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Sparking at cathode tools during electrochemical drilling
&cm&mica Acm, Vol. 3~7). No. 1. PP. 43-49. 1985. Primed in Orea1Briain.
SPARKING AT CATHODE ELECTROCHEMICAL
TOOLS DURING DRILLING
P. NOVAK,* 3. SAJDL and I. Department
of Inorganic
Technology,
ROU~R
Prague Institute of Chemical Czechoslovakia
(Receiued 26 August 1983; in revisedform
Technology,
166 28 Prague 6,
16 May 1984)
Abstract-The current density used in electrochemical machining can be increased only up to a certain value, above which the formation of electric sparks on the cathode (tool) is observed, whereby the latter and its insulation arc damaged. The present work is devoted to the measurement of this critical current density for metal capillaries provided with an external insulation. Experiments are given for the cases of turbulent and laminar flow of the electrolyte inside the cathode tool. The results are correlated by criterion equations which gave the values of the limiting (cathodic) current densities, jr, with an average error of f 12%.
LIST
OF
SYMBOLS
during the process and if the working conditions are kept constant the accuracy in the shape of the workpiece is very high. By increasing the rate of removal, not only the process can be accelerated but the machined surface becomes smoother[2]. However, the current density on the tool (cathode) can be increased only up to a certain limiting value given by the shape of the tool and hydrodynamic conditions. A further increase of the current density causes the formation of electric sparks on the cathode[3-6], whereby the latter and its insulation are damaged. Sparking during electrochemical machining was studied also by Drake and McGeough[ 151 who elaborated a very efficient method for drilling by simultaneous ECM and electrochemical arc machining (ECAM). They used an oscillating anode fed with pulsed direct current; the appiied peak voltage was 25-55 V. They also studied the cathode tool wear during ECAM. The electrolyte flow rate depended on the hole depth and changed from a nominal value at the beginning of the drilling to about one half at the end of drilling.
specific heat of electrolyte,
J kg-’ K-r inner diameter of cathode, m outer diameter of cathode without insulation, &iting current for sparking, A limiting current density for sparking, A mm2 multiplicative constants in Equations (la) and (lb) characteristic length, Equation (6), m Nusselt number, Equation (4) see Equation (11) exponents, Equations (la) and (lb) Prandtl number, Equation (9) density of heat flow, Wm-’ Reynolds number, Equation (8) electrolyte density, Lam-’ characteristic temperature diflerence, K
see Equation (7), K linear velocity of electrolyte
flow through cathode, ms-’ specific conductivity of electrolyte, !X r m- 1 heat conductivity of electrolyte, W m-’ K-r dynamic viscosity of electrolyte, kg m-’ s- ’
The subscript o! refers to the cathode located 10 mm from the anode, j7 to the cathode 0.2 mm apart from the insulator plate, C to a value calculated from Equation (12), L to a value for laminar fiow,T to avalue for turbulent flow (Re 2 2300), M to a modified quantity,
ELECTRIC
SPARKS IN ELECTROCHEMICAL DRILLING
We shall consider electric discharges in an apparatus (described elsewhere[7]) for drilling small holes. The tool (cathode) is a metal capillary provided with a good external insulation; its end is ground in a plane perpendicular to the capillary axis. An electrolyte flows through the capillary into the gap between the workpiece and the tool. The electric quantities (current, voltage) were measured to an accuracy of 1%- The average electrolyte flow rate setting accurate to 2%. The maximum pulse deviations abaut this setpoint (caused by the metering pump) did not exceed f 5 %. When the voltage of the electrolyser is gradually increased, the current flowing through it attains a limiting value, which is approximately maintained during further increase of the voltage. In this phase,
INTRODUCTION
principle of electrochemical machining[l] is the anodic dissolution of a workpiece in the medium of a flowing electrolyte. The shape of the tool as cathode is copied into the workpiece as anode with relatively small deviations given by the width of the gap between the material and the tool. The tool is not consumed The
l The J. Heyrovsk~ Institute of Physical Chemistry and Electrochemistry, Cxechoslovak Academy of Sciences, U tov&ren 254, 102 ODPrague 10, Czechoslovakia.
