点溶接における半径方向への熱伝導

概要

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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/R_0 times of the spot radius r_0 is considered and the temperature is calculated when heat is generated uniformly in the inner zone of radius r_0. 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 r_0,a are 3mm, 10mm, k being 0.065(cm)^2/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 τ_1=a^2/λ_1^2k where λ_1 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<τ_1,when we take R_0=r_0/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=∞.
社団法人溶接学会の論文
1970-11-25