technologies
Article
Wire Tool Electrode Behavior and Wear under
Discharge Pulses
Sergey N. Grigoriev 1 , Marina A. Volosova 1 , Anna A. Okunkova 1, * , Sergey V. Fedorov 1 ,
Khaled Hamdy 1,2 , Pavel A. Podrabinnik 1 , Petr M. Pivkin 1 , Mikhail P. Kozochkin 1 and
Artur N. Porvatov 1
1
2
*
Department of High-Efficiency Processing Technologies, Moscow State University of Technology
«STANKIN», Vadkovsky per. 1, 127055 Moscow, Russia;
[email protected] (S.N.G.);
[email protected] (M.A.V.);
[email protected] (S.V.F.);
[email protected] (K.H.);
[email protected] (P.A.P.);
[email protected] (P.M.P.);
[email protected] (M.P.K.);
[email protected] (A.N.P.)
Production Engineering and Mechanical Design Department, Faculty of Engineering, Minia University,
Minia 61519, Egypt
Correspondence:
[email protected]; Tel.: +7-909-913-1207
Received: 16 August 2020; Accepted: 16 September 2020; Published: 20 September 2020
Abstract: This work is devoted to researching the tool electrode behavior and wear under discharge
pulses at electrical discharge machining. The experiments were conducted on the workpieces of
12Kh18N10T (AISI 321) chrome-nickel anti-corrosion steel and D16 (AA 2024) duralumin by a
0.25-mm-diameter CuZn35 brass tool in a deionized water medium. The developed diagnostic and
monitoring mean based on acoustic emission registered the oscillations accompanying machining at
4–8 kHz. The obtained workpiece and non-profiled tool surfaces were investigated by optical and
scanning electron microscopy. Calculated volumetric and mass removal rates showed the difference
in the character of wear at roughing and finishing. It was shown that interaction between material
components in anti-corrosion steel machining had an explosive character between Zn of brass and Ni
of steel at a micron level and formed multiple craters of 30–100 µm. The secondary structure and
topology of worn tool surfaces were caused by material sublimation, chemical interaction between
material components at high heat (10,000 ◦ C), explosive deposition of the secondary structure.
Acoustic diagnostics adequately registered the character of interaction. The observed phenomena at
the submicron level and microstructure of the obtained surfaces provide grounding on the nature of
material interactions and electrical erosion wear fundamentals.
Keywords: erosion; tool wear; sublimation; ZnNix ; explosive deposition
1. Introduction
The subject of electrical discharge machining (EDM) and wear of a wire tool electrode is not new,
but the physical processes that occur during processing are still not sufficiently studied [1–4]. It is
related to the absence of the possibility of visual control over the processes occurring in the discharge
gap during EDM especially for large workpieces [5,6]. Plenty of studies are devoted to the processes
related to the physical phenomena of erosion wear with various conclusions [7–11]. However, at the
industrial level, there is no solution to avoid the negative consequences of the accident wire electrode
breakage or dumping of the machined part into the working tank at the end of machining. It is
especially actual in the case of splitting two co-dependent parts—die and punch for the injection mold,
micro-gears [12,13].
Technologies 2020, 8, 49; doi:10.3390/technologies8030049
www.mdpi.com/journal/technologies
Technologies 2020, 8, 49
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An experienced operator often determines the control over processing and process conditions
by the specific noise that occurred in the working area. It grows with an increase in the intensity of
processing (roughing or finishing) and varies during the electrical discharge machining of materials
with uneven structures—porous material, set of tubes, nanocomposites, or composites. The changes in
the specific sound are especially noticeable during wire tool penetration into the workpiece and at the
end of machining.
The electrical discharge machining of materials occurs in specific conditions between two electrodes.
A bias increase is followed by ionizing the space between two electrodes at the moment of their
approach. Dielectric breakdown by spark provokes a discharge channel that creates the conditions
of low-temperature plasma with 10,000 ◦ C that can be observed in particular conditions (forming
intermetallics of Al2 Cu [14,15], ZnNix [16], CeNi2 [17], burning titanium at 1200 ◦ C [18,19]) in the form
of an instant growing gas bubble surrounded the discharge channel. Then, pulses interrupt to restore
the breakdown conditions for the next pulse—the bias in the gap, erosion products’ washing away
from the working area. The occurred conditions are close to the conditions of lightning formation [20].
The temperature in the interelectrode gap achieves high value in a microsecond [21–23].
All monitoring means can be divided into optical and non-optical—electrical and vibroacoustic.
The absence of visual contact with the working zone due to its tiny sizes hampers the application of any
optical monitoring means. At the same time, the existed monitoring of the electrical parameters does
not provide adequate data on the effectiveness of the discharge pulses since for the modern control
systems all the produced pulses in the working zone are counted as working ones when a part of
them can be spending on the destruction of erosion products [24,25]. It can be grounded by difficulties
that met electrical discharge machining in processing materials with threshold conductivity, uneven
structure, or microstructure, and inclined surfaces with a thickness of more than 100 mm.
The vibroacoustic monitoring method does not have this kind of disadvantage, as it counts only
effective discharge addressed to the material to be processed on the destruction of the surface that was
recorded with the help of the accelerometers placed at the working table of the machine [26,27]. It can
be an effective means for not only tool behavior investigation and its influence on the quality of the
machined surfaces but also an effective means for adaptive control of electrical discharge machining in
real manufacturing conditions.
Simultaneously, research of the character of tool electrical erosion wear, sublimation
phenomena [28–30], and the nature of the material destruction of the machined surfaces can give
additional, comprehensive, and exhausting data.
This paper is aimed at the research of electrical discharge machining by the developed diagnostic
means to obtain new data on the influence of wire tool behavior on the quality of the machined surfaces;
wire tool wear at roughing and finishing, the nature of material destruction under discharge pulses,
and sublimation phenomena.
The research is conducted for two materials:
•
•
12kH18N10T (AISI321) chrome-nickel anti-corrosion structural steel that is often used in injection
mold manufacturing;
D16 (AA 2024) duralumin used for aviation purposes.
The work’s scientific novelty is in new data on electrical erosion wear of materials, sublimation
phenomena, nature and mechanism of material destruction for two types of structural materials,
dependencies between detected acoustic emission and machined surface quality, and classification of
the eroded surfaces of the tool.
The tasks of the study are:
1.
2.
Applying the vibroacoustic means for research on dependencies between the tool behavior and
surface quality;
Research of the tool and machined surface morphology and chemical composition;
Technologies 2020, 8, 49
3.
