The skin-effect in ferromagnetic electrodes for wire-EDM
Summary (3 min read)
Introduction
- High frequency current pulses in wire-EDM lead to excellent machining performance, in terms of work piece roughness, material integrity of the cut and material removal rate.
- To reach the highest frequencies the wire-EDM generator mostly consists of a voltage source with an as low as possible internal inductance.
- The working current delivered to the spark and hence the material removal rate of the process depends on the total impedance of the electrical circuit.
- In this article the importance of the wire’s impedance will be shown.
- Due to the skin-effect this impedance depends on the frequency of the current signal, especially for ferromagnetic wires, such as steel wire.
1 The high current needle-impulse generator
- All modern wire EDmachines are equipped with a high current needle-impulse generator [10].
- In the spark’s ignition phase (1) S2 and DH are engaged, after a while (2) the working current is imposed by engaging S1 and S2.
- On the other hand there is more electrode wear but this is not so important in wire-EDM since the wire is continuously renewed.
- A voltage source delivers a current that depends on the load: impedance of the machine, the wire, the gap and the work piece, which is a disadvantage while compared to current sources, who are supposed to deliver a fixed current independently of the process’s impedance.
2 The skin-effect in ferromagnetic wire-electrodes
- The skin-effect results from eddy currents within the wire that counteract the current in the core, and forces the current to the surface of the wire.
- Figure 2 shows the resulting current density distribution along the wire’s radius for a steel and a copper wire as it is simulated at 100kHz [7].
- It hence experiences higher resistance and lower inductance.
- The following subsections will discuss the frequency and material dependence of both.
2.1.1 Plain wires
- This is the ground frequency of the current signal.
- It shows that the skin-effect only plays an important role for steel wires, and especially for steel wires with big diameter.
- Interesting to see is that the lower carbon content steel wire has a lower resistance at D.C., but at high frequencies it rises to the same level as the higher resistant high carbon content wire.
- This can be fully explained by equation 2: the importance of the skin-effect rises with conductivity and permeability.
2.1.2 Coated wires
- The influence of the skin-effect on the overall resistance of a steel wire can be minimized by introducing non-magnetic-permeable materials in the coating that are good conductors.
- For a steel wire the resistance of the core and hence of the whole wire is frequency dependent.
- The table shows first of all that the D.C-resistance of the coated wires is smaller because of the good conductive coating that is electrically in parallel, but secondly the rising of the resistance is less compared to plain wires (table 2.1.1).
- For wires of smaller diameter, e.g. 100 µm, this will be valid to a lesser extent, because the increase in resistance due to the skin-effect is smaller in absolute numbers (table 2.1.1).
- Relatively speaking it is even smaller compared to the D.C. resistance.
2.2.1 Plain wires
- The calculated values are given in table 2.1.1.
- With increasing frequency the inductance decreases by 40% for a 100µm steel wire and 75% for a 250µm steel wire.
- It should be noted that in this section only the internal inductance of the wire was calculated.
- The magnetic energy stored in the field outside the wire was disregarded.
- This is achieved by fixing the work piece geometry and material (in this case Böhler K107 steel (DIN X210CrW12) of 30 mm height).
2.2.2 Coated wires
- The internal inductance of a coated a-magnetic wire can be calculated by calculating the energy stored in the magnetic field inside the wire.
- A simple decomposition into parallel inductances, analogous to the calculation of the resistance, is not valid.
- Appropriate conclusions can however also be made from physical insights.
- When the coating becomes thick on the other hand the inductance will again be lowered.
- Most of the current will flow in this non-permeable high conductive coating, which is electrically parallel to the steel core.
3.1 Working current and roughness
- This includes the machine, the wire, the working gap and the work piece.
- Since the pulse rise time A is fixed, the inductance also influences the height of the current pulse .
- The current peaks were averaged over 1000 samples.
- Comparing the two experimental steel wires (E0/1 and E10/10) shows the impact the conductive coating has on the average peak current.
- It will almost instantly evaporate when a spark appears.
3.2 Material Removal Rate
- The current is, of course, firmly correlated to the removal rate of the process.
- Here the current is not at all the only parameter of determinative influence.
- But if this is done the positive properties of the steel core (its high allowed pre-load) [6, 8] disappears.
- From figure 4 and table 3.1 it is clear that not only the impedance of the wire defines its cutting speed.
3.3 Joule’s heating
- Another impact of the skin-effect on the machining performance is directly related to the resistance of the wire.
- It will be possible to deliver more energy to the process, as long as the energy loss in the increased working gap [9] and its contamination stays within acceptable limits.
