Journal of Theoretical and Applied Mechanics

Volume 37, Number 4, 2007

### Contents

F. Chaari, H. Trabelsi, T. Fakhfakh, M. Haddar

Dynamics of Mechanical Systems Research Unit,

National School of Engineers of Sfax,

BP W. 3038-Sfax–Tunisia,

e-mails

INFLUENCE OF CAM PROFILE ERRORS ON THE DYNAMIC BEHAVIOUR OF A CAM FOLLOWER SYSTEM

Abstract. In this paper an investigation on the dynamic behaviour of a cam follower system in presence of cam profile errors is carried out. A lumped parameter dynamic model of a cam follower transmission including drive system, cam mechanism and load system was developed. The preloading of the retaining spring, characteristics of the various motion curves and flexibility of the various components are all taken into account and an analytical method to calculate the spring constant between cam and follower considering Hertzian contact is presented. Cam profile errors such as manufacturing errors or wear are also modelled by taking first a sinusoidal error and then a random error. The influence of flexibility and errors on the dynamic behaviour of the system was scrutinized.

Key words: cam-follower, dynamic modelling, defects, numerical simulation.

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail

VECTOR ANALYSIS OF THE SLIDING VELOCITY

FUNCTION OF RACK DRIVES

Abstract. The vector analysis of the sliding velocity function of rack drive conjugate surfaces is investigated in this work. Algorithms defining the level surfaces of the scalar field and the vector lines of the vector field of sliding velocity function are developed. A computer program for synthesis and visualization of the elements of the scalar and the vector field in mesh region of spatial rack transformer is derived.

Key words: rack drive, relative velocity vector, vector analysis, mathematical model.

R. Savova

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bontchev Str., Bl.4, 1113 Sofia, Bulgaria,

Ts. P. Ivanov

Faculty of Mathematics and Informatics,

Sofia University St. Kl. Ohridski,

5, James Bourchier Blvd., 1164 Sofia, Bulgaria,

e-mail: tsoloiv@fmi.uni-sofia.bg

ON VISCOUS EFFECTS IN SURFACE WAVE PROPAGATION

Abstract. In the present paper we consider the influence of viscous or viscous and thermal properties of the half-space on the propagation of surface waves of an assigned frequency or of an assigned wavelength. The relation between the complex Lamé moduli, their constant real parts, connected with the elastic properties of the material, and the constant relaxation times, connected with its viscous properties, are discussed.

Key words: complex Lamé moduli, viscoelasticity, thermoviscoelasticity, surface waves, frequency, wavelength.

A. Nedev, A. Baltov

Institute of Mechanics, Bulgarian Academy of Sciences,

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

e-mail

J. Genov

Technical University of Sofia,

8, St. Kl. Ohridski Blvd, 1000, Sofia, Bulgaria,

e-mail

Numerical ANALYSIS OF formABILITY AND CONTACT FRICTION in DEEP DRAWING of WARM MAGNESIUM alloy sheets

Abstract. A circular cup deep drawing process using magnesium (Mg) alloy material is investigated. It is the lightest practical material, which during the last decade has been widely used as a basis for production of constructional components in automotive and electronic industries.

Numerical investigation of Mg alloy (AZ31-O) sheet formability for Limit Drawing Ratio (LDR) at temperatures  is performed. The material strength constants and strain hardening exponents, which have been experimentally obtained at elevated temperatures by S. Yoshihara et al. [3], are used in calculations. The influence of different friction coefficients (lubricants) on Drawing Force (DF) is numerically investigated. The effect of both forming temperatures and lubricants upon LDR is also examined.

The deep drawing process is simulated by using Finite Element Method (FEM)-ANSYS code. The results are presented by “Drawing Force-P–Punch Stroke-S” diagrams. A conclusion about the influence of the friction coefficients and the corresponding to them lubricants upon the DF based on the obtained “P-S” diagrams is drawn.

Key words: deep drawing, magnesium alloy, friction coefficients.

E. Ergun

Engineering Faculty, Pamukkale University,

Denizli, Turkey,

e-mail: eminergun@pau.edu.tr

M. Colakoglu, S. Tasgetiren

Faculty of Technical Education, Afyon Kocatepe University,

Sezer Campus, Afyon-Karahisa, Turkey,

e-mail

FINITE ELEMENT BASED PREDICTION OF FATIGUE AND FRACTURE BEHAVIOR IN A RESISTANCE WELDED STRUCTURE WITH DIFFERENT BOUNDARY CONDITIONS

Abstract. Fatigue and fracture behaviours of welded straight and L-shaped sheets are investigated under the tensile and bending loads using a finite element method. The effects of the boundary conditions are studied for the welded sheet having different thicknesses and different nugget sizes. The behaviour of the crack propagation is analyzed under the conditions of the linear elastic fracture mechanics. Fatigue life of the structure is also estimated. It is observed from the results that the fatigue life of the welded structure depends on the boundary conditions, the ratio between the thickness of the sheets and nugget sizes.

Key words: finite element modelling; fracture; fatigue life; resistance-welding.

L. Parashkevova, N. Bontcheva

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bontchev Str., Bl. 4, BG-1113 Sofia,

e-mails

A. Manescu

Universita Politechnica delle Marche, Ancona, Italy,

e-mail

PROCESSING OF BULK RAPIDLY SOLIDIFIED Al Fe-ENRICHED ALLOYS - MODELLING AND MICROSTRUCTURE

Abstract. The elastic-plastic behaviour of rapidly solidified AlFe9V1Si2 alloy containing intermetallic compound is considered. The mechanical model for the "in situ" composite proposed by the authors earlier is specified and developed for processes of cold and hot extrusion of precompacted material. This model is developed using information provided by microstructural investigations and EDX analysis. It is a part of the multistage modelling of the bulk material manufacturing process from rapid solidified powders or ribbons. The model is implemented as user defined subroutines into the FE code MARC. Numerical simulations are provided, corresponding to different values of metal forming parameters at isothermal and coupled thermomechanical conditions. The influence of the complience parameter, depending on the properties of the matrix and of the inclusions is discussed.

Key words: intermetallics, rapidly solidified aluminum alloy, extrusion, FEM.

N. Petrov

Institute of Mechanics, Bulgarian Academy of Sciences,

Acad. G. Bontchev Str., Bl. 4, 1113 Sofia, Bulgaria,

e-mail

GENERAL THERMODYNAMIC THEORY FOR ACTIVE

BIO-CONTINUUM

Abstract. Molecular motors are nanometric protein-based devices, essential for the movement in living organisms. The aim of the present study is to offer a general thermodynamic theory for the active bio-continua considered as composition including continually distributed assemble of molecular motors. The restrictions following from Clausius–Duhem inequality formulation of Second principle of Thermodynamics on the constitutive equations are under consideration. The capability of the new theory to model active bio-mechanical processes is demonstrated for muscle mechanics by unifying the well known classical heuristic models. Also it is shown that the theory is able to offer an active extension of the classical diffusion model as well.

Key words: active, diffusion, continuum, thermodynamics, thermomechanics, muscle, mixture.