Temperature Distribution at the Begining of Constant Velocity Flash Welding

Abstract

An useful formula of the temperature distribution during flash and butt welding has been established and the relationship between welding variables have become clear and the optimum welding conditions can be obtained easily.
If the heat flow is linear, the material is infinite and the clamp displacement velocity is constant, the following relationships have been acquired by using the theory of thermal conductivity.
For the initial current
θ=qt^1/2/chp√π{e^-w2-√πw(1-erf w)}
For the constant velocity flash welding
θ=4q/cpv√π{e^-vX/4h2∅(√vl/8h², vX/8h²)}
where q is the heat generation, t is the welding time, h is the heat diffusibility, c is the specific heat, x p is the density, w=x/2ht^1/2, X is the distance from the instantaneous flashing surface, x is the distance from the initial contact surface, erf w=2/√π∫ω0 e-ξ²dξ, l is the burn-off distance, v is the clamp displacement velocity.
By comparing these formula with the experimental data, the following conclusions have been obtained.
1) The effective heat generation is proportional to the clamp displacement velocity.
2) Influence of the heat radiation and cooling effect at clamps cannot be neglected
3) There is an upper limit in the temperature distribution and this maximum temperature distribution can be represented by
4) Regarding the flashing surface temperature as a standard, the temperature distribution curves can be obtained according to various clamp displacement velocities and burn-off distances only by calculations without any assumptions.