Valentin Abadjiev, Emilia Abadjieva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria,

Graduate School of Engineering and Resource Science,

Faculty of Engineering and Resource Science,

Akita University, Tegatagakuen – machi 1-1, Akita, Japan

e-mails: abadjiev@imbm.bas.bg, abadjieva@gipc.akita-u.ac.jp

ONE
APPROACH TO THE SYNTHESIS, DESIGN AND

MANUFACTURE OF HYPERBOLOID GEAR SETS WITH

FACE MATING GEARS.

PART 2: REVIEW OF PRACTICAL REALIZATION

MANUFACTURE OF HYPERBOLOID GEAR SETS WITH

FACE MATING GEARS.

PART 2: REVIEW OF PRACTICAL REALIZATION

Abstract. Hyperboloid gear drives with face
mating gears are used to transform rotations between shafts with
non-parallel and non-intersecting axes. A special case of these
transmissions are Spiroid1 and Helicon gear drives. The classical gear
drives of this type are Archimedean ones. The objective of this study
are hyperboloid gear drives with face meshing, when the pinion has
threads of conic convolute, Archimedean and involute types, or the
pinion has threads of cylindrical convolute, Archimedean and involute
types. For simplicity, all three type transmissions with face mating
gears and a conic pinion are titled Spiroid and all three type
transmissions with face mating gears and a cylindrical pinion are
titled Helicon.Principles of the mathematical modelling of tooth
contact synthesis are discussed in Part 1: Basic theoretical and CAD
experience of this study. The second part of this article is a brief
overview of the innovations and inventions created in this field at the
Institute of Mechanics – Bulgarian Academy of Sciences in the last
three decades. This study is also dedicated on elaboration of the
specialized face gear sets for implementation into bio-robot hand. It
is based on the application of 3D software technology, using 3D print
for the realization of the physical models of the

gear drives.

gear drives.

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Athanasios
A. Markou, George D. Manolis

Laboratory for Statics and Dynamics, Department of Civil Engineering,

Aristotle University, Thessaloniki 54124, Greece

e-mails: athanasiosmarkou@gmail.com, gdm@civil.auth.gr

Laboratory for Statics and Dynamics, Department of Civil Engineering,

Aristotle University, Thessaloniki 54124, Greece

e-mails: athanasiosmarkou@gmail.com, gdm@civil.auth.gr

ENERGY AND TRANSMISSIBILITY IN
NONLINEAR

VISCOUS BASE ISOLATORS

VISCOUS BASE ISOLATORS

Abstract.
High damping rubber bearings (HDRB) are the most commonly used base
isolators in buildings and are often combined with other systems, such
as sliding bearings. Their mechanical behaviour is highly nonlinear and
dependent on a number of factors. At first, a physical process is
suggested here to explain the empirical formula introduced by J.M.
Kelly in 1991, where the dissipated energy of a HDRB under cyclic
testing, at constant frequency, is proportional to the amplitude of the
shear strain, raised to a power of approximately 1.50. This physical
process is best described by non-Newtonian fluid behaviour, originally
developed by F.H. Norton in 1929 to describe creep in steel at
high-temperatures. The constitutive model used includes a viscous term,
that depends on the absolute value of the velocity, raised to a
non-integer power. The identification of a three parameter Kelvin
model, the simplest possible

system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under timeharmonic loads.

system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under timeharmonic loads.

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Vikas Rastogi

Department of Mechanical, Production & Industrial and Automotive Engineering,

Delhi Technological University, Delhi-110042, India,

e-mail: rastogivikas@yahoo.com

EFFECTS OF DISCRETE DAMPING ON THE
DYNAMIC

BEHAVIOUR OF ROTATING SHAFT THROUGH

EXTENDED LAGRANGIAN FORMULATION

BEHAVIOUR OF ROTATING SHAFT THROUGH

EXTENDED LAGRANGIAN FORMULATION

Abstract.
The main focus of the paper is touted as effects of discrete damping on
the dynamic analysis of rotating shaft. The whole analysis is being
carried out through extended Lagrangian formulation for a discrete -
continuous system. The variation formulation for this system is
possible, considering the continuous system as one-dimensional. The
generalized formulation for one dimensional continuous rotary shaft
with discrete external damper has been obtained through principle of
variation. Using this extended formulation, the invariance of
umbra-Lagrangian density through extended Noether’s theorem is
achieved. Rayleigh beam model is used to model the shaft. Amplitude
equation of rotor is obtained theoretically and validated through
simulation results. The simulation results reveal the important
phenomena of limiting dynamics of the rotor shaft, which is due to an
imbalance of material damping and stiffness of the rotor shaft. The
regenerative energy in the rotor shaft, induced due to
elasticity/stiffness of the rotor shaft, is dissipated partially
through the inspan discrete damper and also through the dissipative
coupling between drive and the rotor shaft. In such cases, the shaft
speed will not increase with increase in excitation frequency of the
rotor but the slip between the drive and the shaft increases due to
loading of drive.

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Ognyan Y. Kamenov

Department of Applied Mathematics and Informatics,

Technical University of Sofia, P.O. Box 384, 1000 Sofia, Bulgaria,

e-mail: okam@abv.bg

SOLITARY-WAVE
AND PERIODIC SOLUTIONS OF THE

KURAMOTO-VELARDE DISPERSIVE EQUATION

KURAMOTO-VELARDE DISPERSIVE EQUATION

Abstract.
In the present paper, solitary solutions of the Kuramoto- Velarde (K-V)
dispersive equation have been found, using the deformation and mapping
approach. These exact solutions show the dynamics and the evolution of
dispersive solitary waves. In the case α2 = α3, three families of exact
periodic solutions have been obtained by employing the bilinear
transformation method.

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M. M. Bhatti

Shanghai Institute of Applied Mathematics and Mechanics,

Shanghai University, Shanghai China,

e-mails: muhammad09@shu.edu.cn, mubashirme@yahoo.com

A. Zeeshan, R. Ellahi

Department of Mathematics and Statistics,

International Islamic University, Islamabad Pakistan

STUDY
OF HEAT TRANSFER WITH NONLINEAR

THERMAL RADIATION ON SINUSOIDAL MOTION OF

MAGNETIC SOLID PARTICLES IN A DUSTY FLUID

THERMAL RADIATION ON SINUSOIDAL MOTION OF

MAGNETIC SOLID PARTICLES IN A DUSTY FLUID

Abstract.
In this article, heat transfer with nonlinear thermal radiation on
sinusoidal motion of magnetic solid particles in a dust Jeffrey fluid
has been studied. The effects of Magnetohydrodynamic (MHD) and hall
current are also taken under consideration. The governing equation of
motion and energy equation are modelled with help of Ohms law for fluid
and dust phases. The solutions of the resulting ordinary coupled
partial differential equations are solved analytically. The impact of
all the physical parameters of interest such as Hartmann number, slip
parameter, Hall parameter, radiation parameter, Prandtl number, Eckert
number and particle volume fraction are demonstrated mathematically and
graphically. Trapping mechanism is also discussed in detail by drawing
contour lines. The present analysis affirms many interesting
behaviours, which permit further study on solid particles motion with
heat and mass transfer.

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