Hitham M. Tlilan

Non-linear dynamic behaviour of compound planetary gear trains: Model formulation and semi-analytical solution

Abstract A discrete, non-linear, time-varying, torsional dynamic model of a multi-stage planetary train that is formed by any number of simple planetary stages is proposed in this study. Each planetary stage has a distinct fundamental mesh frequency and any number of planets spaced in any angular positions. The model allows the analysis of the gear train in all possible power flow configurations suitable for various gear drive ratios. It includes periodic variation of gear mesh stiffnesses as well as clearance (backlash) non-linearities that allow tooth separations. Equations of motion for the general case are formulated and solved semi-analytically using a hybrid harmonic balance method (HBM) in conjugate with inverse Fourier transform. Relative mesh displacements along lines of action of individual gear pairs were used as the continuation parameters to pass singular points and ill-conditioned equations in their proximity. At the end, a case study of a two-stage planetary train is used to demonstrate the effectiveness of the model and solution methods. The HBM solutions are compared to those obtained by a direct numerical integration method to assess their accuracy.

Strain-Concentration Factor of Circumferentially V-Notched Cylindrical Bars Under Static Tension

The FEM is used to study the effects of notch opening angle (β) and notch radius on the new strain-concentration factor (SNCF) for circumferentially V-notched cylindrical bars under static tension. The new SNCF has been defined under the triaxial stress state at the net section. Nevertheless, the conventional SNCF has been defined under uniaxial stress state. The new SNCF ( ) is constant in the elastic deformation. The range where this elastic value remains constant increases with increasing β and increasing notch radius (ρ o ). The effect of the notch opening angle on the elastic decreases with increasing ρ o . Particularly, the elastic of β = 120° is the minimum for all notch radii employed. The new SNCF increases from its elastic value to a peak value and then decreases with plastic deformation for notches with β = 120°. This peak value is the maximum . Nevertheless, for the notches with β o = 0.5 and 1mm. After that it increases to the maximum SNCF and then slightly decreases for further plastic deformation. The variations in with the ratio of tensile load to that at yielding at the notch root (P/P Y ) are nearly independent of stress-strain curve up to general yielding.

Double vortex generators for increasing the separation efficiency of the air separator

This article presents a numerical analysis of multi–phase flow with powerful swirling streams in a cylindrical separator equipped with two vortex generators in an attempt to predict the separation efficiency of an air–water mixture. New design of a cylindrical separator is introduced for air–water mixture. The mixture multiphase and large eddy simulation (LES) turbulence models were applied. Images that concern velocity field, pressure, and volume fraction are introduced. Air phase is trapped and localized along the centerline of the separator and then migrates toward the upper exit hole, while water phase is distributed and rotated along the wall, then confined at the mid–separator due to two strong clock–wise centrifugal forces before it is expelled through its exit at mid of separator. It was found that the separation efficiency at constant Reynolds number of 8×10 with two feeding volume fractions of 95% and 90% are 97.8% and 96.1%, respectively. Also, the separation efficiency at constant feeding volume fraction of 95% with two Reynolds numbers of 2×10 and 8×10 are 98.6% and 97.8%, respectively. It is revealed that the separation efficiency will increase as the Reynolds number increases and/or increasing the volume fraction.