4.
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Classification of the observed defects and traces of tool destruction at roughing and finishing of
two material types;
Analyses of the chemical interactions between components that occurred in the discharge gap and
conclusions on type material destruction and changes occurred at surface and subsurface layers.
2. Materials and Methods
2.1. Equipment
A four-axis wire electrical discharge machine, Seibu M500S, was used in the experiments for
research of wire tool behavior and wear under pulses. The main characteristics of the machines are
presented in Table 1.
Table 1. Main characteristics of wire electrical discharge machines used in experiments.
Characteristic
Value and Description
Max axis motions along the axes X×Y×Z, mm
500 × 350 × 310
Max angle of conical machining, degree
±10◦
Max weight of workpiece, kg
800
Accuracy of positioning along the axes, µm
±1÷2
Achievable roughness Ra, µm
0.4
Dielectric medium
Deionized water
Machine body
The frame is made of gray cast iron having good
thermal and vibration compensating characteristics
The machines are located in a thermo-constant room to reduce ambient temperature’s effect on
the results of processing. Workpieces were immersed in a dielectric for 10 min before processing to
avoid dimensional fluctuations related to the difference in temperatures between the environment and
working fluid. The dielectric height was established at 1 ÷ 2 mm above the workpiece. The upper
guide of the machine was placed at a minimum distance above 2 ÷ 5 mm from the dielectric [31–33].
The tool electrode is a brass wire with a diameter dw of 0.25 mm made of CuZn35 (Cu—65%;
Zn—35%) with a processing temperature of 260 ◦ C and annealing temperature of 425–750 ◦ C.
The choice of the electrode type was made since a brass tool of 0.25 mm in diameter is the most
widespread for wire electrical discharge machining and suitable for the broad field of applications
when the forced choice of any other electrode is due to a severe technological need and is associated
with the need to purchase and reinstall expensive nozzles.
It should be noted that the positive polarization of the workpiece and negative polarization of the
tool electrode is traditional for the electrical discharge machining. However, modern machine tools
can switch the electrodes’ orientation for some particular modes or even during machining uneven
and hard-to-machine materials in automatic mode.
A CNC program was prepared manually; path offsets were not taken into account. The EDM-factors
were chosen using recommendations mentioned in previously conducted works and developed by
other scientific groups [25,34–36] (Table 2). The maximum working voltage Vo varied in the range of
40–70 V with a pitch of 10 V for characterization of the discharge pulses by for oscilloscope research
and to provoke the conditions of wire breakage for microscopic research. At least five samples and
cuts were produced for each group of parameters.
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Table 2. Electrical discharge machining (EDM) factors during experimental work.
Factor
Value
Seibu M500S
1
Operational voltage in the interelectrode gap before the approach of the tool electrode to
the workpiece, Vo
55, 60, 65
Auxiliary voltage that occurs at the moment of discharge between the tool electrode and
workpiece, Vg
32
Strength of the working current in the interelectrode gap, I
8
Auxiliary current to increase the cutting efficiency when the circuit is turned back on, Ns
43
Time of disconnection of the current source, the percentage ratio of the time of the
discharge pulse to the time of its absence, Toff
6
Time intermittent pause to ensure the stability of the processing process, Ad
305
Speed of the tool rewinding, Ws
35
Feed speed, Sg
5
Wire tension, Wt
30, 35, 40
Dielectric pressure in nozzles for flushing, Fl
245
1
Provided in equivalent unit of the machine.
2.2. Materials
The chemical composition of 12Kh18N10T (AISI 321) austenite steel is presented in Table 3;
the composition of D16 (AA2024, AlCuMg2) duralumin is in Table 4. The thickness of the samples was
20 ± 0.1 mm for both materials.
Table 3. Chemical composition of 12Kh18N10T steel (AISI 321) in wt%.
Element
Fe
Cr
Ni
Ti
Si
S
Mn
Cu
P
C
wt%
Balance
17–19
9–11
About
0.8
Up to
0.8
Up to
0.02
Up to
2.0
Up to
0.03
Up to
0.035
About
0.12
Table 4. Chemical composition of D16 alloy (AA2024, AlCuMg2) in wt%.
Element
Al
Cu
Mg
Mn
Fe
Si
Zn
Ni
Ti
wt%
90.8–94.7
3.8–4.9
1.2–1.8
0.3–0.9
Up to
0.5
Up to
0.5
Up to
0.3
Up to
0.1
Up to
0.1
The high chromium content of the proposed in the research steel ensures the metal’s ability to
passivate and causes strong corrosion resistance of steel. The addition of nickel converts steel to
austenite class. This property is of exceptional importance, allowing to combine the machinability with
an expanded set of performance properties. The addition of strong carbide-forming element titanium
eliminates the tendency to intergranular corrosion. In turn, carbon forms a refractory titanium carbide
and excludes a decrease in the concentration of chromium by chromium carbides formation. It should
be noted that the field of chromium-nickel steel applications dominates in the modern rolled metal
market [37–40].
Duralumin D16 is a structural alloy mainly used in the aviation and space industries. D16 is rarely
used in its pure form since it has less strength and hardness in the non-quenched state. The alloy is
classified as a durable thermo-hardened material [41,42].
A Fischer Sigmascope SMP10 instrument (Helmut Fischer GmbH, Sindelfingen, Germany)
measured the specific electrical resistance ρ of the materials used in experiments (Table 5, Figure 1a).
The device measures the material electric conductance in Siemens and the percentage of the control
Technologies 2020, 8, 49
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sample’s electrical conductance produced from
annealed bronze in the range of 1 ÷ 112%. All measured
𝜴⋅𝒎𝒎𝟐
Ω·mm2
values were converted to m . The melting/sublimation
points of the materials T provided in
𝒎
Figure 1b [43–46].
Table 5. Specific electrical resistance ρρ of some materials at +20 ◦ C.
2
Specific Electrical Resistance ρ [ Ω·mm
m ] ρ
Material
12Kh18N10T (AISI 321) steel
D16 (AA2024) alloy
Brass alloy, CuZn35
0.746
0.028
0.065
(a)
𝜴⋅𝒎𝒎𝟐
𝒎
(b)
Figure 1. Electrophysical properties of the materials used in experiments: (a) specific electrical resistance
ρ (b) sublimation/melting point T.