43
44
P.NOVAK,
B.SAJDL AND
occasional electric sparks are observed on the surface of the cathode. When the voltage attains 45-55 V, the current increases abruptly by lQ-2Ct”~ and begins to oscillate around a mean value which remains practically constant whilst increasing the voltage further. At the same time, acoustical and optical effects are observed; yellow-orange sparks or flames are visible on the cathode (Fig. 1). Its metallic surface does not change in form, only black. If the insulation of the cathode is from an organic compound it also turns black and is damaged (peels off under the action of the streaming electrolyte). This is illustrated in Fig. 2. If the electrolyte flow through the capillary is very slow (hence bad cooling) the metal at the orifice of the cathode melts and a deformation takes place. Only an alumina ceramic insulation withstands the mentioned conditions. An insulation made of inorganic enamels lasts for a limited time. The mentioned phenomena are observed not only in oxidising media (NaN03, NaC103 or their mixture) but also in a neutral solution of NaCl. A typical dependence of current on time during sparking is shown in Fig. 3, and thisat constant voltage. It follows from the observed j-r curves that the discharge has the character of sparks. The form of the dependence does not change with hydrodynamic conditions and is the same regardless of whether the electrode is in the free electrolyte or in the hole formed by drilling; and the same applies for the limiting
I. ROLJ~AR
current of sparking, I,, which is constant to within * 20 ;4. To explain this phenomenon, the following mechanism was proposed in accordance with experimente reported in[8] and[I6]. With respect to the distribution of current density on the cathode[9] (the current density in the capillary is negligible), the electrochemical process is concentrated on the tip of the insulated capillary. The quantity of the evolved gas increases with the current density. At the same time, a considerable amount of heat is evolved at the electrode. Since the latter is thermally insulated by the applied ceramic or enamel, the heat is transferred to the electrolyte mainly by convection, Finally, the temperature of the electrolyte layer at the electrode attains the boiling point. Thus, together with the gas evolved electrolytically, a large number of bubbles appear on the electrode surface, and eventually at a certain current density a continuous layer of gas is formed[S, lo]. The resistivity of the gas-electrolyte mixture on the cathode surface rises abruptly, while the current density remains practically constant regardless of the increasing voltage. For these conditions the fluorescence of bubbles is visible[ll]. When the voitage attains a certain value, s&rking takes place between the electrode and the electrolvterl2-l. The high temperature of the sparks causes the &&age of the cathode tool and its insulation.
Fig. 1%Electric discharge on the cathode.
Sparking at cathode tools during electrochemical drilling
45
Fig. 2. Electrodes damaged by electricdischarges it6electrolyte. An electrode before use is shown on the right for comparison. Insulation made by an eiectrophoretical enamel (CSSR No. S-2201/0625).
Table
1. Characteristics of electrodes used
Symbol
d,, mm
dl. mm
Insulation
A B C D E F
1.07 0.66 0.28 0.21 0.71 0.30
1.50 0.99 0.5 1 0.43 1.03 0.52
Enamel 0.06 mm Ceramics 0.3 mm Enamel 0.06 mm Ceramics 0.2 mm Ceramics 0.3 mm Ceramics 0.2 mm
Fig. 3. Dependence of current on time of sparking. Vertical division corresponds to 0.34 A, horizontal division to 0.5 rns, sparking frequency 68 kHz.
