Dynamic modelling of planetary gear systems for gear tooth fault

Geared systems have been widely used in mechanical applications for more than a hundred years. A large range of literature has been published especially for spur/helical gear systems and the investigations into technical areas of spur/helical gears have been very well developed, including understanding of condition monitoring systems, diagnostic and prognostic methods. However, there is a lack of understanding on the general dynamic behavior of planetary gear systems with tooth faults. Planetary gears are normally used as effective power transmission elements with high power to weight/volume ratios, large speed reductions in compact volume, and high reliability. They tend to have high efficiency and are used in many applications, such as automotive, heavy truck/tractor, helicopter, wind turbines and bucket wheel reclaimer gearboxes.The purpose of this research is to develop a vibration analysis system that simulates dynamic behavior of large low speed, high torque planetary spur gear systems such as used in bucket wheel reclaimer and wind turbine gearboxes, with and without gear element faults. This thesis investigates lumped mass modelling methods for planetary gearbox dynamic behavior based on previous gearbox modelling research including the use of the coupled torsional-transverse behavior of the gear body. The dynamic model of the planetary spur gear system includes effects such as: variable tooth mesh stiffness, dynamic transmission error effects, and pitch and profile excitation for gear fault detection purposes. Different tooth faults are simulated using the concept of combined torsional mesh stiffness. The dynamics of spur planetary gear systems with and without tooth faults are compared and analyzed to improve the understanding of fault detection in the present gear systems.Dynamic modelling of gear systems, such as outlined in this thesis can assist in understanding the consequence of large transient events, including the fluctuations in tooth loads which can reduce gear fatigue life and lead to further tooth damage. Early detection of faults on gear teeth can be used to initiate maintenance actions in order to reduce repair work and avoid catastrophic breakdown

On the density and multiplicity of solutions to the fractional Nirenberg problem

This paper is devoted to establishing some results on the density and multiplicity of solutions to the fractional Nirenberg problem which is equivalent to studying the conformally invariant equation $P_\sigma(v)=K v^{\frac{n+2\sigma}{n-2\sigma}}$ on the standard unit sphere $(\mathbb{S}^n,g_0)$ with $\sigma\in (0,1)$ and $n\geq 2$, where $P_\sigma$ is the intertwining operator of order $2\sigma$ and $K$ is the prescribed curvature function. More specifically, by using the variational gluing method, refined analysis of bubbling behavior, extension formula, as well as the blow up analysis arguments, we obtain the existence of infinitely many multi-bump solutions. In particular, we show the smooth curvature functions of metrics conformal to $g_0$ are dense in the $C^{0}$ topology. Moreover, the related fractional Laplacian equations $(-\Delta)^{\sigma} u=K(x) u^{\frac{n+2\sigma}{n-2\sigma}}$ in $\mathbb{R}^n$, with $K(x)$ being asymptotically periodic in one of the variables, are also studied and infinitely many solutions are obtained under natural flatness assumptions

On Sun-to-Earth Propagation of Coronal Mass Ejections: 2. Slow Events and Comparison with Others

As a follow-up study on Sun-to-Earth propagation of fast coronal mass ejections (CMEs), we examine the Sun-to-Earth characteristics of slow CMEs combining heliospheric imaging and in situ observations. Three events of particular interest, the 2010 June 16, 2011 March 25 and 2012 September 25 CMEs, are selected for this study. We compare slow CMEs with fast and intermediate-speed events, and obtain key results complementing the attempt of \citet{liu13} to create a general picture of CME Sun-to-Earth propagation: (1) the Sun-to-Earth propagation of a typical slow CME can be approximately described by two phases, a gradual acceleration out to about 20-30 solar radii, followed by a nearly invariant speed around the average solar wind level, (2) comparison between different types of CMEs indicates that faster CMEs tend to accelerate and decelerate more rapidly and have shorter cessation distances for the acceleration and deceleration, (3) both intermediate-speed and slow CMEs would have a speed comparable to the average solar wind level before reaching 1 AU, (4) slow CMEs have a high potential to interact with other solar wind structures in the Sun-Earth space due to their slow motion, providing critical ingredients to enhance space weather, and (5) the slow CMEs studied here lack strong magnetic fields at the Earth but tend to preserve a flux-rope structure with axis generally perpendicular to the radial direction from the Sun. We also suggest a "best" strategy for the application of a triangulation concept in determining CME Sun-to-Earth kinematics, which helps to clarify confusions about CME geometry assumptions in the triangulation and to improve CME analysis and observations.Comment: 37 pages, 13 figures, accepted for publication in ApJ Supplemen