ρ at +20 ◦ C;
The stress-strain curves of chosen materials have the presence of elastic and plastic deformation
zones [47,48]. The fracture formation schemes have a ductile phase that increases with the material’s
plasticity—from 12Kh18N10T (AISI 321) steel and brass to D16 (AA2024) alloy. The reduction area
for these materials is ~38 ÷ 42 % for steels [47], ~52 ÷ 53 % for brass alloys [49], and ~75 ÷ 77 % for
aluminum alloys [50]. Tensile strength σ
σB (UTS) for these materials are 510–830 MPa for 12Kh18N10T
(AISI 321) steel, 450 MPa for CuZn35 brass alloy, and 345–420 MPa for D16 (AA2024) alloy.
Reduction area SRA is calculated by the following equation [47]:
𝑆 −𝑆
= S0 − Smin ·100
∙ 100[%],
[%],
S𝑆RA =
S𝑆0
(1)
where S0 is an original transverse area, mm2 , and Smin is a minimal area of the final neck, mm2 .
2.3. Monitoring
A digital oscilloscope TDS2014B (Tektronix, Berkshire, UK) produced the characterization of the
discharge pulses.
The vibroacoustic monitoring was provided by piezoelectric accelerometers mounted on the
elastic system of the machine [23,25–27,51,52] (Figure 2). The data received by the accelerometers
signals were forwarded to preamplifiers, amplifiers VShV003 (JSC Izmeritel, Taganrog, Russia), and an
analog-to-digital converter E440 (L-card, Saint-Petersburg, Russia), and recorded with a personal
computer (PC). Data were recorded at 1 min, 30 s, and 5 s before the end of processing. Spectral analysis
was performed at frequencies 4–8 kHz. The signal was preliminarily cleaned from low-frequency noise
using a high-frequency filter. The signal’s effective amplitude was determined. The square of this
amplitude is proportional to the signal that arises in the machine’s elastic system under disturbing
influences of the discharge pulses. The cutoff frequency of filters is 2 kHz.
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Figure 2. Scheme of monitoring sensor setup at electrical discharge machine: (1) is a workpiece; (2) is a
wire tool; (3) is a current sensor; (4) is accelerometers; (5) is a workpiece fastening system; ADC is the
analog-digital converter; PC is a personal computer.
2.4. Physical Relationship of EDM Factors and Vibration Amplitude
Typically, electrical discharge machining has a very narrow range of working factors for machining
every material type. Nevertheless, up to 16 factors can be varied during machining [6]. The papers
related to EDM research concentrate on some of them as we have done regarding the research subject.
It was decided to vary two of the most important factors—operational voltage, which influences
the density of discharge pulses distribution, and wire tension, which influences system stiffness and
consequently wire oscillation amplitude. The detailed force diagram is presented in [27].
The amplitude of the wire can be presented by summarized force of working impulses in the
system’s action ΣFimp and stiffness kn :
P
Fimp
An =
.
(2)
kn
Σ
At the same time, the stiffness of the system is determined by its mass:
∑
𝐴 =
mn
kn = 4π2 2
(3)
T
𝑚
where T is a period of self-oscillations;
= 4𝜋 the signal amplitude has an inverse relationship with
𝑘 thus,
𝑇
the weight.
Regarding operational voltage, it has a physical dependence on the signal’s amplitude, since
it influences the density of the discharge pulses and, consequently, the summarized force factor.
The electrical impulse itself is a short-term burst of electrical breakdown voltage and working current
that can be presented as follows:
X
Fimp = I·V0 .
(4)
The energy of pulses then will be:
∑ 𝐹 X= 𝐼 · 𝑉
Eimp = I·An .
The wire tension has dependence that ∑
is 𝐸even=
more
𝐼 · 𝐴evident—Wt influences the system stiffness:
Fe
,
kn =
∆l
𝑘 =
(5)
(6)
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where Fe is a restoring force that is opposite and equal to the applied wire tension Wt and ∆l is a change
in the wire length. Thus:
|Wt |
.
(7)
kn =
∆l
Moreover, the height of the workpiece also influences the stiffness of the system and wire amplitude:
kn =
E·S0
,
ln
(8)
where ln is a wire length, E is Young’s modulus, and S0 is a wire area.
2.5. Characterization of the Samples, Wear Rate, and Discharge Gap
An EL104 (Mettler Toledo, Columbus, OH, USA) laboratory balance with a measurement range of
0.0001 ÷ 120 g weighed the obtained samples with an error of 0.0001 g.
The samples’ surface roughness was controlled by a high-precision profilometer, Hommel Tester
T8000 (Jenoptik GmbH, Villingen-Schwenningen, Germany) with a resolution of 1 ÷ 1000 nm and a
measurement error of 2%.
An Olympus BX51M instrument (Ryf AG, Grenchen, Switzerland) provided the optical microscopy;
the discharge gap was measured optically.
A VEGA 3 LMH instrument (Tescan Brno s.r.o., Brno, The Czech Republic) with magnification up
to 1,000,000× provided the scanning electron microscopy and spectrometry of the sample.
The cross-sections were prepared according to the standard probe techniques by an ATM sample
equipment—Opal 410, Jade 700, and Saphir 300 (ATM, Haan, the Netherlands). Epoxy resin with
quartz sand provided pouring of the samples as a filler was used.
The worn area of the tool can be calculated by the equation of the circle segment area (Sw ):
Sw =
h
i
1 2 π·α
2
−
sin
α
mm
,
rw
2
180◦
(9)
where rw is a wire radius, mm and α is an angle of the segment, degree. The volumetric (Rv ) and mass
wear rates (Rm ) are calculated by the following equations [53,54]:
Rv =
i
∆V h
mm3 ·s−1 ,
t
(10)
∆m h −1 i
g·s ,
t
(11)
Rm =
where ∆V is volumetric wear, mm3 , ∆m is a worn mass, g, and t is the wire length wear time; for a
thickness of 20 mm, t = 0.343 ± 0.005 s.
The discharge gap is calculated by the following equation:
∆DB =
ls − dw
[mm],
2
(12)
where ls is the measured width of the slot, mm, and dw is the wire diameter, mm.
3. Results
3.1. Electrical Discharge Pulses
Electrical discharge machining occurs at the value of Vg , approximately half of the value of
operational voltage V 0 . Idle pulses of a particular amplitude and frequency were detected with the
value of the interelectrode gap ∆ (distance between two electrodes) more than the value of the gap
of dielectric breakdown ∆DB (∆ > ∆DB ), Figure 3a. The idle pulse repetition frequency is f = 10 kHz,
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and the amplitude depends entirely on the factor of the voltage in the interelectrode gap (V 0 ) applied
to the electrodes when the electrodes are at a distance ∆.