EXPERIMENTAL During electrochemical ensure that the current
drilling,
it is necessary
to
does not surpass the limiting value above which the sparking begins, I,. Since this depends on hydrodynamic conditions, we measured the dependence of Is on the Reynolds number Re, and this for six electrodes whose outer diameters (without insulation) were in the range 0:43-1.50 mm. The insulation was made either of alumina ceramics or inorganic enamel. The description of the electrodes is apparent from Table i and Fig. 4. The velocity of electrolyte flow was raising from the laminar to the turbulent region, its upper limit was given by the maximum pressure of 10MPa in the apparatus. Physical data about the electrolytes used are given in Table 2; the temperature of the electrolyte at the inlet was 20°C. The method ofwork was the following. First the rate of flow of the electrolyte through the cathode
Fig. 4. Scheme of the cathode. K. metal capillary; P, insulation; arrow denotes direction of electrolyte flow; v,, velocity of electrolyte flow; d,, d,, inner and outer diameter of metal capillary: L, thickness of the metal capillary. was set as desired; the attainment of the stationary state was indicated by a record of the pressure in the apparatus. Then the electric current was switched on and the voltage was gradually raised. The instant when the sparks began to form on the cathode was determined visually in a dimmed light. The value of I, was determined as the current which passed at a
46
P.Nov.k,
B.
SAJDL
AND
I. ROUSAR
Table 2. Characteristicsof electrolytesused (20°C)[14] Symbol
fiE x lo3
1, W m-l K-’
Composition
5.5 kJ kg-l K-’
kg m-is-L
1
15 % NaNO, 20 % NaClO,
18.0
1329
0.550
1.60
3.40
2 3 4 5 6
25 % 20 % 15% 10% 5%
21.4 19.6 16.4 12.1 6.7
1191 1148 1109 1071 1034
0.572 0.578 0.584 0.590 0.594
1.81 1.58 1.28 1.14 1.09
2.73 3.06 3.39 3.72 4.05
Nail NaCl Nail NaCl Nacl
voltage lower by 1 V than that at which the sparking began. Two dependences of I, on Ra were measured For various electrode-electrolyte combinations. The the cathode was placed either 10 mm from anode (case a) or an insulating plate was placed at a distance 0.2 mm from the orifice perpendicular to the capillary axis (ease fi), in which case the outflowing electrolyte was forced to change its direction abruptly. Since no dependence of the value of I, on the character of flow near the capillary orifice was observed, the results for both cases GC and p were evaluated together. In total, 365 data (cases (z and 8) were measured for various electrode-electrolyte combinations; some of them are given in Tables 3 and 4.
Table 3. Measured
RESULTS
In evaluating the measured data, we assume that the whole process is governed by heat transfer from the bubble-electrolyte layer formed on thecathode tip. For the turbulent electrolyte flow, we assume the validity of the equation Nu = KTRePPro-4(d, ,/I#: Re & 2300 (la) and for the laminar flow regime Nu = K LR e RFr”.333(dl/L)S: The Nusselt number is given as
Al4
B/1
C/2
J-V5
l Symbols and 2.
Nu = qd, /&AT,
and calculated limiting current sparking. Turbulent regime
Fxperimental Symbol*
Rt?
2900 4670 6580 8420 10240 12050 13880 15700 17530 19360 4510 7260 10230 13090 15920 18720 3140 4030 4910 5780 6660 7530 2670 4370 5980
correspond
AND DISCUSSION
(*‘!-*) 126 150 180 191 196 203 212 219 224 226 220 241 299 318 360 374 385 392 392 413 448 526 289 407 434 443
to electrodes
data
densities
for
Theory Equation (12~1)
@‘6T;Is_2) 142 173 184 191 212 214 217
220 225 227 215 241 297 311 355 377 371 392 399 413 427 427 298 298 307 353
an& electrolytes
is c
(A &I-‘) 136 156 172 IS4 196 205 213 221 228
235 229 262 290 311 330 346 :z 413 434 448 470 280 325 362 389
in Tables 1
Re < 2300.
(lb)
(2)
Sparking at cathode tools during electrachemicat
Table 4. Measured and cakulated limiting current for sparking Laminar regime Experimental data
Symbol*
Re 1806 1204 602 1921 1281 640 1913 1793 896 2023 1348 674 1672 836 2260 1507 7.53 21% 1464 732
* Syxnbols correspond
and 2.where express in unit on the length,
is. c (Arm-“)
231 229 201 222 217 202 305 345
209 201 199 200 201 202 293 295 331 1.57 149 143 141 174 166 185 182 178
220 214 203 216 209 199 299 305 290 168 163 154 124 118 196 190 180 210 203 193
;z 209 222 167
to electrodes and electrolytes
q = j$L/KE.
