What do you mean by current?
TWI Bulletin, August 1985
by Chris Needham
Chris Needham, BSc (Eng), is Chief Control Engineer at Abington.
How should waveforms which fluctuate or cross zero be represented in convenient numerical form for procedural and QA purposes? Conventional manipulation of data relates to resistive loads but the arc is non-linear. This article describes some methods of dealing with the problems.
Current is fundamental to arc welding and its measurement is vital to establish welding procedures for quality assurance. [1] However, depending on the instruments used, there can be discrepancies of 10% or more. This is a much larger error than can be tolerated in high quality welding so great care is needed both in measurement methods and in specifying operating currents.
Steady or fluctuating DC
There is no problem with measurement of steady currents. The amplitude is clearly unique and can be represented by a single numerical value, such as 143A ( Fig.1) However this alone gives no indication of fluctuation, whether inherent (as with the ripple from a 3-phase rectifier supply) or accidental because of changes in arc length. The degree of fluctuation in the latter instance may be small, especially with steeply drooping or so-called constant current supplies, and could be quoted as maximum/minimum limits, e.g. 149/137A ( Fig.2).
Fig.1. Analogue representation of a steady DC value
Fig.2. Symmetrical fluctuation above and below the mean
More usually the current is given as the mean or average value with the deviation about the mean. This can be stated as the commonly occurring extreme limits of deviation, i.e. maximum highs and minimum lows, but is not in general the worst value of each. These commonly occurring deviations may not be symmetrically disposed about the average level ( e.g. falls may be greater than rises) and are expressed as differences from the mean, as in
Fig.3. Asymmetrical fluctuations about the mean
Mathematically if the deviations are random then the deviation is better expressed by a statistical index called the standard deviation. * This index implies that 2/3 of all measured values (taken at regular or random instants) fall within one deviation from the mean, and less than 1% of such readings exceed three standard deviations high or low from the mean ( Fig.4).
* The standard deviation is calculated from the individual readings of differences from the mean value, by the formula:
where δ is each difference, and n the number of readings.
Fig.4. Fluctuations expressed as standard deviations from the mean
For instance, if the standard deviation for a current reading of 143A were 2A, the majority of readings would lie in the range 145/141A, and less than 1% of such readings would be greater than 151A, or lower than 137A.
To measure such fluctuations the instrument must have a sufficiently fast response i.e. only those fluctuations which occur over longer periods than the time to establish a reading can sensibly be measured.
Thus digital instruments (which update every 1 or 2 seconds) can only indicate the longer term fluctuations - say over periods of 5-10sec and more. Analogue instruments are generally an order of magnitude faster in response (down to say 0.1 sec at best), but to record the instantaneous readings for analysis later requires use of a chart recorder or equivalent system.
Microprocessor-based instruments provide the advantages of digital presentation with large storage capacity for thousands of readings taken in rapid sequence. How many readings and how fast is a matter of judgement with respect to the type of arc welding concerned, and the time scale for significant deviations to be found.
The Welding Institute printing arc monitor continuously registers instantaneous values ( Fig.5), (or samples at some 250 readings per sec) and their averages over a set period - upwards of 1 sec. (For general purpose applications 2sec averages are normal, but in the more advanced units printout can be obtained for averages taken over any period from 1-90sec). These 1 or 2sec averages are stored in the microcomputer to provide a grand average, as well as to determine the degree of fluctuation of the short term averages. The fluctuation is expressed as the high/lowest values, and as the standard deviation (called variation index on the multichannel printing monitor) about the grand average ( Fig.6).
Fig.5. The Welding Institute's seven channel printing monitor for submerged arc welding
Fig.6. Printout of running values and processed data
What about dip transfer welding?
The previous comments apply to steady currents with a low degree of ripple and only moderate longer term fluctuation. How do they apply to dip transfer welding which operates with a rapid succession of short circuits and large amplitude current fluctuations ( Fig.7)
Fig.7. Current waveform typical of dip transfer welding
It may appear meaningless to read the average current from the detailed waveform derived from an oscilloscope - the mean is the value of current which in fact is not operating for 99% of the time! However, from an analysis of the electrical circut, [2] it can be proved for a simple case that as long as the ratio of arc time to short circuit time is constant then the long term mean current is constant irrespective of frequency. Thus, independent of how large the instantaneous current swing is, the average current taken over any number of complete short circuit/arc cycles is unchanged ( Fig.8). This fact is true, independent of inductance (which also affects the current swing).
