Issue 3

JTAM, Sofia, vol. 44 Issue 3 (2014)

Computer Synthesis Approaches of Hyperboloid Gear Drives with Linear Contact

Valentin Abadjiev1, Emilia Abadjieva1, Haruhisa Kawasaki2, Tetsuya Mouri2
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria
2Mechanical Engineering Department, Faculty of Engineering, Gifu University, Yanagido 1-1, Gifu, Japan

The computer design has improved forming different type software for scientific researches in the field of gearing theory as well as performing an adequate scientific support of the gear drives manufacture. Here are attached computer programs that are based on mathematical models as a result of scientific researches. The modern gear transmissions require the construction of new mathematical approaches to their geometric, technological and strength analysis. The process of optimization,synthesis and design is based on adequate iteration procedures to find out an optimal solution by varying definite parameters. The study is dedicated to accepted methodology in the creation of software for the synthesis of a class high reduction hyperboloid gears – Spiroid and Helicon ones (Spiroid and Helicon are trademarks registered by the Illinois Tool Works, Chicago, Ill). The developed basic computer products belong to software, based on original mathematical models. They are based on the two mathematical models for the synthesis: “upon a pitch contact point” and “upon a mesh region”. Computer programs are worked out on the basis of the described mathematical models, and the relations between them are shown. The application of the shown approaches to the synthesis of commented gear drives is illustrated.

JTAM, Sofia, vol. 44 Issue 3 pp. 03-20 (2014), [Full Article]

Walking Robot Locomotion System Conception

D. Ignatova, E. Abadjieva, V. Abadjiev, Al. Vatzkitchev
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria

This work is a brief analysis on the application and perspective of using the walking robots in different areas in practice. The most common characteristics of walking four legs robots are presented here. The specific features of the applied actuators in walking mechanisms are also shown in the article. The experience of Institute of Mechanics – BAS is illustrated in creation of Spiroid and Helicon1 gears and their assembly in actuation of studied robots. Loading on joints reductors of robot legs is modelled, when the geometrical and the walking parameters of the studied robot are preliminary defined. The obtained results are purposed for designing the control of the loading of reductor type Helicon in the legs of the robot, when it is experimentally tested.

JTAM, Sofia, vol. 44 Issue 3 pp. 21-30 (2014), [Full Article]

Seismic Soil-Tunnels Interaction via BEM Part I. Mechanical Model

P. Dineva1, S. Parvanova2, G. Vasilev2, F. Wuttke3
1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Bl. 4, Sofia 1113, Bulgaria
2Department of Structural Engineering, UACEG, 1, Hristo Smirnenski Blvd, 1046 Sofia, Bulgaria
3Marine and Land Geomechanics and Geotechnics, Christian-Albrechts-University of Kiel, Institute of Applied Geo-science, Germany

Two-dimensional elastodynamic problem for seismic response of unlined and lined tunnels located in a layered half-plane with free sur face relief is solved. The computation tool uses the idea of the global matrix propagator method which allows derivation of a relation between the wave field quantities along different interfaces in the layered half-plane. The numerical realization of this idea is performed with the help of the sub-structured boundary element method (BEM) well suited when objects with arbitrary geometry are considered. A relation between displacements and tractions along the free surface and arbitrary interface of the soil stratum is derived. It works for arbitrary geometry of the interfaces between soil layers. Finally, in the companion paper, numerical results are presented which show both a validation study of the proposed computational methodology and extensive numerical simulations demonstrating the influence of some important factors as type and characteristics of the incident wave, dynamic tunnels interaction, soil-tunnel interaction, free surface relief, type of the tunnel construction and mechanical properties of the layered half-plane on the complex seismic field near and far-away from the underground structures.

JTAM, Sofia, vol. 44 Issue 3 pp. 31-48 (2014), [Full Article]

Surface Wave Speed of Functionally Graded Magneto-Electro-Elastic Materials with Initial Stresses

Li Li1,2, P. J. Wei2
1Department of Mathematics, Qiqihar University, Qiqihar, 161006, China
2Department of Applied Mechanics, University of Sciences and Technology Beijing, Beijing, 100083, China

The shear surface wave at the free traction surface of half infinite functionally graded magneto-electro-elastic material with initial stress is investigated. The material parameters are assumed to vary exponentially along the thickness direction, only. The velocity equations of shear surface wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magneto-electro-elastic material with the initial stresses and the free traction boundary conditions. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are discussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.

JTAM, Sofia, vol. 44 Issue 3 pp. 49-64 (2014), [Full Article]

Response to Concentrated Moving Masses of Elastically Supported Rectangular Plates Resting on Winkler Elastic Foundation

T. O. Awodola, B. Omolofe
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria

The dynamic response to moving concentrated masses of elastically supported rectangular plates resting on Winkler elastic foundation is investigated in this work. This problem, involving non-classical boundary conditions, is solved and illustrated with two common examples often encountered in engineering practice. Analysis of the closed form solutions shows that, for the same natural frequency (i) the response amplitude for the moving mass problem is greater than that one of the moving force problem for fixed Rotatory inertia correction factor R0 and foundation modulus F0, (ii) The critical speed for the moving mass problem is smaller than that for the moving force problem and so resonance is reached earlier in the former. The numerical results in plotted curves show that, for the elastically supported plate, as the value of R0 increases, the response amplitudes of the plate decrease and that, for fixed value of R0, the displacements of the plate decrease as F0 increases. The results also show that for fixed R0 and F0, the transverse deflections of the plates under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Hence, the moving force solution is not a save approximation to the moving mass problem. Also, as the mass ratio Γ approaches zero, the response amplitude of the moving mass problem approaches that one of the moving force problem of the elastically supported rectangular plate resting on constant Winkler elastic foundation.

JTAM, Sofia, vol. 44 Issue 3 pp. 65-90 (2014), [Full Article]

Exact Periodic Seismic Waves in the Nikolaevskii Model

Ognyan Y. Kamenov
Department of Applied Mathematics and Informatics, Technical University of Sofia, P.O. Box 384, 1000 Sofia, Bulgaria

In the present paper three different in their structure families, of exact periodic solutions of the nonlinear evolution equation of Nikolaevskii, have been obtained. The common dynamic structure of these families of periodic solutions has been shown as well as the spatial displacements, typical of the non-integrable evolution equations, for each separate harmonics. These exact solutions are published for the first time.

JTAM, Sofia, vol. 44 Issue 3 pp. 91-106 (2014), [Full Article]