The Directional Transport of Self-Propelled Ellipsoidal Particles Confined in 2D Channel

Transport phenomenon of self-propelled ellipsoidal particles confined in a smooth corrugated channel with a two-dimensional asymmetric potential and Gaussian colored noise is investigated. Effects of the channel, potential and coloured noise are discussed. The moving direction changes from along x axis to opposite x axis with increasing load f. Proper size of pore is good at the directional transport, but too large or too small pore size will inhibit the transport speed. Large x axis noise intensity will inhibit the directional transport phenomena. Proper y axis noise intensity will help to the directional transport. Transport reverse phenomenon appears with increasing self-propelled speed v0. Perfect sphere particle is more easier for directional transport than needlelike ellipsoid particle

A New Strategy of Guidance Command Generation for Re-entry Vehicle

Guidance command for re-entry vehicle can be in lots of formats, but the Euler angles can be provided directly by gyros, so designers used to develop autopilot with commands of Euler angles. After the generation of commands of attack angle and sideslip angle, it’s important to settle how to convert commands of attack angle and sideslip angle to commands of Euler angles. Traditional conversion strategy relies on bank angle, solution to bank angle comprises complicated calculation and can’t be precise. This paper introduces a new conversion strategy of guidance command. This strategy relies on the relative position and velocity measured by seeker, an auxiliary coordinateis established as a transition, the transformation matrix from launch coordinate to body coordinate is solved in a new way, then the commands of Euler angles are obtained. The calculation of bank angle is avoided. The autopilot designed with the converted Euler-angle commands, can track commands of attack angle and sideslip angle steadily.The vehicle reaches the target point precisely. Simulation results show that the new conversion strategy based on seeker information from commands of attack angle and sideslip angle to Euler-angle commands is right.Defence Science Journal, 2013, 63(1), pp.93-100, DOI:http://dx.doi.org/10.14429/dsj.63.236

Effects of Coronal Density and Magnetic Field Distributions on a Global Solar EUV Wave

We investigate a global extreme-ultraviolet (EUV) wave associated with a coronal mass ejection (CME)-driven shock on 2017 September 10. The EUV wave is transmitted by north- and south-polar coronal holes (CHs), which is observed by the Solar Dynamics Observatory (SDO) and Solar Terrestrial Relations Observatory A (STEREO-A) from opposite sides of the Sun. We obtain key findings on how the EUV wave interacts with multiple coronal structures, and on its connection with the CME-driven shock: (1) the transmitted EUV wave is still connected with the shock that is incurvated to the Sun, after the shock has reached the opposite side of the eruption; (2) the south CH transmitted EUV wave is accelerated inside an on-disk, low-density region with closed magnetic fields, which implies that an EUV wave can be accelerated in both open and closed magnetic field regions; (3) part of the primary EUV wavefront turns around a bright point (BP) with a bipolar magnetic structure when it approaches a dim, low-density filament channel near the BP; (4) the primary EUV wave is diffused and apparently halted near the boundaries of remote active regions (ARs) that are far from the eruption, and no obvious AR related secondary waves are detected; (5) the EUV wave extends to an unprecedented scale of ~360{\deg} in latitudes, which is attributed to the polar CH transmission. These results provide insights into the effects of coronal density and magnetic field distributions on the evolution of an EUV wave, and into the connection between the EUV wave and the associated CME-driven shock.Comment: 16 pages, 8 figures, and 3 animations available at http://doi.org/10.13140/RG.2.2.12408.29442 , http://doi.org/10.13140/RG.2.2.25830.06723 , and http://doi.org/10.13140/RG.2.2.19119.18088 ; published in Ap