- Not only the overall temperature of the wire drops because of the thick coating.
- This can easily be calculated assuming the core to be electrically parallel to the coating.
- Pcore Pcoating = Rcoating Rcore (8) This once again makes the use of steel wires in high precision applications a good choice.
4 Conclusions
- A steel core wire allows high pre-load on the electrode in Wire-EDM, which leads to an increase of precision at an affordable price, compared to the normally used refractory metals like tungsten and molybdenum.
- It has been shown by the examination of the wire’s impedance, that the skin-effect becomes a predominant phenomenon in wire-EDM, while machining with ferro-magnetic wires.
- The skineffect rises the electrical resistance of the wire.
- Since the generator is essentially a voltage source, the higher electrical load, leads to lower machining currents.
- The importance of using a thick conductive coating becomes less with thinner diameters.
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Frequently Asked Questions (17)
Q2. What is the effect of the skin-effect on a copper wire?
The skin-effect results from eddy currents within the wire that counteract the current in the core, and forces the current to the surface of the wire.
Q3. What is the effect of the coating on the cutting speed of the wire?
Since the coating is substantially less electrical resistant than the steel core, most of the Joule heating power will be dissipated in the coating.
Q4. How much does the resistance of a steel wire increase at high frequencies?
For the steel wire of diameter 100µm the influence of the skin-effect is less, it yields an increase of the resistance by a factor 2 to 3, resulting in a value which is 30 times as high as a copper wire.
Q5. What is the disadvantage of a voltage source?
A voltage source delivers a current that depends on the load: impedance of the machine, the wire, the gap and the work piece, which is a disadvantage while compared to current sources, who are supposed to deliver a fixed current independently of the process’s impedance.
Q6. What is the effect of conductive coatings on steel wires?
It is also mentioned that conductive coatings out of non-permeable materials on top of steel wires lower the impedance even at high frequencies.
Q7. What is the frequency dependence of a wire’s inductance?
The frequency dependence of a wire’s internal inductance is approximately given by equation 5, with ξ given by equation 2.2πνL R0 ≈ ξ2 − ξ66 if ξ << 12πνL R0 ≈ ξ − 3 64ξ + 3 128ξ3 if ξ >> 1 (5)The wire’s inductance L0 at low frequencies equals µ 8π [7].
Q8. How can the inductance of a coated a-magnetic wire be calculated?
The internal inductance of a coated a-magnetic wire can be calculated by calculating the energy stored in the magnetic field inside the wire.
Q9. What is the effect of the skin-effect on the resistance of a steel wire at frequencies?
Since the resistance of a steel wire at the frequencies under consideration seems to be independent of carbon content, the 0.7%C wire can be chosen to profit from its higher tensile strength in precision applications [6, 8].
Q10. How much resistance does a wire have?
When calculated for a steel wire (0.7%C) with a 4 µm Zn-coating the D.C. resistance is 17.32 Ω/m, compared to 22.73 Ω/m without coating.
Q11. What is the effect of the skin-effect on the resistance of a steel wire?
Since all known coatings (Cu, CuZnx, Zn,...) are a-magnetic, the skin-effect can be neglected in the calculation of the resistance of the coating.
Q12. What is the resistance of a wire with a thick coating?
For thick coatings the D.C. as well as the high frequency resistances are comparable to those of plain brass wires, while the tensile strength of their cores stays considerably higher.
Q13. What is the effect of the Joule effect on the cutting speed of a plain steel?
This means that e.g. a plain steel wire with high resistance will be weakened and broken even at lower peak currents (erosion energy), and hence lower speed, than a coated steel wire which has low resistance.
Q14. How is the resistance of a steel wire calculated?
For a coating with outer radius ro and inner radius ri it is given byRcoating = 1σcoatingπ(r2o − r2i ) (4)The total value of the wire’s resistance is then found by assuming that the core of the wire is electrically parallel to the coating.
Q15. What is the effect of the skin-effect on the inductance of a steel wire?
The dropping of the inductance due to the skin-effect in steel wires, as explained in section 2.2.1, will be counteracted by using a thin conductive coating which is non-permeable (copper, brass, zinc, . . . ) in the same way the rising of the resistance in counteracted.
Q16. What is the effect of the skin effect on the wire?
It has been shown by the examination of the wire’s impedance, that the skin-effect becomes a predominant phenomenon in wire-EDM, while machining with ferro-magnetic wires.
Q17. What is the effect of the skin-effect on the resistance of a wire?
In this sense the resistance electrically parallel to the steel core is smaller and less able to lower the total resistance of the wire.