of action due to the misalignment of the carrier. In the analytical model, each potential line of contact on the gear mesh is discretized into finite independent time-varying stiffness. External and internal gear stiffness is obtained through the potential energy method. The dynamic responses, load distribution along the tooth width, load sharing between planets, trajectories of sun gear are simulated and analyzed with carrier misalignment error in planetary gear set.

Fast low-energy halo-to-halo transfers between Sun–planet systems

In this paper, the problem of fast low-energy halo-to-halo transfers between Sun–planet systems is discussed under ephemeris constraints. According to the structure of an invariant manifold, employing an invariant manifold and planetary gravity assist to save fuel consumption is analyzed from the view of orbital energy. Then, a pseudo-manifold is introduced to replace the invariant manifold in such a way that more transfer opportunities are allowed. Fast escape and capture can be achieved along the pseudo-manifold. Furthermore, a global searching method that is based on patched-models is proposed to find an appropriate transfer trajectory. In this searching method, the trajectory is divided into several segments that can be designed under simple dynamical models, and an analytical algorithm is developed for connecting the segments. Earth–Mars and Earth–Venus halo-to-halo transfers are designed to demonstrate the proposed approach. Numerical results show that the transfers that combine the pseudo-manifolds and planetary gravity assist can offer significant fuel consumption and flight time savings over traditional transfer schemes.

Dynamic and phenomenological vibration models for failure prediction on planet gears of planetary gearboxes

Faults detection in planet gears of planetary gearboxes by vibration analysis is not as straightforward as the detection of failures in conventional gear transmissions. This is because the driving flanks are different between the inner contact (ring–planet gear) and the external contact (sun–planet gear). Furthermore, the failure position varies with respect to the fixed transducer located on the ring gear, a situation leading to differences in the transient amplitude of the acceleration signals. In the present study, the planet gear fault is simulated based on two models: dynamic and phenomenological. These models have been used in other publications for the study of non-faulty planetary gearboxes. For the first model, the equations of motion are solved by temporal integration using HHT; whereas the second model is solved using algebraic equations. The fundamental results from the simulation of both models are shown in terms of waveforms and spectral content. They are also compared and validated later with the experimental results extracted from two test benches. It is concluded that the dynamic model has larger difficulties for spectral analysis, due to numerical errors from the temporal integration and mainly by the non-inertial reference frame used. Regarding the detection of failures in planet gears through vibration signals, this will not necessarily generate periodic transients every half rotation of this component, as it depends on if the planet gear is damaged on one or both flanks of the tooth. The conducted analysis also permits to conclude that when one flank is damaged, it can be detected more clearly when it meshes with the sun gear than when it meshes with the ring gear.

The Research on Natural Characteristic and Eigensensitivity of Ravingneaux Compound Planetary Gear Sets

The dynamic model of Ravingneaux compound planetary gear sets has been built. Then the Natural frequency and vibration model have been solved in the Ravingneaux compound planetary gear sets. The eigensensitivity to parameters have been researched based on the dynamical model. The varying trend of natural frequency according to the varying of parameters have been researched, which include gear mass (sun gear, ring gear , or planet gear), the moment of inertia of gears, the support stiffness , the torsional stiffness.

Analytical investigation of tooth profile modification effects on planetary gear dynamics

This study investigates the impact of tooth profile modification on spur planetary gear vibration. An analytical model is proposed to capture the excitation from tooth profile modifications at the sun–planet and ring–planet meshes. The accuracy of the proposed model for dynamic analysis is correlated against a benchmark finite element analysis. Perturbation analysis yields a closed-form approximation of the vibration response with tooth profile modifications. The perturbation solution is used to investigate the effects of tooth profile modification. The tooth profile modification parameters that minimize response are readily obtained. Static transmission error and dynamic response are minimized at different amounts of profile modification, which contradicts common practical thinking regarding the correlation between static transmission error and dynamic response. Contrary to expectations, the optimal sun–planet and ring–planet tooth profile modifications that minimize response when applied individually may increase dynamic response when applied simultaneously. System parameters such as mesh stiffness and mesh phase significantly affect the influence of tooth profile modification.

Studying Sun–Planet Connections Using the Heliophysics Integrated Observatory (HELIO)

The Heliophysics Integrated Observatory (HELIO) is a software infrastructure involving a collection of web services, heliospheric data sources (e.g., solar, planetary, etc.), and event catalogues – all of which are accessible through a unified front end. In this paper we use the HELIO infrastructure to perform three case studies based on solar events that propagate through the heliosphere. These include a coronal mass ejection that intersects both Earth and Mars, a solar energetic particle event that crosses the orbit of Earth, and a high-speed solar wind stream, produced by a coronal hole, that is observed in situ at Earth (L1). A ballistic propagation model is run as one of the HELIO services and used to model these events, predicting if they will interact with a spacecraft or planet and determining the associated time of arrival. The HELIO infrastructure streamlines the method used to perform these kinds of case study by centralising the process of searching for and visualising data, indicating interesting features on the solar disk, and finally connecting remotely observed solar features with those detected by in situ solar wind and energetic particle instruments. HELIO represents an important leap forward in European heliophysics infrastructure by bridging the boundaries of traditional scientific domains.