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



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.

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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


ENERGY AND TRANSMISSIBILITY IN NONLINEAR
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.



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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

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

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

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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