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where K,, K2, K3 and K4 are constants. By arranging the terms in equation (2.9), L
can be directly obtained as follows:
L. --
(Va - K2)I - K312 - K4
K11
(2.10)
It is, however, very difficult to measure the arc voltage directly. Its value must
be estimated through the calculation of the voltage drop in the wire extension (VI).
For the spray transfer mode, it is generally accepted that the electrode wire is heated
according to Ohm's law as it is fed through the extension length or stick-out [ref.
128]. There are two approaches for V, calculation that consider the resistivity as
either independent or dependent on the temperature. The second approach is more
realistic and was used by Hamoy [ref. 13] to obtain a relationship, which estimates the
voltage drop in the wire extension:
X2WFS (2.11)
j
In equation (2.11), %1 is a constant equal to the effective resistivity at the end of the
extension, in units of Q. mm, X2 is a constant depending upon the room-temperature
resistivity of the wire, j= 1/At is the current density in the wire and A, is the wire
cross-section area. Cook et al. [ref. 128] adopted this relationship for the
implementation of a through-the-arc seam tracking system
The arc voltage can then be obtained by subtracting V, from the welding
voltage, V, as follows:
va =v- ve (2.12
The value of VQ is then applied in the equation (2.10), resulting in the arc
length, La. The addition of L. and Le gives the contact tip-to-workpiece distance, SO,
which is the figure of interest.
SO = L. + Lt (2.13)
In the case of Oct, heavy-gauge V-groove butt and narrow gap joints, by
oscillating the welding torch across the joint it is possible to generate an error signal
which corresponds to the torch-to-joint deviation. This signal is fed into an adaptive
control system which calculates the positioning correction necessary for the torch to
track the joint [refs. 128,129].
Although this method has been derived for the spray transfer mode of
GMAW, it can also be applied to the short-arc (dip-transfer) [ref. 128] and pulse [ref.
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