The skin-effect in ferromagnetic electrodes for wire-EDM
Summary (3 min read)
- 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 .
- It is able to deliver very short (0.2µs) and high current pulses (400A).
- 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 .
- It hence experiences higher resistance and lower inductance.
- The following subsections will discuss the frequency and material dependence of both.
- ∗Katholieke Universiteit Leuven, Division PMA, Celestijnenlaan 300B, 3001 Leuven, Belgium C u rr en t d en si ty r at io j (r )/ j( 0 ).
2.1.1 Plain wires
- This depends on its radius r0, its electrical conductivity σ, its magnetic permeability µ and the frequency of the current signal ν. ξ = r0 2 √ πνσµ (2) R0 is the D.C. resistance per unit length of the wire and is given by Pouillet’s formula as R0 = 1 πσr20 (3) The value of equations 1, 2 and 3 is calculated for steel and copper wires of diameter 100 and 250µm at 100kHz.
- 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 Influence of wire impedance on the process’s performance
- The wire impedance is immediately reflected in the working current and the attained surface roughness of the work piece.
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.
- Some wires also have a subcoating of copper (10 µm for 250 µm wires (table 2.1.2) and 4 µm for 100 µm wires).
- 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  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.
- 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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Cites background from "The skin-effect in ferromagnetic el..."
...High frequency discharge causes the current concentrating on the surface of the electrode due to skin effect, which strengthens the breakdown of dielectric and leads to more abnormal discharge ....
Cites background from "The skin-effect in ferromagnetic el..."
...It resulted in about 100nm Ra surface roughness [9, 10]....
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