A Mathematical Analysis of the Temperature Distrbution during Flash Welding and Determination of Optimum Welding Condition (Report 2)

Abstract

In the second report, a mathematical analysis of temperature distribution during flash welding is presented to discuss satisfactorily the establishment and the form of the stabilized temperature distribution, and to introduce mathematically the fundamental non-dimensional parameters which are essential in correlating the temperature data in various metals and alloys. Linear, parabolic as well as the general flashing patterns are discussed. The fundamental parameters are: Ψ=(T-T₀)/(T_m-T₀), and n=(na/kⁿ)^1/(2n-1)ξ, where T is the temperature, T₀ the initial temperature, T_m the melting point of the material being flashed, and ξ is the distance from the instantaneous flashing interface, k the thermal diffusivity, n and a are constants to determine the displacement of moving platen with a relation Xp=atⁿ, t being the time from the start of flashing.
In parabolic flashing, η=(gp/k²)^1/3ξ where gp is the platen acceleration. The effect of cooling by the clamping jaws is the more pronounced when a parameter: η1=(gp/k²)^1/3(l₀-B_c+vD) is the smaller, where l₀ is one half the initial clamping distance, D the diameter or thickness of speciamen, v=1/2 for round and v=1 for rectangular sections, and B_c the critical burn-off per specimen. The critical burn-off is estimated with: B_c=(gp/k²)^-1/3.
It has also been shown that the effect of heat of transformation in steels is negligible, and a reasonable and theoretical determination of the average value of thermal diffusivity over the temperature range from room temperature to melting point, has been proposed.