Fig.8. Identical mean currents for widely differing waveforms
Moreover even with a random sequence of short circuits (varying individually in duration but at a given constant arc/short circuit time ratio) the current taken over even a few short circuit/arc cycles is substantially constant to within 1 or 2% ( Fig.9). Thus, as in practice the frequency of shorting is in the region of 40 - 90 per sec, the current is, as a mean, constant when averaged over a period of 0.5 sec or more.
Fig.9. Mean current for a series of random current peaks
Therefore in dip transfer welding it is valid to quote the mean current and ignore the detailed waveform. There are inherent fluctuations in this mean value because of variations in arc operation which ultimately (with a given power supply) lead to corresponding variations in the arc/short circuit ratio. However, for some other purposes, such as quantifying the dynamic characteristics (inductance and slope settings, etc), it may be advantageous to quote the value of the current peak or the degree of variation in current peak about the mean peak and so forth, [3] as well as the overall mean value (and its long term variation).
Thus, one procedure for dip transfer welding in a quality application, as well as specifying wire composition and shielding gas, could state for example mean current 127A (4A standard deviation) with average current peaks not exceeding 240A (13A standard deviation), i.e. virtually no instantaneous peak exceeding about 280A.
What about pulsed current welding?
In MIG welding, pulsed current is used to control metal transfer, particularly at low wire feed rates where otherwise the metal would melt in large globules. The current levels and durations for the pulse and background are very different, but compared with dip transfer welding the current waveform ( Fig.10) is more consistent as it is principally determined by the power source.
Fig.10. Ideal regular waveform of pulsed current MIG welding
Again, the mean current is relevant, as it is directly associated with the wire feed rate. To a first approximation, the burnoff rate, which must be matched to the feed speed, is proportional to the average current. (Only at relatively high current levels in the normal spray transfer region, or with high amplitude, short duration current pulses, is there a significant further increase in burnoff rate associated with resistance heating of the electrode wire, specially with fine wires and long extensions).
Within limits, for a given wire feed speed, the mean current is the same irrespective of the pulse current waveform or the size (frequency) of the metal transfer. Therefore, the process is defined by mean current averaged over any number of complete pulse/background cycles, as was found for dip transfer welding.
Two features of the pulse itself are important; amplitude and duration. For a sharply defined square wave, no problems arise as the two values can easily be measured. In practice, however, the waveforms of most commercial equipments are not square, and can exhibit strong ripple, slow rise and fall, or be even more triangular than square! ( Fig.11). At present there is no agreed method for comparing one pulse waveform with another, since both amplitude and duration contribute to metal transfer. For the time being the mean of the pulse current (determined over its corresponding duration) can be taken as a satisfactory index of operating conditions. Here the pulse is determined over that period for which the instantaneous pulse current is above the overall mean level.
Fig.11. Nominally square current waveform of commercial pulsed MIG welding set
In low frequency thermal pulsing (pulse TIG welding), the pulse is the important feature as this influences the characteristics of the molten weldpool and its penetration. Again, the pulse is defined by its mean value over the time period when the instantaneous current is above the overall long term average value. In both these pulse examples special instrumentation is needed to extract the mean pulse data, as distinct from the overall mean. Alternatively, measurements can be made from oscillographic recordings of the current waveform.
What about alternating currents?
For a symmetrical AC wave the mean is strictly zero, irrespective of its amplitude and a modified definition is required, such as the mean of one halfcycle, or of the full rectified wave (which is numerically identical).
For an alternating square wave ( Fig.12) there is no difficulty in defining its magnitude - the operating level is clear and the mean of the (rectified) wave is identical to the peak value. Different current waveforms should not be compared by their peak values alone ( Fig.12,13), and skilled interpretation is needed to make valid comparisons of the effect of waveshape on welding performance.
Fig.12. Square waveform showing identical peak and mean (rectified) values
Fig.13. Sine waveform - ratio of mean to peak value is 2/ π:1 (or 0.6366:1).
Although the peak amplitude uniquely defines a sine wave ( Fig.13) there is a choice in expressing the overall content either as the mean (rectified) value (which for a pure sine wave is
or 0.6366 of the peak) or the commonly quoted RMS value * (which is
or 0.7071 of the peak).
* The RMS of any waveform (including sine waves), can be derived using the following formula:
where n is the number of readings of instantaneous current i in time t (which must be a whole number of waves).
Nearly all instruments designed to read AC give the RMS value, but for arc welding the mean (rectified) value is needed. The RMS value of current of any waveform is defined as that value I which as a steady DC provides the same heating (I 2 R) in a resistance (R). Thus the RMS value is relevant to heating of cables, transformer windings, etc, and in defining currents in resistance welding, but not in arc welding as the arc does not follow Ohm's Law - (see Appendix).