(a)
(b)
(c)
(d)
Figure 3. Electrical discharge machining pulses detected by the oscilloscope: (a) idle pules at a distance
∆
≥ ∆
∆ > ∆DB ; ∆
(b) interrupted
introduction of operational pulses at the distance ∆ ≥ ∆DB ; (c) ∆
operational
∆
pulses during machining ∆ = ∆DB ; (d)∆interrupted
operational pulses during unstable wire feed and
variation with the factors, ∆ ≈ ∆DB . ∆ ≈ ∆
An infrequent dielectric breakdown of the gap occurs with a decrease in distance ∆∆≥≥∆∆DB by a
single series of pointed operational pulses (Figure 3b). Regular operational pulses that are similar to
damped harmonic oscillations followed the tool penetration (Figure 3c). The working pulses frequency
is quite high and is equal to tenths of MHz and detected at a level of about 0.2 MHz. Furthermore,
the idle and operational pulses start to alternate with different frequencies and amplitudes that depend
on factors present in the stable mode (Figure 3d).
3.2. Wire Electrode Oscilations
It was determined that the vibroacoustic signal has a periodic character and decreases gradually
during the first 2–3 s after tool penetration. It continues to decline during the next 15–20 s of machining
(Figure 4a). At the same time, it increases approximately 20 s before the end of the machining. At 5–7 s
before the end of machining, the signal interrupts repeatedly. The character of the signal at the
beginning and the end of machining has a parabolic character. It corresponds to the final bridge
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destruction under the cutoff sample’s weight (Figure 4b) that was detected for the samples of both
materials with a weight up to 1.8 g.
(a)
(b)
(c)
Figure 4. Recorded signal and its root-mean-square value during electrical discharge machining of
12Kh18N10T (AISI 321) samples: (a) at 30 s of the tool penetration into the workpiece; (b) at 30 s before
the end of the processing; (c) octave spectra of the root-mean-square value of the signal amplitude of
24.5 g sample, V 0 = 65 c.u., Wt = 35 c.u., where (1) at 30 s before the end of the operation, (2) at 5 s.
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Octave spectra of the root-mean-square value of the signal amplitude (RMS) in Figure 4c showed
that RMS differs more than 2.5 times at 60 s and 5 s at a frequency band of 4 ÷ 8 kHz. Simultaneously,
the frequency band of 0.125 ÷ 4 kHz does not show significant changes during the recorded periods.
The changes in RMS were also observed during the variation of EDM factors and unstable processing.
The changes in a signal’s amplitude in the frequency band of 4–8 kHz at 60 s and 5 s before
the end of processing has a character that mainly increases with the augmentation of operational
factors and weight of the cutting-off sample (Figure 5). The changes at RMS of the signal amplitude
at a frequency of 8 kHz were noticeable for 12Kh18N10T (AISI 321) at three various values of the
operational voltage Vo. However, the changes in average RMS for the samples of ~2 g from D16
(AA2024) alloy are controversial.
The samples’ weight was 24.51 ± 0.0327 g and 4.28 ± 0.0450 g for steel and 10.70 ± 0.0375 g and
1.82 ± 0.1800 g for aluminum for a width of 10 and 2 mm correspondingly based on data of 15 steel
samples and five aluminum samples of each width.
10
10
at 60 s
5
at 5 s
RMS at 8 KHz, mV²
RMS at 8 KHz, mV²
15
0
8
6
4
at 60 s
2
at 5 s
0
4.3
1.8
24.5
Weight, g
Weight, g
(a)
(b)
12
10
8
6
at 60 s
4
at 5 s
2
RMS at 8 KHz, mV²
12
RMS at 8 KHz, mV²
10.7
0
10
8
6
at 60 s
4
at 5 s
2
0
4.3
24.5
1.8
Weight, g
10.7
Weight, g
(c)
(d)
Figure 5. Cont.
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10
RMS at 8 KHz, mV²
RMS at 8 KHz, mV²
14
12
10
8
6
at 60 s
4
at 5 s
2
0
8
6
4
at 60 s
2
at 5 s
0
4.3
1.8
24.5
Weight, g
10.7
Weight, g
(e)
(f)
Figure 5. RMS of the recorded signal’s amplitude at 8 kHz for two types of materials at various
operational voltage V 0 : (a) 12Kh18N10T (AISI 321) steel, V 0 = 55 V; (b) D16 (AA2024) alloy, V 0 = 55 V;
(c) 12Kh18N10T (AISI 321) steel, V 0 = 60 V; (d) D16 (AA2024) alloy, V 0 = 60 V; (e) 12Kh18N10T (AISI
321) steel, V 0 = 65 V; (f) D16 (AA2024) alloy, V 0 = 65 V.
The changes in RMS of the signal at 60 s and 5 s before the end of processing with the variation in
operational voltage V 0 and wire tension Wt are more noticeable for 12Kh18N10T (AISI 321) steel than
for D16 (AA2024) alloy, that is more ductile (Figure 6). Adequate data were obtained even for tiny pieces
with a weight of 3.7 g and 1.8 g correspondingly. It should be noted that stable processing corresponds
to the RMS’s minimal value at 60 s. RMS of the signal amplitude is higher at 12Kh18N10T (AISI 321)
steel machining (Figure 6a,b), by 12.5%, compared to D16 (AA2024) alloy machining (Figure 6c,d).
RMS of steel is in the range of 5 ÷ 14 mV2 with arithmetic mean of 8.54 mV2 ; RMS of duralumin is in
the range of 4.5 ÷ 9 mV2 with arithmetic mean of 7.475 mV2 .
12Kh18N10T (AISI 321) steel
16
RMS at 8 KHz, mV²
14
12
10
at 60 s, 25 g
8
at 60 s, 4 g
6
at 5 s, 25 g
4
at 5 s, 4 g
2
0
54
56
58
60
62
Operational voltage V₀, V
(a)
₀
Figure 6. Cont.
64
66
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12Kh18N10T (AISI 321) steel
16
RMS at 8 KHz, mV²
14
12
10
at 60 s, 25 g
8
at 60 s, 4 g
6
at 5 s, 25 g
4
at 5 s, 4 g
2
0
30
35
40
Wire tension Wt, N
(b)
D16 (AA2024) alloy
12
RMS at 8 KHz, mV²
10
8
at 60 s, 11 g
6
at 60 s, 2 g
4
at 5 s, 11 g
at 5 s, 2 g
2
0
54
56
58
60
62
Operational voltage V₀, V
(c)
Figure 6. Cont.
