Spherical Pendulum Small Oscillations for Slewing Crane Motion

The present paper focuses on the Lagrange mechanics-based description of small oscillations of a spherical pendulum with a uniformly rotating suspension center. The analytical solution of the natural frequencies’ problem has been derived for the case of uniform rotation of a crane boom. The payload paths have been found in the inertial reference frame fixed on earth and in the noninertial reference frame, which is connected with the rotating crane boom. The numerical amplitude-frequency characteristics of the relative payload motion have been found. The mechanical interpretation of the terms in Lagrange equations has been outlined. The analytical expression and numerical estimation for cable tension force have been proposed. The numerical computational results, which correlate very accurately with the experimental observations, have been shown

Effects of Material Rheology and Die Walls Translational Motions on the Dynamics of Viscous Flow during Equal Channel Angular Extrusion through a Segal 2 θ

The present article is focused on a phenomenological description of a polymer workpiece Equal Channel Angular Extrusion (ECAE) through 2θ-dies of Segal and Iwahashi geometries with a channel intersection angle 2θ = 105° with fixed and movable external inlet and outlet die walls. The local flow dynamics, including the formation of macroscopic rotation and a dead zone appearance during the flow of plasticine, paraffin, and wax workpiece models through the subject die configuration was studied using physical simulation techniques. The present article utilizes a Computational Fluid Dynamics (CFD) numerical approach to a theoretical description of 2D viscous flow of incompressible Newtonian continuum through the stated die geometries. The boundary value problem for the Navier-Stokes equations in the curl transfer form for the local viscous flow was formulated and numerically solved with a finite-difference method. Theoretical CFD-derived plots with computational flow lines, dimensionless flow and curl functions, flow velocities, and tangential stresses for viscous material flow through the stated die geometries have been generated and described. As a first rheological approximation the derived computational results provide the theoretical description of physical simulation experiments and visualize the formation of ECAE-induced rotational modes of large deformations like macroscopic rotation and rotational inhomogeneity

2D CFD description of the kinematic effects of movable inlet and outlet die wall transport motion and punch shape geometry on the dynamics of viscous flow during ECAE through Segal 2θ-dies for a range of channel angles

Minimization of the dead zone (DZA) in the process of material forming is a materials science problem. Geometric and kinematic approaches to the minimization of the DZA during Equal Channel Angular Extrusion (ECAE) have been proposed, developed, analyzed, and documented. The present article is focused on a 2D Computational Fluid Dynamics (CFD) description of the kinematic effects of punch shape geometry and inlet (IDW) and outlet (ODW) die wall motion on the DZA during ECAE of Viscous Incompressible Continuum (VIC) through a Segal 2θ-die for a range of channel angles 60° ≤ 2θ ≤ 135°. Due attention has been given to the independent alternating transport motions of the IDW and ODW. Punch shape geometry and the kinematic modes of IDW and ODW motions for DZA minimization have been determined with a numerical solution of the boundary value problem for the Navier-Stokes equations in curl transfer form for VIC. Experimental verification was accomplished with an introduction of initial circular gridlines-based physical simulation techniques. For the first time, experimental verification of CFD-derived results was made through an additional superposition of empirically-derived digital photos with deformed elliptical gridlines in the channel intersection deformation zones and correspondent 2D numerical plots with CFD-derived flow lines and full flow velocities. An empirical DZA localization was experimentally determined as the location of minimally-deformed near circular markers. The computational DZA localization was numerically determined as a flow-lines-free zone (the first hypothesis) or as a zone with near-zero values of full flow velocities (the second hypothesis). The relative DZA was estimated as a ratio of the measured DZA with respect to the area of the deformation zone in the channel intersection region. A good agreement was obtained between DZA values obtained with the first hypothesis and experimental results