= ⋅π⋅ω⋅τ ⋅ −× ⋅π⋅ω⋅τ ⋅ 2 3 contact 3 3 1 (13) Q R 2 0 6155 . a contact shoulder 3 The heat generation from the probe surface represents = H H R a probe probe = ∫ ∫ ⋅ω⋅τ ⋅ ⋅ Q R dx dy probe 0 H 0 2 2 = ⋅ω⋅τ ⋅ ⋅ 2 = × × ⋅ω⋅τ ⋅ 2 ⋅ = ⋅ω⋅τ ⋅ 2 ⋅ The factor 5 denotes the five sides of the PEN probe. Heat generation from the tip surface is 0 8506 R . a probe θ=π 5 = ∫ ∫ ω⋅τ ⋅ ⋅ ⋅ θ⋅ The factor 10 denotes the ten different regions that form a PEN surface. From Equations 13–15, QTotal can be calculated as QTotal = Q1 + Q2 + Q3 2 0 6155 3 2 0 6155 3 1 8088 ⋅ ⋅ ⎛⎝ ⎜ 3 2 1 8088 ⋅ ⋅ ⎛⎝ ⎜ 2 3 1 8088 2 3 2 3 2 3 3 75 The energy per unit length of the weld can be calculated as dividing Equation 16 by weld speed () as WELDING RESEARCH Analytical Heat Generation Equation for Hexagonal Pin Profile Figure 5 shows the simplified tool design for the HEX pin profile. The heat generation from the shoulder surface is calculated by subtracting the heat generated due to the probe tip (Q3) from the heat generated due to the shoulder (QShoulder). a = Rprobe is the side of the HEX pin. Therefore, Q1 is calculated as Qshoulder – Q3, i.e., Equations 2–20 2 contact 3 1 (18) The heat generation from the probe surface is H H R a probe probe Q R dx dy = = = = probe The factor 6 denotes the six sides of the HEX probe. Heat generation from tip surface is as follows: = R a probe 6 Q R R d dr = θ=π θ= The factor 12 denotes the twelve different regions that form a HEX surface. From Equations 18–20, QTotal can be calculated as QTotal = Q1 + Q2 + Q3. 2 3 Total contact shoulder contact probe 2 contact 3 3 2 3 2 3 3 Total contact shoulder contact probe ⋅ ⋅ ⎛⎝ ⎜ contact 2 3 9 2 Total contact shoulder probe ⋅ ⋅ ⎛⎝ ⎜ 2 3 9 2 The energy per unit length of the weld can be calculated as dividing Equation 21 by the weld speed () as Q contact R R d dr R probe probe probe (15) 3 0 0 = = θ= = = = . a H Q . a a H . a H contact R contact probe contact probe contact probe probe 0 36176 5 036176 1 8088 (14) = ⋅π⋅ω⋅τ ⋅ −× ⋅π⋅ω⋅τ ⋅ + ⋅ω⋅τ ⋅ ⋅ +× ⋅π⋅ω⋅τ ⋅ = ⋅π⋅ω⋅τ ⋅ + ⋅ω⋅τ ⋅ ⋅ = ⋅π⋅ω⋅τ ⋅ + π ⎞⎠ ⎟ = ⋅π⋅ω⋅τ ⋅ + π ⎞⎠ ⎟ Q R . a . a H . a Q R . a H Q R . a H or Q R . R H Total contact shoulder contact contact probe contact Total contact shoulder contact probe Total contact shoulder probe Total contact shoulder probe probe (16) 3 3 2 3 3 2 3 2 3 2 = ⋅ ω⋅μ⋅ υ⋅ 2 3 3 2 ⋅ ⋅ ⎛⎝ ⎜ ⋅ + π ⎞⎠ ⎟ 1 8088 = ⋅ ω⋅μ⋅ υ⋅ 2 3 3 75 ⋅ ⋅ ⎛⎝ ⎜ ⋅ + π ⎞⎠ ⎟ Q F R R . a H or F Q R R . R H Energy/length shoulder shoulder probe Energy/length shoulder shoulder probe probe (17) 2 3 2 2 3 2 = ⋅π⋅ω⋅τ ⋅ − ⋅π⋅ω⋅τ ⋅ Q R a contact shoulder 2 3 3 3 = ∫ ∫ ⋅ω⋅τ ⋅ ⋅ =ω⋅τ ⋅ ⋅ = ⋅ω⋅τ ⋅ ⋅ = ⋅ω⋅τ ⋅ ⋅ a H Q a H a H H contact R contact probe contact probe contact probe probe 2 6 2 3 (19) 2 0 0 2 2 2 2 = ∫ ∫ ω⋅τ ⋅ ⋅ ⋅ θ⋅ = π⋅ω⋅τ ⋅ = ×π⋅ω⋅τ ⋅ = ⋅π⋅ω⋅τ ⋅ Q a a Q a R contact probe probe contact contact contact probe 18 12 18 2 3 (20) 3 0 0 3 3 3 3 3 = ⋅π⋅ω⋅τ ⋅ − ⋅π⋅ω⋅τ ⋅ + ⋅ω⋅τ ⋅ ⋅ + ⋅π⋅ω⋅τ ⋅ = ⋅π⋅ω⋅τ ⋅ + ⋅ω⋅τ ⋅ ⋅ = ⋅π⋅ω⋅τ ⋅ + π ⎞⎠ ⎟ = ⋅π⋅ω⋅τ ⋅ + π ⎞⎠ ⎟ Q R a a H a Q R a H Q R a H or Q R R H Total contact shoulder probe probe (21) 3 3 2 3 3 2 3 2 3 2 APRIL 2015 / WELDING JOURNAL 121-s
Welding Journal | April 2015
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