64
66
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D16 (AA2024) alloy
12
RMS at 8 KHz, mV²
10
8
at 60 s, 11 g
6
at 60 s, 2 g
4
at 5 s, 11 g
at 5 s, 2 g
2
0
30
35
40
Wire tension Wt, N
(d)
Figure 6. RMS of the received electrical discharge machining oscillation signal at 8 kHz for two types
of materials: (a) 12Kh18N10T (AISI 321), in dependence on operational voltage V 0 ; (b) 12Kh18N10T
(AISI 321), in dependence on wire tension Wt ; (c) D16 (AA2024), in dependence on operational voltage
V 0 ; (d) D16 (AA2024), in dependence on wire tension Wt .
3.3. Morphology of the Samples
Roughness profile Ra and recorded signal at 30 s before the end of machining are presented in
Figure 7. As can be seen, the density of the signal amplitude is higher at 12Kh18N10T (AISI 321)
−
−
steel machining (Figure
7a,b), by 20%,
compared to D16 (AA2024) alloy machining (Figure 7c,d);
−1
approximately 30 µm − and ~24 µm−1
− , correspondingly. The three-dimensional (3D) graphs of the
EDM factors’ influence on the average roughness Ra are presented in Figure 8, where minimal value is
associated with the stable machining process and the lowest RMS values of the signal’s amplitude.
(a)
(b)
Figure 7. Cont.
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(c)
(d)
Figure 7. Roughness Ra and recorded signal amplitude: (a) 12Kh18N10T (AISI 321) steel of 24.5 g,
Ra of 2.00 µm, V 0 = 55 V; Wt = 35 N; (b) 12Kh18N10T (AISI 321) steel of 4.3 g, Ra of 1.89 µm, V 0 = 55 V;
Wt = 35 N; (c) D16 (AA2024) alloy of 10.7 g, Ra of 3.04 µm, V 0 = 60 V; Wt = 35 N; (d) D16 (AA2024)
alloy of 1.8 g, Ra of 2.68 µm, V 0 = 60 V; Wt = 40 N.
(a)
(b)
Figure 8. Three-dimensional (3D) graphs of the surface roughness Ra dependences on operational
voltage V 0 and wire tension Wt : (a) 12Kh18N10T (AISI 321) steel; (b) D16 (AA2024) alloy.
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Δ
3.4. Discharge Gap
Δ
Figure 9 shows the measured
offset ∆*DB of the path in the dependence of EDM factors for two
Δ
types of materials. The offset ∆*DB includes the wire radius rw of 0.125 mm. The optically measured
effective discharge gap ∆DB is in the range of 45 ÷ 53 µm for 12Kh18N10T (AISI 321) steel and in the
range of 71 ÷ 78 µm for D16 (AA2024) alloy. The minimal values—170 µm for anti-corrosion steel and
196 µm for aluminum alloy—are associated with the stable machining process and corresponds to the
lowest RMS values of the signal’s amplitude.
(a)
(b)
Δ DB dependencies on operational voltage V 0 and wire tension Wt :
Figure 9. 3D graphs of the offsets ∆*
(a) 12Kh18N10T (AISI 321) steel; (b) D16 (AA2024) alloy.
3.5. Tool Wear
The tool electrode’s rupture point (Figure 10) shows cup neck formation before destruction that
corresponds to the ductile properties of the brass with the reduction area:
=
S𝑆RA =
0.049
−0.003
0.003
0.049 −
∙ 100
93.8[%],
[%],
·100
==
93.8
0.049
0.049
(13)
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(a)
(b)
(c)
Figure 10. Wire tool: (a) microphotograph, 5×; (b) microphotograph, 10×; (c) SEM-image, 2.0k×.
Figure 11 presents the electrode wear after roughing and finishing at the electrical discharge
machining of 12Kh18N10T (AISI 321) steel and D16 (AA 2024) duralumin.
Figure 11a shows the conjugation of two interdependent surfaces with two types of wear—lateral
at left and front at right. The wear has a different character. The front wear surface has the appearance
of the typical eroded surface—sublimated and heat-affected material coated by the secondary structure
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of electrode components with pores and cracks. Moreover, the surface is covered by craters of solidified
secondary material—usually consisting of the metallic material of the first order, solid solutions,
and complex compounds of the second order (mostly oxides in the case of machining in deionized
water). The craters have an explosive character that is not observed at lateral surfaces. The line of two
wear surfaces conjugation is pronounced.
Figure 11b shows lateral wear at finishing. The formed surface has visible edges; the conjoined
surface’s left side has no presence of wear when the right side is also blank but with clear traces of
secondary structure explosive deposition at the blank surface. The lateral wear surface showed two
types of material destruction—the classical eroded surface of material sublimation with secondary
structure deposition and mechanical wear traces.
Figure 11c shows the conjugation of two surfaces—of lateral wear and blank surface at roughing.
The left side of the image—blank surface—has pronounced traces—drops, copious splashes—of
explosive character of interaction occurred in the discharge gap at lateral wear. A significant volume
of uneven sublimated material coated by the secondary structure with pores and cracks presents the
surface with lateral wear at the right side of the image.
The front wear surface at roughing (Figure 11d) has secondary structure pellet formation that
coat the sublimated surface. The secondary sublimated surface shows typical nanoframe structure
formation—more easy-to-melt material components sublimate from the secondary structure’s coating
(pellets) and are adsorbed by the refractory matrix.
Figure 11e shows the conjugation of two surfaces—front and lateral wear at roughing. The left
side of the image—front wear surface—has a coating of secondary structure.
Figure 11f shows the lateral wear’s surface at finishing when the obtained surface has traces of
two types of wear—thermal and mechanical, which can be easily identified.
The cross-sections of the electrodes at roughing and finishing are presented in Figure 11g,h.
Both the cross-sections showed quite intensive wear with affluent loose of the electrode material.
The worn area, volume, and mass of the tool, volumetric, and mass wear rates were calculated using
Equations (8)–(10) (Tables 6 and 7).
(a)
(b)
Figure 11. Cont.
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(c)
(d)
(e)
(f)
Figure 11. Cont.
