COMPARISON OF SIMULATION AND EXPERIMENTAL AXIAL LOADINGS FOR HYDROMECHANICAL BULGE FORMING OF COPPER CROSS-JOINTS COMPARISON OF SIMULATION AND EXPERIMENTAL AXIAL LOADINGS FOR HYDROMECHANICAL BULGE FORMING OF COPPER CROSS-JOINTS

Hydromechanical bulging is applied mainly to the series production of hydraulic installation and sanitary facilities including tubes with a changeable diameter, T-pipes and cross-joints. The process consists in placing a tube segment in a die-cavity, pouring some liquid over it and sealing the faces. As a result the liquid pressure rises and the pipe is upset. The basic parameters of the hydromechanical process of bulge forming are: liquid pressure and axial loading. The simulations of hydromechanical bulge forming were performed using MSC Marc software based on the finite element method. The calculation results were compared with the experimental data especially to study axial loading for different ratios d/D, s o /D and for different variations of internal pressure. The results of numerical simulations of axial loading are in good agreement with the experimental data for established (cid:2) = 0,15.


Introduction
The method of hydromechanical bulging of cross-joints was patented in 1973 [1]. Since then many research teams have been investigating the problem especially for steel T-pipes and crossjoints [2][3][4][5][6][7][8]. The technology involves placing a tube segment in a die-cavity, pouring some liquid over it, and sealing the faces. As can be seen from Fig. 1, the rising pressure of the liquid upsets the pipe.
As a result, we obtain bulged cross-joints with identical or different branch and outer diameters, the shape and dimensions being presented in Fig. 2.  Except for the liquid pressure, the upsetting force is also responsible for hydromechanical bulge forming. As the stub pipe bulge on two sides, the lengths can be considerable. By applying appropriate pressure, it is possible to obtain a cross-joint with exactly the same dimensions -radius and diameter -as those of the die-cavity.

COMPARISON OF SIMULATION AND EXPERIMENTAL AXIAL LOADINGS FOR HYDROMECHANICAL BULGE FORMING OF COPPER CROSS-JOINTS
The paper discusses the significance of the upsetting forces in the hydromechanical bulge forming of copper cross-joints with the same and different branch and outer diameters. The forces values obtained by computer modelling were compared with the experimental data. The analysis takes into account various d/D and s o /D ratios and pressure changes.

Methodology
MacNeal-Schwendler software was used for modelling. The basic calculation package was the general-purpose MSC. Marc program [4][5][6][7]. As the analysis concerned plastic working, it was required to apply MES program as well. The model was developed and analysed with the aid of MSC/MENTAT presented in [6]. A simulation of the hydromechanical bulge forming process was conducted for copper cross-joints with a relative wall thickness s o /D ϭ 0.05. Table 1 presents the dimensions and mechanical properties of the samples of copper pipe sections used both in the modelling and testing of the bulged pipes. The properties were determined experimentally by static tensile testing (columns 4-7) and using the Heyer method of stepped specimens (columns 8-9).
The calculations and the experiment aimed at the following final geometry: length of the tubular blank section after bulging l ϭ 70 mm, diameters of the stub pipes d ϭ 20 mm and d ϭ 22 mm if all diameters are identical (d/D ϭ 1) and d ϭ 18 mm and d ϭ 16 mm if the diameters are different (d/D ϭ 0.9 and d/D ϭ ϭ 0.8 respectively).
The pipe was covered with a square mesh consisting of 7800 coating type elements, the thickness of which was established to be 1 mm. It was assumed that the matrix and dies/ were stiff rigid enough and could not be affected by any deformations [4][5][6][7]. The physical and mechanical properties of the deformed elements were compared with those of a model of a uniform material with good elasticity and plasticity. Thus, we had p ϭ 524 0.33 for pipes with s o /D ϭ 0.05, and p ϭ 517 0.27 for pipes with s o /D ϭ 0.068. In the simulation, the changes in pressure p, which were dependent on the relative pipe bulging ⌬l/l o , were assumed from the experimental data [3,7,8] obtained with a test facility described in [8]. The values of the coefficients of friction, ϭ 0.1 and 0.15, were assumed to be the same as in [2].

Simulations and experimental results
The graph in Fig. 3 shows selected values of the upsetting forces obtained in the simulation and experiment. In this case, the cross-joints were hydromechanically bulged for a selected change in pressure (Fig. 3b) and the ratios d/D ϭ1; s o /D ϭ 0.05 assuming that the coefficient of friction was equal to 0.1 and 0.15 in the simulation.
As can be seen from In cross-joints with the relative wall thickness s 0 /D ϭ 0.068, the changes in the upsetting forces for various d/D are similar to those with s 0 /D ϭ 0.05; the values of the upsetting forces, however, turn out to be greater not only due to greater pressures but also due to thicker wall at the ends and in the centre of the cross-joints. The difference in the values of the forces for cross-joints with s 0 /D ϭ 0.068 (d/D ϭ 1 Ϫ 73kN and d/D ϭ 0.9 Ϫ 81kN) at ⌬l/l o ϭ 0.42 was 9.8%.
As the maximum values of the forces had to be assessed, the following tabulation was made ( Table 2).
The greatest coincidence of the maximum values of upsetting forces obtained in the simulation and the experiment was reported for the assumed coefficient of friction equal to 0.15. The difference ranged 4.54-16.85%. The simulation results were almost always smaller than the experimental data. The only exception concerned the modelling of a cross-joint with s o /D ϭ 0.05 and d/D ϭ 1, where the maximum force was 4.54% greater than that in the experiment. This was the case when the smallest difference between the force values was established for ⌬l/l o ϭ 0.42.

Conclusions
1. The values of the forces responsible for the bulge forming process calculated by computer modelling were reported to Dimensions and mechanical properties of copper tubes Table 1 D 0 x s 0 l 0  • if there is a rise in the pressure used for the bulging; this is due to the fact that the greater the pressure, the greater the loads of the liquid on the swelling dies faces; moreover, this causes an increase in unit loads [2] in the contact area of the cross-joint and the die cavity,   • if there is a rise in the relative bulging ratio ⌬l/l o , caused by an increase in the wall thickness in body area of the cross-joint [7] and in the material strength [4], • if there is a decrease in the d/D ratio caused for example by greater plastifying stresses [4] in body area near the faces.