Journal of
Theoretical and Applied Mechanics
Volume
34, Number 2, 2004
Acad.
G. Bonchev Str., Bl. 4, 1113
e-mail: boicho_marinoff@yahoo.co.uk
ON THE BEHAVIOUR OF POWER TRANSMISSION LINES IN VEHICLES SUBJECTED TO
COMPLEX LOADING
Abstract. The power transmission
lines are complex mechanical systems. They serve to deliver the working torque
from the engine to the working machine. This paper presents analysis of the
behaviour of power transmission lines in some vehicles subjected to complex
loading. The influence of inertial and elastic characteristics of each unit is
studied when applying loads on the one hand, and during the system operation in
a resonance regime on the other hand. The author proposes an algorithm for
designing of power transmission lines that would operate in a stable regime
even under most unfavorable dynamic loads. A numerical example is derived to
verify the developed theory.
Key words: engine, machine,
resonance, frequency, dynamics, force, torque, axial stress.
R. Blagoeva
Acad. G. Bonchev Str. Bl. 4,
email: rumi@imbm.bas.bg
ON A NUMERICAL APPROACH TO
SOLVING A DIFFUSION WITH RELAXATION PROBLEM
Abstract.
A
recently proposed numerical approach to solving an initial boundary value
problem for diffusion with relaxation in polymers [1] is considered. The
correctness of two non-linear numerical schemes is studied and some sufficient
conditions for their stability are derived. These conditions representing
constraints for the time step in respect to some model parameters assure the solution
physical correctness. The present research improves the accuracy and stability
of the time difference schemes used in combination with a finite element domain
approximation in modelling the penetrant diffusion with relaxation in a polymer
matrix.
Ts. P. Ivanov
Faculty of Mathematics and
Informatics,
5,
e-mail: tsoloiv@fmi.uni-sofia.bg
Acad. G. Bontchev Str.,
Bl.4, 1113
e-mail: radianka@imech.imbm.bas.bg
Abstract. Stability of
relative equilibria of an elastic top with stress-free surface and a fixed
point moving in a gravitational field is considered. The Koiter's definition for stability with
respect to the deformation due to the gravitation and an arbitrary rotation and
the usual Lagrange definition for stability of the motion of the deformed top
as a rigid one are adopted. Relative equilibrium states are determined and
criteria for stability are proved. The obtained results are applied for the
case of a sleeping heavy when the top is an elastic circular cylinder.
Key
words:
stability, elasticity, relative equilibrium, top.
Ivan Vladikov
1, Hr. Smirnenski Str., 1046
e-mail: vladik_fce@uacg.bg
Abstract.
On the basis
of the finite strip method a methodology of obtaining the eigenvalues and
eigenvectors of skew plates is worked out. A computer program developed by the
author was applied in the investigation of the flexural vibration of skew
plates for various skew angles and various support conditions. The first six eigen frequencies of skew plates with four different support
conditions are obtained. The results presented here are compared with solutions
obtained by the other authors.
Key words: plate,
free vibration, finite strip method.
Acad. G. Bonchev Str., Bl.
4, 1113
e-mail:
n.nikolov@imbm.bas.bg
8,
e-mail: ialt@tu-sofia.bg
BLANK DIAMETER ANALYSIS
FOR DIFFERENT METALS DURING DEEP DRAWING PROCESS
Abstract.
The influence of blank diameter increasing over critical one, calculated theoretically by
the permissible coefficient of deep drawing, is investigated. Forming process
of cup piece with inside diameter 50 mm and thickness 1.5 mm produced from
different materials is the object of this paper. The changes of diameters are
within the interval 80 – 117mm. The materials used in simulations of deep
drawing processes are Steel 08, Steel 10, Aluminum, Copper and Brass 63.
Simulations of the forming processes with an optimal designed forming tool are
performed using an Approximate Discrete Method (ADM). The values of punch and
die roundness radii and gap between punch and die are taken as optimal ones
obtained under a condition characterized by equal weight coefficients of
importance of drawing force to punch travel.
The results are presented
by diagrams “Drawing force – Punch travel” (“P-S”-diagrams). In some cases
numerical results obtained by ADM are compared with the same ones obtained by
Finite Element Method (FEM), and for Steel 08 by experiment also. Similar
“P-S”-diagrams are obtained for the forming process of steels, aluminum and
cooper blank. Different kind of the brass blank forming is obtained, and some
reasons for that are given. The influence of flange sizes upon the character
and magnitude of “P-S”-diagrams during forming is shown. An increase 2.7% of
blank diameter over the theoretically calculated critical one appears for the
Aluminum and Copper. The obtained numerical results can be used for next
planning of real experiments and enlargement of the investigations in this
field.
Key
words:
deep drawing process, approximate discrete method, finite element method.
67, Shipchenski
prohod Str., 1517
e-mail: veneta@ims.bas.bg
University of Chemical Technology and Metallurgy,
8, Kliment
Ohridski Blvd., 1756 Sofia, Bulgaria,
e-mail:
An improvement of heat treatment conditions of springs made of U8A steel
Abstract. The heat-treatment conditions for springs made of
U8A steel with special shape and function have been studied. The investigation
concerns the effect of heat treatment on hardness, tensile strength and
microstructure. Several methods of heat-treatments have been applied for producing U8A steel made springs with optimal
working properties. The optimal properties have been obtained after
isothermal hardening.
Key
words: spring steel,
heat-treatment, microstructure.
Institute
of Mechanics, Bulgarian Academy of Sciences,
Acad.
G. Bonchev Str., Bl.4, 1113 Sofia, Bulgaria,
e-mail:
valko@imbm.bas.bg;
J. Timmer
Centre
for Data Analysis and Modelling, University of Freiburg,
1,
Eckerstr. 79104 Freiburg, Germany,
e-mail:
jeti@fdm.uni-freiburg.de
Abstract. The well-known
dynamical model of Novak and Tyson for mitosis (M-phase) control in fertilized
Xenopus oocytes is analyzed qualitatively and quantitatively. For this purpose
the two nonlinear ordinary differential equations of the model are transformed
in a canonical form centered in a steady state solution. On the base of
determining Lyapunov value of the steady state solution at the bifurcation
point it is concluded that a stable limit cycle emerges or vanishes depending
on the direction of parameter variation. This paradigmatic effect in the
non-linear dynamics (Hopf bifurcation) is interpreted in terms of the biochemical
kinetics of the cell cycle.
Key
words:
dynamical system, bifurcation, cell mitosis.