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(g)
(h)
Figure 11. SEM-images of wire tool electrode sample: (a) conjugation of front and lateral wear at
roughing of 12Kh18N10T (AISI 321) steel, 916×; (b) lateral wear at finishing of 12Kh18N10T (AISI
321) steel, 909×; (c) conjugation of lateral wear and blank surface at roughing of 12Kh18N10T (AISI
321) steel, 780×; (d) front wear at roughing of D16 (AA2024) duralumin, 909×; (e) conjugation of front
and lateral wear at roughing of D16 (AA2024) duralumin, 1.61k×; (f) lateral wear at finishing of D16
(AA2024) duralumin, 2.04k×; (g) cross-section after steel roughing, 696×; (h) cross-section after steel
finishing, 1.02k×.
Table 6. Volumetric wear rate of electrical discharge machining of 12Kh18N10T (AISI 321) steel.
Type of
Machining
Worn
Surfaces
Measuring
Error
Worn
Area Sw
[µm]
[mm2 ]
0.0014 ±
0.00015
Front
Roughing
Lateral
Finishing
±1÷2
1
Volumetric
Wear ∆V
Δ
Volumetric
Wear Rate 2 Rv
Error
− ]
[µm3 ·µs−1
[mm2 ]
[%] 1
[mm3 ]
[mm3 ·s−1−]
0.021 ±
0.0022
51 ±
10.5
0.42 ±
0.0002
1.22 ± 0.04
0.0048 ±
0.0010
0.0045 ±
0.00005
Lateral
Summarized Worn
Area Ss
± 20 ÷ 40
0.009 ±
0.0001
18 ±
5.56
0.18 ±
0.00001
0.52 ± 0.002
Calculated to the entire cross-sectional area; 2 rewinding rate of 3.5 m/min.
Table 7. Mass wear rate of electrical discharge machining of 12Kh18N10T (AISI 321) steel.
Measuring Error
Type of
Machining
Roughing
Finishing
1
Worn Mass 1 ∆m
Δ
[g]
[g]
±0.0001
−
3.3 × 10−3 ± 0.00005
1.4 × 10−3 ± 0.00004
−
Mass Wear Rate 2 Rm
Error
[g·s−1 ]
[g·µs−1 ]
9.6 × 10−3 −± 0.01
4.0 × 10−3 ± 0.008
± 0.01 ÷ 0.02
−
−
−
Density of 7.9 × 103 kg/m3 or 0.0079 g/mm3 at +20 ◦ C; 2 rewinding rate of 3.5 m/min.
3.6. Chemical Content
The chemical content of the tool electrode’s cross-section at roughing of 12Kh18N10T (AISI 321)
steel is presented in Figure 12.
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(a)
(b)
(c)
(d)
Figure 12. Chemical analyses of the worn tool electrode cross-section after machining: (a) chemical
elements along the line at front wear; (b) chemical elements along the line at lateral wear; (c) EDX
spectrum at front wear; (d) EDX spectrum at lateral wear.
4. Discussion
4.1. Discharge Pulses and Oscillations Control
Currently, a large number of EDM factors determine the machining mode, the value of which
adaptively adjusts by the CNC system during processing. It is called an adaptive pulse-width
modulation based on electrical response (Figure 3). At the same time, the value of interelectrode
gap, the stability of processing, and consequently the quality of the obtained surfaces depend on the
homogeneity of workpiece structure and microstructure, effectiveness of the erosion debris washout
by the working fluid, the workpiece thickness, and electrophysical and electrochemical properties
of the materials in the working zone. In this connection, the discharge pulses have a more chaotic,
probabilistic nature, depending on many factors.
The vibroacoustic signal reflects the changes in the weight and structure of the workpiece, the main
discharging factors that correlated with the force diagram in the working zone [27,55] that influence
the amplitude of the signal in the wide range of spectra [23,25,26,51,52].
The recorded signal arises during processing and increases by 1.5 times from the initial level at
the end of processing (Figure 4). The signal interruptions can be observed at 5 s before the end of
processing, which is associated with the direct contact between the workpiece and tool electrode that
occurs during changes in the cutting-off sample position in the working space in relation to the rest of
the workpiece. It leads to the consequent clamping of the tool electrode to the workpiece by moving
the sample and short circuits.
Optimum electrical discharge machining factors have the least value compared to the closest
values (Figure 6a–c, except for the duralumin of 2 g). The EDM factors for the stable electrical discharge
machining are V 0 = 60 V, Wt = 35 N for steel and V 0 = 55 V, Wt = 30 N for duralumin. At the same
time, the sensibility of the system grows with its stiffness (Figure 6b,d) and decreases with the weight
of the sample (Figure 6c,d).
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An increase in RMS of the signal amplitude for stable factors at 8 kHz at 5 s before the end of
processing was 40 ÷ 55% for steel and 12.5 ÷ 25% for aluminum alloy compared with data recorded at
60 s (Figure 5b,c and Figure 6).
The developed system showed its controversial response for the samples of 2 g of aluminum and
adequate data for the samples’ weight more than 4 g for the steel and 10 g of aluminum. The samples’
weight varies by more than six times, but the RMS of the recorded signal demonstrates similar trends.
The observed behavior of the signal (Figures 5 and 6) can be correlated with the particular features
of elastic and plastic deformation during the ductile failure according to the stress-strain curves and
scheme of fracture formation (Figure 2) as aluminum shows better ductility during destruction that
actually associated with a stretch of the interatomic bonds [56–60]. It correlates with the recorded
signal when more brittle material—steel shows an adequate signal response even for the samples of
4 g when data received for ductile aluminum alloy are less significant but can also be registered for
monitoring and control of samples of more than 2 g. That all make a basis for the development of
multi-parameter control systems and switch to the next technological paradigm [61–67].
The minimum value of the measured roughness Ra of the samples (Figure 8) correlates with stable
machining signals. The same tendency is observed for the measured discharge gap (Figure 9).
4.2. Wire Breakage and Tool Wear
The optical and scanning electron microscopy (Figure 10) showed that the character of rupture
had mechanical nature corresponding to cup neck formation and stress-strain curve of middle ductile
material destruction—brass alloy [47–49]. The observed area has the topology of the wire breakage
that occurs in most of the cases during electrical discharge machining with unstable factors, in case the
surface inclination or uneven structure of the workpiece need to be processed. There is no presence
of thermal defects except an ashy shade at the formed cup. Additionally, there is no evidence of the
rupture’s external origin that can occur during the wire cut.
The excess in bias during wire blockage between the workpiece and cutting-off sample that did
not allow adequate debris removal probably caused this rupture, since the current and pulses factors
were constant. An increase in bias gave a denser distribution of discharges, while an increase in current
gave more expressed discharges [28–30] (Figure 13a).