(3) The characteristic length, L, should be equal to or should depend on the thickness of the bubbleelectrolyte layer. This quantity is unknown, but we can suppose its dependence on the Reynoids number in the capillary and on the electrode thickness (d2 -d,)/2. Both quantities should be inserted as variables in the heat transfer [Equations (la, b)]. Hence,
The limiting
current
density
j, = 41,/r@:
for sparking -d:).
(6)
The quantity AT in Equation (2) is the characteristic temperature difference related to the given phenomenon; in our case it is constant. This quantity involves also the change of the electrolyticconductivity rcr with temperature and gas evolution in the boundary layer, as well as the change of other properties of the electrolyte with temperature. For the evaluation of our experiments it was necessary to introduce a new quantity AT* defined as AT.+ = &AT:
Re 2 2300
(Ta)
AT: = K,AT:
Re -z 2300.
(7b)
and
in Equation
Re = vBdrP;l~c,,
(1)are (8)
Pr = CpEPJ&.
(9) We denote rcr the specific conductivity of the electrolyte, A, its heat conductivity, p; its density, pE its dynamic viscosity, and cPE its specific heat. AI1 quantities refer to the temperature of the bulk of the electrolyte. Finally, ur is the linear velocity of the electrolyte flowing through the cathode (the hollow needle). The measured data were correlated by Equations {la) and (lb) rearranged by introducing AT*, Equation (7) in the form:
(4)
(5)
in Tables 1
The ReynoIdsand Prandtl numbers defined in the usual way as
is defined as
The symbol dl denotes the inner diameter of the cathode, d, its outer diameter (without insulation). We set the value of L equal to L = (d3 - d,)/2.
Theory Equation (12b)
js.8 (A cm-‘)
for the case of the formation of sparks we the heat Bow density as the formation of heat volume of the bubble-electrolyte layer formed cathode tip multiplied by the characteristic L:
Nu = jidlL/KE&AT.
densities
Js.01 (A cm-‘)
188 184 176 148
47
drilling
Nu,* = RePPro~4(dl/L)Q:
Re 2 2300,
(l&a)
Nu: = ReRPr0~J33(dl/L)S:
Re < 2300,
(lob)
where Nu; = jid,
L./u&ATT,
Nur = j,’ d, LIKE&AT,+.
(1 la) (1 lb)
The exponents P, Q, R, S and the characteristic temperature difference AT,*, AT,* are considered as unknowns, whose values were determined from 356 experiments by using the least squares method with modified Equations (lOa, b) as fohows (see Appendix): (1) for turbulent regime: ATT = 88.3 K, P = 0.58, Q = 0.49. (2) for laminar regime: AT,+ = 2723 K, R = 0.15, S = 0.67. Hence for Re 2 2300 we have in accordance withE 131 Nu,* = Re0.58Pr0.4(d, /L)“.4g (I&) and for Re < 2300 we have NuZ = Re”~‘5Pr0~“3(d,/~)0~67,
II2b)
48
B.
P.NovAK,
SMDLAND
The calculated limiting current densities for sparking j, c from Equations (12a, b) are given with an averaie error of f 12 y0 (See Tables 3 and 4, also Fig 5.) It can be concluded that Equations (12a, b) are suitable for proposing the working conditions for electrochemical drilling of small holes. The limits of applicability of calculating js according to Equations (12a, b) are as follows: (a} ECM drilling with electrolytes dissolved in water; (b) the anode metals form no firmly adherent passive films in given electrolyte; (c) the process of sparking for (a) and (b) is governed by heat transfer from the bubble-electrolyte layer formed on the cathode tip. The most interesting question arising from Equations (l&t) and {12b) is whether the characteristic length for the Reynolds number should be L or d,. Rearranging Equations &!a, b) we obtain j.$ L’/K&,AT,
= (L~~p~/p~)“.~~ x Pr0.4(di/L)0.07,
ji L’ju,J,AT
(13a)
p’ /G E)‘-I5 L = (Lv BE x Pr”.333(d,/L)-o.‘6.
