A Consideration of Heat Conduction in Redial Direction in Spot Welding

Abstract

Heat conduction in radial direction in spot welding of infinite wide plate is treated neglecting the heat conduction to electrodes.
Instead of infinite wide plate, an isolated cylinder (Fig. 2) whose radius α is 1/R₂ times of the spot radius r₀ is considered and the temperature is calculated when heat is generated uniformly in the inner zone of radius r₀. See Fig. 3.
The temperature is calculated by using Bessel function series for two extreme cases of boundary condition at cylinder surface r=a, namely h=0 and h=∞. See eq. (1)
Fig. 6, 7 show the temperature variation when the dimensions r₀, a are 3 mm, 10 mm, k being 0.065 cm²/sec.
Fig. 11, 12 show the temperature variation of r=0 and r=a for h=∞, 0.
The time constant of the first term of Bessel function series which express the temperature variation is given as
τ1=a²/λ₁²k
where λ₁ is equal to 2.41 or 3.83 according as h=∞ or h=0. See eq. (6), Table 1.
We see the heat does not reach to r=a for t<τ₁, when we take R₀=r₀/a<0.3. Therefore the calculated temperature for the cylinder of radius a gives the real value for the spot welding in infinite wide plate. The calculated result also shows that the temperature at r=a for infinite wide plate is a little lower than the average value of the results obtained for cylinder by h=0 and h=∞