(a)
(b)
Figure 13. Electrical discharge machining principles: (a) dependencies of the discharge pulse character
on bias and current, where (1) is a tool electrode, (2) is a workpiece, (3) is a discharge channel, (4) is a
plasma cloud, (5) is dielectric medium, and Fe is discharge force; (b) submicron structure of erosion wear.
The calculated enlarged value of the reduction area (SRA = 93.8%) is obviously caused not only
by mechanical rupture but a mechanical rupture in the softened state [68,69] due to the heat of the
discharge gap that was definitely above 600–650 ◦ C (dark red color) since the brass’s surface around
the formed cup neck is covered by the ashy shade of zinc oxide (Figure 10a) [70–72].
The formed craters that have different from the typical erosion morphology are 30–100 µm
(Figure 11a). The explosive droplets reached a distance of ~100 µm from the wear edge on the backside
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surface (Figure 11c). The submicron structure of these droplets (Figure 11e) is different from the typical
eroded surfaces as on the lateral surface at roughing and at finishing (Figure 11a,b,e,f).
The observation area of the wire tool presented in the SEM-microphotographs showed:
•
•
•
Thermal traces (Figure 11a,e), which partly have a relation to the erosion that occurred
between electrodes;
Mechanical traces (Figure 11b,f), which has no relation to the processing;
A topology that is more correlated to the electrical erosion of the materials under discharge pulses
(Figure 11c,d).
The samples with typical erosion wear traces (Figure 11c,d) correlate to non-oxide (oxygen
unsaturated) structures [73,74]—secondary submicrostructures of the complex compounds (of second
order) adsorbed by the eroded surface of the base material—of the first order (Figure 14b) [75–77],
which probably contain metastable and insoluble solid solution in the form of adherent and brittle thin
film and heat-affected sublayer [78–81].
(a)
(b)
Figure 14. Non-profiled tool electrode wear: (a) at roughing; (b) at finishing, where (1) is a tool
electrode, (2) is a workpiece, (3) is machined surface, (4) is front wear, (5) is lateral wear, and Sg is a
guidance feed of wire.
The mechanical traces on the surface of the wire at lateral wear correspond to the mechanical
destruction of the tool during rewinding (Figure 11b,f) that occurred after electrical erosion (secondary
wear). Probably, wire tool pinch rollers or diamond nozzle destroyed the morphology of the lateral
wear mechanically.
The thermal traces were very pronounced at roughening (front wear), which are different from
the lateral wear morphology that was especially apparent at the conjunction of the front and lateral
wear surfaces (Figure 11a,e), and the lateral and blank surfaces (Figure 11c) have a different origin,
related to the chemical composition of the tool and workpiece.
This is due to the picture of the erosion process observed visually and based on the interaction of
the components of the electrodes—CuZn35 brass alloy and 12Kh18N10T (AISI 321) steel. The nickel
2𝑍𝑛𝑂 𝑂 → 2𝑍𝑛𝑂,
and zinc reaction at a temperature of 1000 ◦ C has an explosive character and results in the formation of
intermetallic ZnNix (x = 0, 5, 10, 15, 20 wt%) [82–86]. It can be easily observed by the formation of
𝐶𝑢𝑂 𝐻 → 𝐶𝑢 𝐻 𝑂.
non-periodic orange flashes in the discharge gap with the release of abundant black sediment during
the processing of anti-corrosion austenite (nickel-containing) steels [25,34,87–89]. Visually, the density
of the flashes is less than the density of discharges and occurs with a lower frequency. However,
the flashes cannot be detected with a higher workpiece, especially with a height of more than 100 mm
that often occurred at machining in tool and mold production, when the visual access to the working
zone is absent. Thus, the signal was adequately registered by the developed vibroacoustic diagnostic
mean—RMS of the amplitude signal was higher by 12.5% and more intense by 20% for 12Kh18N10T
(AISI 321) steel than for D16 (AA 2024) alloy for the thickness of the sample of 20 mm.
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As can be seen, the deposition of the secondary submicron structure of the sublimated electrodes’
components and working medium in the case of anti-corrosion steel processing occurred explosively
(with craters of 30 ÷ 100 µm). The presence of the explosive character of reaction between metals
accompanies the electrical erosion wear can be seen in Figure 11c on the blank surface when a clear
edge limits the area of deep EDM wear on the lateral surface during roughing. However, the explosive
nature of the secondary phase deposition overcomes the wear edge and is visible from the electrode’s
blank side.
The front wear at roughing has a more pronounced topology that correlates with the non-oxidized
erosion wear an explosive reaction between wire and workpiece components (Figure 14), where the
deposed film of secondary structure coat eroded base metal surface. The lateral wear at roughing has a
less pronounced topology that corresponds to the typical wear that occurred under discharge pulses.
It correlated to the degree of the involvement of the sides of the electrode in the formation of the slot
when the front surface has the presence of secondary wear of the formed films: the front side is more
involved in the formation of the slot, and the side surfaces are involved in the erosion process only
partly by secondary “polishing” formed surfaces [24,90,91]. The lateral wear at finishing has a similar
character. However, wire tool pinch rollers destroyed the morphology of the lateral wear mechanically.
The electrode’s cross-section shows the intensity of the two types of wear (Figure 11g,h). In the
considered sample, the front wear does not predominate the lateral one at roughing, and distributes
quite even at the periphery of the tool (Figure 11g). The conjugation of the worn surfaces was
pronounced for all of the samples.
Analysis of chemical elements along the line and EDX spectrum of the wire tool at roughing and
finishing (Figure 12) showed mostly chemical elements except for chemical elements of the brass wire
in balance—61.8 ÷ 64.3% of Cu and 34.8 ÷ 35.5% of Zn. However, less than 3.4% of oxygen is proof
of semiconductive and amphoteric zinc oxide formation, which usually occurs during brass heating
(Figure 10a) [92,93], when copper (II) oxide decomposes in the presence of hydrogen [94,95]:
2ZnO + O2 → 2ZnO,
(14)
CuO + H2 → Cu + H2 O.
(15)
Both of the oxides do not interact with water. Zinc oxide gets yellow with heating and sublimates
at 1800 ◦ C. It should be noted that that oxygen was present quantitatively more in the samples after
finishing and at later wear of roughing, while it was not possible to quantify it along the line in some
cases at front wear after roughing. A small amount of carbon that was not quantitatively evaluated
(less than 0.2%) is associated with normal atmospheric contamination.
