270
9 Dynamical Behaviors of Keyhole and Weld Pool …
P(V )
a function that takes into account the displacement of the keyhole
with a welding speed V and increases with it.
At low welding speed (1 m/min as shown in 9–12), the effect of P(V ) can be
neglected. For usual values of different parameters involved in Eq. (9.15), one can
also neglect P h (P h ≈ 1.6 kPa for L K H ≈ 20 mm). So, Eq. (9.15) becomes:
P 0 ≈ P amb + P c
(9.16)
From the above equation, it is clear that the minimum pressure inside the keyhole
that keeps it open is its closing pressure P c (=σ/r ), which is obtained under complete
vacuum. Hence, the lower limit of evaporation temperature inside the keyhole will
be defined by this pressure P c . So one can define a critical ambient pressure:
P C R ≈ P c /10
(9.17)
Below this critical ambient pressure, the effect of ambient pressure can be considered negligible in Eq. (9.16). Using this theory, the P C R1 (σ ≈ 2 N/m, r ≈ 0.2 mm)
in No. 120 reference is about 1.0 kPa. It can be seen in Fig. 9.12a that the experimental saturated ambient pressure is about 1.0–2.0 kPa, which well agrees with the
predicted result. Using the same method, the P C R1 (σ ≈ 2 N/m, r ≈ 0.2 mm) in No.
121 reference is about 1.2 kPa, while the experimental saturated ambient pressure
is about 1.0 kPa as shown in Fig. 9.12b. To sum up, in laser welding under vacuum
conditions, it is unnecessary to lower the degree of vacuum to a minimum possible
value. A suitable vacuum degree can be calculated using the critical ambient pressure
formula (Eq. (9.17)) to obtain a big penetration depth.
When the welding speed increases, the effect of P(V ) in Eqs. (9.16) and (9.17)
must be considered. Thus, it is easy to know that the critical ambient pressure
P C R increases with the welding speed, though this behavior is not obvious. This
phenomenon is shown in Fig. 9.12. Additionally, as shown in Fig. 9.17, the keyhole
wall temperature increases as the welding speed increases. When the increments are
the same, the variations of keyhole wall temperature under lower ambient pressure is
larger. This demonstrates that in high-speed welding, the penetration depth is more
sensitive to the welding speed under lower ambient pressure, which is consistent with
the experimental results of Abe et al. and Börner et al. (Fig. 9.12) and the simulation
results of Pang et al. (Fig. 9.18).
It is interesting to notice that a keyhole can be considered as a nozzle that ejects a
vapor inside an ambient atmosphere. Based on the aerodynamic theory, the threshold
condition for vapor to eject from the keyhole to the environment with ambient
pressure of P amb at a supersonic speed is given by the relation:
P 0
P amb
= K =
γ + 1
2
(γ /γ −1)
(9.18)
9 Dynamical Behaviors of Keyhole and Weld Pool …
P(V )
a function that takes into account the displacement of the keyhole
with a welding speed V and increases with it.
At low welding speed (1 m/min as shown in 9–12), the effect of P(V ) can be
neglected. For usual values of different parameters involved in Eq. (9.15), one can
also neglect P h (P h ≈ 1.6 kPa for L K H ≈ 20 mm). So, Eq. (9.15) becomes:
P 0 ≈ P amb + P c
(9.16)
From the above equation, it is clear that the minimum pressure inside the keyhole
that keeps it open is its closing pressure P c (=σ/r ), which is obtained under complete
vacuum. Hence, the lower limit of evaporation temperature inside the keyhole will
be defined by this pressure P c . So one can define a critical ambient pressure:
P C R ≈ P c /10
(9.17)
Below this critical ambient pressure, the effect of ambient pressure can be considered negligible in Eq. (9.16). Using this theory, the P C R1 (σ ≈ 2 N/m, r ≈ 0.2 mm)
in No. 120 reference is about 1.0 kPa. It can be seen in Fig. 9.12a that the experimental saturated ambient pressure is about 1.0–2.0 kPa, which well agrees with the
predicted result. Using the same method, the P C R1 (σ ≈ 2 N/m, r ≈ 0.2 mm) in No.
121 reference is about 1.2 kPa, while the experimental saturated ambient pressure
is about 1.0 kPa as shown in Fig. 9.12b. To sum up, in laser welding under vacuum
conditions, it is unnecessary to lower the degree of vacuum to a minimum possible
value. A suitable vacuum degree can be calculated using the critical ambient pressure
formula (Eq. (9.17)) to obtain a big penetration depth.
When the welding speed increases, the effect of P(V ) in Eqs. (9.16) and (9.17)
must be considered. Thus, it is easy to know that the critical ambient pressure
P C R increases with the welding speed, though this behavior is not obvious. This
phenomenon is shown in Fig. 9.12. Additionally, as shown in Fig. 9.17, the keyhole
wall temperature increases as the welding speed increases. When the increments are
the same, the variations of keyhole wall temperature under lower ambient pressure is
larger. This demonstrates that in high-speed welding, the penetration depth is more
sensitive to the welding speed under lower ambient pressure, which is consistent with
the experimental results of Abe et al. and Börner et al. (Fig. 9.12) and the simulation
results of Pang et al. (Fig. 9.18).
It is interesting to notice that a keyhole can be considered as a nozzle that ejects a
vapor inside an ambient atmosphere. Based on the aerodynamic theory, the threshold
condition for vapor to eject from the keyhole to the environment with ambient
pressure of P amb at a supersonic speed is given by the relation:
P 0
P amb
= K =
γ + 1
2
(γ /γ −1)
(9.18)