Theoretical approach to the humping phenomenon in welding processes

Abstract

The conjecture which explains the humping phenomenon in terms of Marangoni convection is discussed and rejected. Instead, Rayleigh's theory of the instability of a free liquid cylinder due to surface tension is applied. The width-to-length ratio of the weld pool has to exceed 1/2 pi to avoid humping. The growth time of a disturbance is found to be approximately the same as the growth time of a hump. The analysis of a bounded cylinder provides a new stability criterion which allows the introduction of a bounding function to distinguish between arc and laser welding. The weld pool dimensions are estimated in terms of a simple heat conduction model. The threshold value predicted theoretically for the travel speed above which humping commences agrees well with the experimental value. It decreases with increasing power, which is in qualitative agreement with experimental results.