### Contents of Journal of Mechanical Engineering *57,* 5 (2006)

ŠTIGLER, J.: Tee junction as a pipeline net element. Part 1.
A new mathematical model 249
ŠTIGLER, J.: Tee junction as a pipeline net element. Part 2.
Coefficients determination 263
SINGH, S., MAHESHWARI, S., DEY, A.: Electrical Discharge
Machining (EDM) of aluminium metal matrix composites using
powder-suspended dielectric fluid 271
KADRY, S.: Generalization of probabilistic transformation
method for solving random differential equations 291
MOCHNACKI, B., PAWLAK, E.: Micro/macro models of crystallization
process - comparison of the results of numerical simulations 300

# Abstracts

### Tee junction as a pipeline net element. Part 1.
A new mathematical model

JAROSLAV ŠTIGLER

The problem of mathematical model of the tee junction is divided into two parts. The
first part is theoretical. It is focused on the derivation of a new mathematical model of the tee
junction as a pipeline net element. New loss coefficients, which describe fluid flow in the tee
junction, are introduced. The mathematical model is derived for the unsteady incompressible
fluid flow.

### Tee junction as a pipeline net element. Part 2. Coefficients determination

JAROSLAV ŠTIGLER

A new mathematical model of the tee junction has been established in Part 1. In Part 2,
the attention is focused on the numerical experiment of turbulent fluid flow in the tee
junction. Domain size and loss coefficients of the tee junction are determined on the basis of
numerical experiment.

### Electrical Discharge Machining (EDM) of aluminium metal matrix composites using
powder-suspended dielectric fluid

SHANKAR SINGH, SACHIN MAHESHWARI, ALOKE DEY

Aluminium Metal Matrix Composites (AMMCs), owing to their better multiple
functional characteristics, find a vast range of applications in the aerospace, automobiles,
defence, sports and tools industries. These materials pose a greater challenge to manufacturing
engineers due to the constraints in traditional machining to form complex shapes and achieve
fine surface finish because of their abrasive reinforcements, high hardness and brittleness.
This paper reports experimental investigations of the effect of process parameters on the
performance measures, namely Material Removal Rate (MRR) and surface roughness, via a
hybrid manufacturing process Abrasive Electrical Discharge Machining (AEDM) involving the
interaction of mechanical abrasion and thermal process, on stir-casted
6061Al/Al_{2}O_{3}p/20p work
specimens with copper electrode and SiC abrasive powder-suspended dielectric fluid. A mixed
orthogonal array L18
(2^{1}´ 3^{7}) experimental design was chosen to identify the effect of seven
control factors viz. pulse current (*I*_{p}), pulse ON time
(*T*_{ ON}), duty cycle (*t*),
gap voltage (*V*_{g}), tool
electrode lift time (*T*_{L}), Abrasive Powder Concentration
(APC) and Abrasive Particle Size (APS)
with three levels each, and a noise factor, aspect ratio having two levels.

An attempt has been made to develop models for optimizing AEDM characteristics, and
the significance of the models was checked using the Analysis of Variance (ANOVA) technique
and F-tests. The experimental results have shown that MRR and the surface roughness increased
with an increase in the addition of abrasives into the dielectric fluid.

### Generalization of probabilistic transformation
method for solving random differential equations

SEIFEDINE KADRY

The probabilistic transformation method with the finite element analysis is a new
technique to solve random differential equations. The advantage of this technique is finding
the expression in an "exact" form of the probability density function of the solution when the
probability density function of the input is known. The disadvantage is that it is limited to
some special cases and it depends on the characteristics (geometry and materials) of the
analysed structure, which is included in the random differential equation.
In this paper, a developed formula is used to generalize this technique by obtaining the
"exact" joint probability density function of the solution in any situation. Also, a technique for
the non-linear case is proposed.

### Micro/macro models of crystallization
process - comparison of the results of numerical simulations

BOHDAN MOCHNACKI, EDYTA PAWLAK

The micro/macro models of crystallization (the second generation ones) based on the
assumption that the kinetics of nucleation and nuclei growth is proportional to the
undercooling below the solidification point are discussed. In particular, the linear
model described among others in scientific works, the exponential one
and its modification are considered. The aim of our research is to estimate the
influence of the assumed mathematical description on the results of numerical
simulation of solidification process. On the stage of computations the control volume
method has been used.