Therefore, great care is needed in quoting current values on AC. So long as like is compared with like, then it is unimportant whether the values of an alternating current are peak, RMS or mean. However, where different waveforms are involved, apparently diverse values are obtained. For example, a manual metal arc electrode could be rated at 220A maximum on AC, but only 200A maximum on DC. In fact these two statements are the same since for a sine wave a current which is 220A (RMS) has a mean (rectified) value of 200A - the same as the DC example. Therefore, it is better to keep to mean values throughout to avoid possible confusion.
Which instrument shall I use?
In general engineering practice, meters were almost invariably mean reading for DC, but RMS reading for AC. Modern electronic instruments can be RMS reading on both AC and DC. However for steady DC the RMS value is the same as the mean - as this is the basic definition of RMS - that which gives the same heating as a steady current. In the context of arc welding such instruments give the correct (that is mean) numerical value for steady DC, but are 11.1% high on sine wave AC as they give the (true) RMS figure, and not the (rectified) mean value. Even more confusing is the fact that some instruments for AC actually respond to the mean (rectified) value of the wave but are scaled to read RMS values (presuming that the waveform of the current is sinusoidal). Nevertheless, the correct (mean) value is still obtained by dividing the reading by 1.111, so unless the instrument is labelled to the contrary, it is safe to multiply the apparent AC value by 0.9 to give the desired mean value, provided that the current is essentially sinusoidal.
Welding Institute instruments for monitoring arc welding are designed to give mean values for consistency between AC and DC operation, unless otherwise indicated.
However, until instrumentation for arc welding is rationalised, it will be desirable at least for specifying welding schedules to mention what current reading instrument has been used if it is not known for certain whether the reading is RMS or mean. The International Institute of Welding has noted the problem and has accepted the recommendation of Commission XII on 'Flux and gas shielded welding processes' for mean currents to be specified for DC and AC welding arcs.
Summary
In DC and AC arc welding only mean current values are significant. For AC the mean is that of one half cycle, or of the rectified waveform. It is important to know what instrument is being used as its reading may well be 11.1% high.
For pulsed current operation the mean of the pulse (and its duration) is relevant in both TIG (low frequency pulsing) and MIG (medium frequency pulsing). Also the overall mean current (pulse and background) defines the burnoff rate in MIG welding.
For dip transfer MIG welding the current peaks and their variation are a measure of the dynamic stability, while the mean current defines the overall equilibrium.
References
| N° | Author | Title |
|
| 1 | Street J A: | 'Practical measurement of voltage and current in arc welding.' Welding Institute Research Bulletin 1985 26 (4) 113-115. |
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| 2 | Needham J C and Percival D F: | 'Parametric relationships in short-circuit MIG welding.' Welding Institute Members Report 214/1983. |
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| 3 | Lucas W and Butler M: | 'An evaluation of minicomputer techniques for data acquisition and analysis in arc welding process research.' Welding Institute Members Report 134/1981. | Return to text |
Appendix
Mean or RMS?
The significance of the RMS value of any current wave is that it is the value of the steady current which provides the same heating over the same time (in a linear resistive load) as the waveform concerned. The current waveform may be unidirectional but regularly changing in amplitude (as in pulse current MIG arcs), or alternating (as with a simple sine wave).
The power (watts, W) expended at any instant in a resistor (or in an arc) is directly given by the product of voltage across the load and current through it, viz., vi = W where v and i are the instantaneous values of voltage and current. Therefore, in a time t the total energy (joules, J) expended is the integral of the instantaneous power or
and the average power is energy/time or
Now in a resistor, by Ohm's Law, v = iR where R (ohms, Ω) is the resistance. Thus the average power can also be written as
But with a steady current I, the power expended in the resistor R is simply I 2 R. Equating these two expressions for power, then I 2 =
This defines the current I as the 'RMS' value of the waveform, i.e. the Root of the Mean of the Square of the instantaneous current.
On the other hand an arc does not obey Ohm's law, since the voltage across it is not proportional to the current through it. In other words the arc, though a resistive load, does not exhibit a constant resistance. However, to a reasonable approximation the arc voltage (for a given arc length, shielding gas, etc.) is nominally constant over a wide range of current, as shown by the so-called arc characteristic.
Therefore, the average power can be written as
where V a is the average value of the approximately constant arc voltage. But the term
is the average of the instantaneous current, i, over the time period concerned. Thus the power expended in the arc is given by (V a I a a) where (I a ) is the average or mean current and (V a ) the (approximately constant) mean arc voltage.
Therefore to compare one current waveform with another, and particularly in comparing AC with DC, it is the mean value of current which is relevant in arc welding and not the RMS value.
