Temperature range determination for butt welding.

Catana, Dorin

1. INTRODUCTION

Heat transfer is the process which transforms thermal energy from high value parameters to low value parameters. Temperature is the parameter which estimates the quality of heat and could be defined as a global measure of process intensity which gives the level of energy inside the body. Heat exchange complies with the second principle of the thermodynamics which establishes the natural sense of heat propagation which is always from the source with a high temperature to the source with a low temperature. Heat transfer penetrates more or less in all current areas of method and its importance is growing. Heat transfer is produced in three distinct ways: conduction, convection and radiation. Thermal conduction is the process of heat transfer from an area with a high temperature to an area with a low temperature. The transfer takes place inside of a solid, liquid or gaseous medium, or between different medium in direct contact. Conduction is the only heat transfer process through opaque bodies.

2. THEORETICAL CONSIDERATIONS

Butt pressure electric welding is presented in figure 1 (Iovanas, 2004). This method is differentiated by other welding processes such as spot welding, line welding etc. not only regarding the theoretically scheme but also considering that the welding seam is stretched on both welded section. From a dimensional point of view a single, continuously part is obtained and from a metallurgical point of view a homogeneous with uniform mechanic characteristics is the result of this process (Eftimie et al., 1998).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The parts to be welded are heated using Joule-Lentz effect and by connecting them to electrical current. Maximum temperature is achieved on contact surfaces area between the parts and diminishes toward the fastening area. In order to determine the evolution of temperature (the establishment of temperature range) a model of a thermal system which is similar in behaviour should be found in order to see what is happening when butt welding is in progress.

For butt welding is to be considered as a model one that is closest to reality and that is a wide surface (conductive-convective systems). This system is made of an acicular rib (figure 2) with limited values of the cross section (d) which are smaller in comparison with the rib length (Catana, 2007).

For a rib with a cross section area (S = S(x)) and perimeter (P = P(x)), both variable, in contact with a fluid (air) with constant temperature and convection coefficient ([alpha] = ct), in some sections, including side perimeter, rib temperature is the same and is given by equation:

t = t(x)> [t.sub.f] (1)

The differential equation for the analyzed thermal transfer process is:

[d.sup.2] [theta] / d [x.sup.2] - 1/S x dS / dx x d [theta] / dx - [m.sup.2] x [theta] = 0 (2)

where:

- 0 = t - [t.sub.f];

- [m.sup.2] = [alpha] x P / [lambda] x S.

Equation (2) can be used for different cross section shapes. For an acicular bar with length (l), diameter (d) and constant section (S = ct) the equation becomes:

[d.sup.2] [theta] / d [x.sup.2] - [m.sup.2] x [theta] = 0 (3)

[theta] = [C.sub.1] [e.sup.mx] + [C.sub.2] [e.sup.-mx] (4)

By solving the equation and considering the limit conditions, temperature distribution on rib's length is:

[theta] / [[theta].sub.0] = t - [t.sub.f] / [t.sub.0] - [t.sub.f] = ch m x (b - x) / ch m x b (5)

where:

- ch x = [e.sup.x] + [e.sup.-x];

- b = l;

- [t.sub.0] temperature at the rib's toe (Catana, 2006).

In case of the butt welding, temperature value in contact area is known (the free rib end) and based on this value, temperature range can be determined during rib's length, from tip to toe.

For a hexagonal steel bar with a 15 mm free length, 12 mm key aperture and [[lambda].sub.1200] = 21.17 W/(m[degrees]C) temperature values established with equation (5) are presented in the table 1 (Catana, 2005).

In table 1 difference between temperatures do not exceed -6.70% and that is why a mathematical method is recommended. Due to laborious calculus FEM is recommended.

When FEM software is not available the equations can be easily used by technical personnel in order to calculate the temperatures for butt welding.

It is necessary to know the temperature of the parts to be welded in order to use butt welding and to finalize the process. Knowing the temperatures range in piece makes possible to perfect the welding process.

In figures 3 and 4 is presented the evolution of established temperature through simulation for a steel bar with specific features presented before.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

3. CONCLUSIONS

Considering that is very laborious to determine thermal transfer value during welding processes using numerical method could be a real advantage. Besides the rapidity of getting the results, another benefit is given by the accuracy of the solutions when suggested model is closer to reality.

Obtained temperature range can be used when hot plastic deformation is studied for bars butt welded. Also if the simulation is made for more diameters, the diagram can be used in order to determine the temperature evolution. The bar type of diagram can be used in order to facilitate the access of specialists from production considering that mathematical relations are difficult and final results are similar.

The developed model offers close results to simulated ones (+5.25% ... -6.70%), which confirms the initial analogism. As well the validity of developed model for different cross section and free lengths will be checked.

After improving the model, digital integration into dedicated software to determine these temperatures is expected.

Calculated and simulated results will be verified by measuring the temperature of the parts while welding them.

This final test will determine a substantial improvement of the developed theoretical model for butt welding.

4. REFERENCES

Catana, D. (2005). Theoretic contributions for the plastic deformation simulation process, Proceedings of International Scientific Conference "Modern Technologies, Quality, Restructuring" TMCR 2005, pp. 333-337, ISBN 9975-9875-4-0, Technical University of Moldova, 05-2005, University of Moldova, Chisinau

Catana, D. (2006). Possibilities of simulation of the axial deformation for the butt head welding, Proceedings of International Scientific Conference "Modern Technologies, Quality, Restructuring" TMCR 2006, Musca, G., pp. 1135-1140, ISSN 1011-2855, Jassy, 05-2006, Bulletin of Polytechnic Institute of Jassy, Jassy

Catana, D. (2007). The evolution of the temperature field in the time of butt head welding, Proceedings of International Conference on Materials Science and Engineering, Catana, D., pp. 481-484, ISSN 1223-9631, Transylvania University, 02-2007, Supplement of Bulletin of Transylvania University of Brasov, Brasov

Eftimie, L.; Dinescu, I. & Catana, D. (1998). Materials Engineering, Lux Libris, ISBN 973-9240-55-0, Brasov

Iovanas, R., (2004). Spots pressure welding, Lux Libris, ISBN 973-9240-71-8, Brasov

Tab 1. Temperature evolution with distance.
General solution of the equation is:

 Temperature
Distance [[degrees]C]
 from through [DELTA]
free rib t
end [mm] Calculus FEM [%]

 0 1200 1200 0
 2.5 945 980 -3.70
 5 876 830 5.25
 7.5 642 685 -6.70
 10 631 608 3.56
 12.5 583 559 4.12
 15 486 497 -2.26