5. Conclusions
5.1. Monitoring System and Tool Behavior
A comprehensive study of the tool electrode’s wear process during electrical discharge machining
was accomplished by the developed monitoring system based on oscillation detecting. That gives
detailed data on the character of electrode tool wear and stability of workpiece machining in the
high-frequency acoustic band of 8 kHz.
The optimum electrical discharge machining factors are detected by monitoring the vibroacoustic
signal—RMS value of the amplitude at 8 kHz for steels and more ductile duralumin with a weight
of more than 2 g. The stable electrical discharge machining are V 0 = 60 V, Wt = 35 N for steel and
V 0 = 55 V, Wt = 30 N for duralumin. An increase in RMS of the signal amplitude at 5 s before the
end of processing was 40 ÷ 55% for steel and 12.5 ÷ 25% for aluminum alloy compared with data
recorded at 60 s. The proposed approach can be used to develop a multiparameter controlling system
of EDM-equipment to carry out the modern CNC-systems at a principally new level.
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5.2. Wire Tool Topology and Wear Rate
Classification of the obtained surface topology of the tool electrode determines two types of wear
under discharge pulses related to the thermal nature: material sublimation and chemical interaction
between components of the working zone when mechanical destruction of the finishing electrode
sample has a different origin.
Volumetric wear rate Rv was 1.22 ± 0.04 mm3 ·s−1 at roughing and 0.52 ± 0.002 mm3 ·s−1 at finishing;
mass wear rate Rm —9.6 × 10−3 ± 0.01 g·s−1 and 4.0 × 10−3 ± 0.008 g·s−1 , respectively. 41 ÷ 62% of the
tool subjected wear under discharge impulses at roughing during electrical discharge machining of
anti-corrosion steel when summarized lateral wear exceed front wear by 29.17%. 12 ÷ 24% of the tool
sublimates under lateral wear at finishing.
The study showed that the processing of the materials with inadequate process parameters
or the not proper combination of tool and workpiece materials causes more intensive wear of the
tool correlated with the chemical interaction of the electrodes and dielectric medium components.
This leads to the micro explosive character of processing with formation intermetallic ZnNix (x = 0, 5,
10, 15, 20 wt%), with Zn of the brass and nickel of austenite steel that was also registered the mean
of vibroacoustic diagnostic. The crater diameter was of 30 ÷ 100 µm; RMS of the amplitude signal
was higher by 12.5% and more intense by 20% for 12Kh18N10T (AISI 321) steel than for D16 (AA
2024) alloy.
5.3. Further Procpects amd Paractical Significance of the Work
As was shown, the amplitude is up to 55% higher for steel and up to 25% higher for duralumin
at convenient machining than 5 s before the end of processing that always stays critical for precision
cutting, especially in the conditions of tool production—profiled cutters, hot channels, and injection
molds. The obtained data were for the thickness of 20 mm when it stays one of the most often used
thickness for EDM workpieces in tool production. The developed system proved its reliability for the
samples up to 2 g when the standard sample weight for discharge gap and machining mode verifying
is 15.6 g for steels and 5.4 g for aluminum for a sample of 10 × 10 mm in the plan with a thickness of
20 mm.
The tool wear under electrical discharge pulses has a complex character related to the thermal
type of wear with a heat-affected sublayer, and the upper layer consisted of a secondary structure
formed from the components of electrodes with the traces of chemical reactions at a heat of 10,000 ◦ C.
Thus, electrical discharge machining wear forms in the following stages:
-
Sublimation of the electrode surfaces under discharge;
Chemical interaction of the sublimated electrode components in the presence of high heat;
Explosive deposition of the formed secondary structure of first and second order material;
Re-sublimation of the secondary structure.
The explosive character of interaction between Zn and Ni should be considered while
designing experiments and electrical discharge machining of chrome-nickel anti-corrosion steels.
For high-precision and nano-works, machining of nickel-containing steels should be provided by a
tool with no Zn in its content—copper, steel, or tungsten wire have a few disadvantages due to the
softness of copper, the relatively low electrical conductivity of steels, and heat-resistance of tungsten.
However, it is a promising direction for further research.
The obtained knowledge has a fundamental character and can be used as a recommendation for
the industrial applications on the choice of the electrode tool material and searching the optimum
EDM-factors; in this context, not only structural requirements are addressed for the working and
auxiliary surfaces of the final product, but also functionality in the exploitation conditions.
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Author Contributions: Conceptualization, S.N.G.; methodology, M.P.K.; software, K.H.; validation, P.M.P.,
A.N.P.; formal analysis, S.V.F.; investigation, M.P.K.; resources, P.M.P. and S.V.F.; data curation, P.A.P. and K.H.;
writing—original draft preparation, A.N.P.; writing—review and editing, A.A.O.; visualization, P.A.P. and A.A.O.;
supervision, M.A.V.; project administration, M.A.V.; funding acquisition, S.N.G. All authors have read and agreed
to the published version of the manuscript.
Funding: This project has received funding from the Ministry of Education and Science of the Russian Federation
within the framework of the state task for scientific research, under Grant Agreement No. 0707-2020-0025.
Acknowledgments: The research was done at the Department of High-Efficiency Processing Technologies of
MSTU Stankin.
Conflicts of Interest: The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to
publish the results.
Nomenclature
Symbol
Vo
Wt
I
f
∆
∆DB
∆*DB
dw
rw
SRA
S0
Smin
Sw
α
An
An ’
RMS
ΣFimp
ΣEimp
kn
mn
ln
∆l
T
Fe
E
Rv
Rm
∆V
∆m
t
ls
Description
Operational voltage
Wire tension
Strength of the working current
Frequency of discharge pulses
Distance between electrodes
Effective discharge gap
Offset of the path
Wire diameter
Wire radius
Reduction area
Original transverse area
Minimal area of the final neck
Circle segment area
Segment angle
Wire amplitude of nth vibration, n is a positive integer (1, 2, 3 ,...)
Registered signal amplitude
Root-mean-square mean of signal amplitude
Summarized force of working impulses
Summarized energy of working impulses
Stiffness (coefficient of elasticity)
Mass of system
Wire length
Change in the wire length
Period of self-oscillations
Restoring force (opposite and equal to Wt )
Young’s modulus
Volumetric wear rates
Mass wear rates
Volumetric wear
Worn mass
Wire length wear time
Slot width
Unit
V
N
A
s−1
µm
µm
µm
mm
mm
mm2
mm2
mm2
mm2
degree
mm
mV
mV2
N
J
N·mm−1
g
mm
mm
s
N
Pa
mm3 ·s−1
g·s−1
mm3
g
s
mm
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