Analytical Considerations on the Temperature Distribution in Plate during Flash Welding

Abstract

Time variation of temperature rise of any point P which holds a distance ζ from the flashing surface is calculated in non dimensional form from the fundamental heat conduction equation, assuming that the temperature of the flashing surface is held at the fusion temperature θf, the room temperature being equal to zero. Assumption A.
The burn off per specimen is assumed to be expressed as B=1/n⋅αi⋅tn where αi and n are constant, n being n≥1. The base quantities of distance and time for non dimensional expression are choiced as shown in equ. (12) so that for t=τ0, the burn off becomes B=z0. See Fig. 2. It must be remarked that z0 and τ0 are bound through n and thermal diffusivity k as shown in equ. (17).
The calculated results (Fig. 4, 5) show that the non dimensional temperature ψ=θ/θf for any given point η (=ζ/zo) takes a maximum value ψm at a certain time τm (=tm/τo) and that the tempera-ture ψ holds nearly constant value of ψ m for considerable long time, though the above mentioned tendency decreases as n increases from 1. In Fig. 6 the calculated relations between the maximum temperature ψm for η and the corresponding time τm are plotted. It is remarkable that for case of n=2, 3 the time τm for a given value of η takes smaller (nearly minimum) value compared to the cases of n=1.5, 6. In Fig. 7 the relations between ψ m and η are plotted for n=1.5-6 as well as for n= 1, ∞. In case of n= 1, the curve takes the well known simple exponential form of equ. (21).
Case when the temperature of flashing surface is assumed to rise linearly. with time from zero to θf in time of t=0 to is also calculated. Assumption B. Curves (2) and (3) in Fig. 8 show the case of n=2 for to=0.5 τo and 1.0 τo. Curves (1) are for to=0, which are same as Fig. 4, and we see the degree of decrease of Ψ m and the delay of τm from the figure.
The calculated results of relation of Ψ m and η in case of n=2 are compared with the experimental data executed in Rensselaer Polytechnic Institute, for which Dr. Suzuki et al. have proposed in Welding Journal (34 June 271-s 1955) the experimental formula of Ψm=ε-0.92ηs. See Fig. 9. It is remarkable that our calculated results coincide fairly well with the experimental results of the Institute and the pro-posed formula, though the experimental conditions may not coincide with our assumptions. Several comments on the theoretical considerations in the above mentioned literature are described in our paper.