Mechanism of Bead Ripple Formation

Abstract

In the previous report, the author developed a new method to calculate the rippling pattern by means of the 'solidification equation, ' which was postulated to represent the balance of interfacial tensions at the edge of the solid- liquid interface. Furthermore in this report. he showed analytically that the simple harmonic standing wave of a molten pool can be reproduced in the bead ripple pattern in a scale of v/c (v; welding speed, c; velocity of surface wave of the molten pool, v/c<<1)), only when the mean liquid phase angle θ is 90 deg., and the liquid phase angle θ is always equal to the solidification angle φ. The bead height tends to decrease after each one cycle duration when the inclination angle of advancing solidliquid interface fi is smaller than 90 deg., even if θ=β and θ=θ. Therefore, in order to obtain the stationary flat bead, it is necessary for the molten pool to be of swollen shape, and mean the liquid inclination angle a must increase as β becomes smaller and θs of a material greater.
solidification equation γ_scosφ=γcosθ+γi
γ_s=γcosθs+rγi
θ_s; characteristic value of θ when φ is zero in solidification equation