Online calculation

Index > Thermal history and welding cooling time in arc welding

The calculation is based on the following equation in which the effects of finite plate thickness and heat trasfer on the plate surfaces are considered on the original Rosenthal equation.


T: temperature (°C)

Tph: preheat & interpass temperature (°C)

: ambient temperature (°C)

Tw: temperature increase due to a moving point heat source

x: coordinate in the wedling direction (cm)

z: coordinate in the plate thickness direction (cm)

y: coordinate in the direction perpendicular to the welding direction (cm)

w: moving coordinate in the welding direction, w = x - v*t

v: welding velocity (cm/s)

t: time elapsed after the point heat source passed the static coordinate origin (x = y = z = 0), (s)




Qp: energy of heat source (cal/s)

h: plate thickness (cm)

: arc thermal efficiency, = 1.0 (SAW), 0.80 (SMAW, GMAW), 0.60 for GTAW

: heat transfer coefficient at the plate surfacei =0.0005cm/s (SAW),=0.0020cm/s (SMAW, GMAW, GTAW)

: heat transfer coefficient at the surface except the weld parti =0.0020cm/s

r: heat reflection rate at the plate surface =0.90 (SAW), =0.80 (SMAW, GMAW, GTAW)

: thermal conductiviey =0.06+0.000012*HI (cal/cm s)

: thermal diffusivitys =0.042+0.000016*HI (cm cm/s)

E: arc energy, E = 60*A*V /v (J/cm)

HI: heat input, HI = E (J/cm)

A: welding current (A)

V: welding voltage (V)

The above heat conduction equatiion is mathematically incorrect since the heat reflction rate, r is contained."r" was introduced so that the prediction could be more precisely made.

The accuracy of the prediction is shown in N. Yurioka. "Prediction of weld metal strength", IIW Doc. IX-2058-03