Issue 2

JTAM, Sofia, vol. 18 Issue 2 (1987)

Some Results of the Investigation of the Conditions for Non-existence of Ordinary Nodes on the Contact Lines of Spiroid Gearings

V. Abadjiev, D. Petrova
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

Analytical relations defining the domain of existence of convolute involute and Archimedean spiroid gearings with orthogonally skew axes and without ordinary nodes in their meshing zones are obtained. Technical solutions of this class of spatial gea¬rings are created.

JTAM, Sofia, vol. 18 Issue 2 pp. 009-013 (1987), [Full Article]

Stability of the Vibro-Shock Regimes of a Rotating Shaft Supported by Bearings with Radial Clearance

I. Kochev, I. Ivanov
VIHVP, Plovdiv

The authors study stability of motion of the shaft neck of a statically unbalanced rotor. The rotor, however, is supported by a bearing with a radial clearance and stability is due to a constant inertia force. Free motion and shock are both studied, regarding a phase difference, and theoretical and numerical analysis of stability is performed.

JTAM, Sofia, vol. 18 Issue 2 pp. 014-018 (1987)

Dynamics of an Elastic One-Link Manipulation Robot, Rotating About a Vertical Axis

S. Bachvarov, D. Chotova
High. Inst. Mech Elactr. Eng. "V. I. Lenin"

The paper presents a study of an anthropomorphic robot and link elasticity is accounted for. What is considered furthermore is the actuation in the joints and how rotation is performed. The differential equations of motion are written and Krilov-Bogolyubov's asymptotic method is employed for their solution. The law of motion of the mechanical system is obtained in a first approximation. The results obtained by the authors can be applied to determine the joint reactions and to design the robot links.

JTAM, Sofia, vol. 18 Issue 2 pp. 019-028 (1987), [Full Article]

On a Direct Numerical Method Employed in the Civil Engineering Dynamics

S. Simeonov
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski Blvd.

A step method is proposed to solve the problem of determining the forced oscillations of a system of n degrees of freedom, whereas the law of how the external load varies in time is chosen at random. The method is based on linearly deformable systems and is of Timoshenko-Newmark's type (here Hilbert's a-parameter is employed). Yet, the additional equations (6) are chosen to be of the most general form. This allows for the design of an algorithm that satisfies the conditions of perfect convergence and algorithmic dissipation of O(h2) order (h = ∆h is the integration step). If the second free parameter ζ is also employed in formulas (23), then it becomes possible to obtain a "non-exceeding" solution and to, model the internal viscous resistance. In this case, however, the error of algorithmic dissipation is of order O(h) which is in accordance with the expected value. Fig. 2 shows that unlike Newmark's method, here the error does not take such "drastic" values for small values of ζ. The method, designed by the author, is applied in the case of physically and/or geometrically nonlinear systems as well. The nonlinear system of equations which is ob¬tained after the discretization can be solved in three different manners.

JTAM, Sofia, vol. 18 Issue 2 pp. 029-038 (1987)

On the Co-rotation Derivatives and the Determining Relations in the Theory of Large Plastic Deformations

P. Trusov

The author considers large plastic and small elastic deformations when analysing various deformation processes. He designs determining relations and uses properly co-rotation derivatives of the measures of the process. Moreover, light is thrown on the geometry and physical aspects of the measure itself. The model thus developed appears to extend the applicability of Ilyushin's theory of plasticity when large plastic deforma¬tions are regarded.

JTAM, Sofia, vol. 18 Issue 2 pp. 039-048 (1987)

Secondary Streaming Induced by the Coaxial Torsional Oscillations of Two Spheres in Viscous Liquid

N. Kovacheva, Z. Zapryanov
Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

The axisymmetrical flow induced by the high-frequency synchronized torsional oscillations of two unequal coaxial spheres in unbounded viscous incompressible fluid is investigated by employing matched asymptotic expansions. Provided the amplitude of oscillations is small, an analytical solution for the flow field is obtained for a number of magnitudes of the ratio between sphere radii and the separation distance. Typical secondary flow patterns are shown.

JTAM, Sofia, vol. 18 Issue 2 pp. 049-055 (1987), [Full Article]

A Solution of the Stokes' Problem for a Circular Cylinder

K. Shulev
High. Inst. Arch. Civ. Eng., 1 Hr. Smirnenski Blvd.

The Stokes classical problem is solved, whereas a transversal streaming of a cylin¬der or cylinder motion in a viscous fluid is considered (the cylinder velocity remains con¬stant). Since 1851 this problem is considered to be insoluble, i.e. there does not exist such a solution of the Stokes differential equation as to satisfy all the boundary conditions at the cylinder surface and at infinity. However, this problem is known in hydrodynamics as the Stokes' paradox. Yet, the author has found a solution for the velocity field and pressure which satisfies exactly all the boundary conditions, thus proving that no such paradox exists.

JTAM, Sofia, vol. 18 Issue 2 pp. 056-063 (1987), [Full Article]

Vibrostresses – the Basic Criterion when Determining the Admissible Quasi-Normal Torsional Oscillation in Machine Aggregates

N. Minchev, S. Kazandjiev
High. Inst. Mech. Electr. Eng., Varna

Dynamic stresses occurring under torsional oscillations of machine aggregates appear to be the basic criterion for the machine vibro-reliability. When the general normalizing requirements to the equal quasi-normal co-ordinates are regarded, it becomes clear that the corresponding quasi-normal stresses differ essentially from the expected ones. Hence the authors propose that vibrostresses in the aggregate joints be the basic criterion for the oscillation normalization, which could result in that equal stresses correspond to equal quasi-normal co-ordinates. Such a criterion allows for the estimation of the effect of each quasi-normal co-ordinate when the method of the mean stresses is employed.

JTAM, Sofia, vol. 18 Issue 2 pp. 064-068 (1987)

Model Study of the Dynamic Response of a System with Switch-On Links

S. Dimova, L. Tsenov, A. Karkinski
Centr. Lab. Seism. Mech., Inst. Mech. Biomech., Bulg. Acad. Sci., Bl. 8

The system with switch-on links is used to develop structures which are capable of active resistance to seismic responces. A proper mechano-mathematical model of such a structure is of definite interest from a seismic engineering point of view. Hence a model study of the dynamic responce of a system with switch-on links is performed. The model developed allows for the variation of the basic parameters that characterize the performance of such a system. The authors study forced oscillations due to a harmonically excited vibro-mass. The experimental amplitude-frequency relations are compared to the theoretical results obtained on the basis of the proposed model. The good agreement between theory and experiment proves that the model presented is capable to give the "real" dynamic response of a system with switch-on links.

JTAM, Sofia, vol. 18 Issue 2 pp. 069-073 (1987)

Generalized Failure Criteria in the Principal Stress Space

P. Theocaris

The paper reviews the existing failure criteria and presents a profound analysis of their applicability. All of them are convenient for initially isotropic materials and they are represented by surfaces of revolution about the space diagonal in the principal stress space. However, if one admits a rotation of their axes of symmetry about the origin, a translation of their initial position and some distortion of their shape, he may encounter a really universal failure criterion, where anisotropy of the material can be incorporated. These criteria constitute the so called tensorial failure criteria. Then the rotating elliptic-paraboloid type of criterion may be considered as a generalized failure criterion for all engineering materials.

JTAM, Sofia, vol. 18 Issue 2 pp. 074- (1987)