(13b)
For all our experiments, the values of (dl/LjO.” or (d, /L)-0.16 can be put approximately equal to 1.08 or 0.85, with an error of about + 4 % or + 7 %, respectively. Thus it was necessary to test the hypothesis that the geometrical simplex (d, / L1 ) can be removed from
LROUSAR
Equations (13a, b) giving Nu& Nz&
,
h (A tern*] 300
-
h
Re,
2.104
Re
Equation of observations
P error of P
Q Standard
error of Q constant
Residual
standard
[U*
J. F. Wilson.
Practice and Theory of Electrochemical Machining, p. II. Wiley-Interscience, New York (1971). H. Degenhardt, Elekwochemische Senkarbeit metaliischer W’erkstofe, p. 92. Thesis, Technische Hochschule Aachen, Aachen (1972). R. A. Mirzoev, Colhode Process During ECM. Collected papers on ECM, Schtiinca, Kischinev (197 I) (in Russian). A. D. Davydov, V. D. Kaschtscheev and B. N. Kabanov, Elekrron. Obrab. Mater. No. 6, p. 13 (1969). M. Datta and D. Landolt, Electrochim. Acta 26, 899
Elecrrochim. Acta 27, 385 (1982). 7. P. Novak, 1. RouSar, R. Stefcc and V. &al, Mater. Cheat. Plays. 10, 155 (1984). 8. D. landoh, R. Acosta, R. H. Muller, C. W. Tobias, J. electrochem. Sac. 117, 839 (1970). 9. P. Novdlt, 1. Rot&u, A. Kit&a V. Mejta and V. Cezner, Coil. Czech. them. Commun. 46, 2949 (I 981).
Table 5. Results of multiple regression
Regression
(16)
= L~w&IIL~-
(1981). 5. M. Datta and D. Landolt,
Fig. 5. Mcasurcd and calculated limiting current densities for sparking. Electrode B, electrolyte 1 (see Tables 1 and 2). a, case ce o, case ~3;solid line Equations (12a, b).
Standard
(15a) (15b)
Using the least squares method we obtained AT& = lOI.SK, P = 0.57 and &TTM = 1642IC and R = 0.20. Multiple regression analysis was run on an ICL 4-72 computer using the MREG statistical procedure. All results are given in Table 5. On the basis of Table 5 we can conclude that the Equations (I 2a, b) can be recommended for the calculation of the sparking current densities. The calculated values for the turbulent regime are rendered with a high degree of probability because the multiple correlation coefficient is 0.92; less satisfactory is the situation for laminar flow where the multiple correlation coefficient is only 0.54. The simplex (d,/L) cannot be removed from Equations (13a, b) as this would cause a remarkable decrease in the multiple correlation coefficients for Equations (14a, b). At the F level of 2.75, all variables were significant in Equations (12a, b) and Equations (14a, b).
5.
10'
Number
=j~Lz/~E~,rAT&,
and
4.
-*
-
(14b)
Nu TM= j,’ La /K_&AT&
3.
00
100
(14a)
Re < 2300,
Nu;t,
2.
l
0
200
o
b
Re > 2300,
for
REFERENCES
I
I
for
where
1. 400
= Re: P? = Re$Pr0.333
(12a)
analysis
Equation
using Equations (l2b)
(12) and (14)
Equation
(14a)
Equation
(14b)
270
86
270
86
0.5806
0.1504
0.5732
0.1966
0.0238
0.0563 0.6689
0.0237 -
0.0431
0.4872 0.0366
0.1144
(K)]
88.25
2723
101.53
1642
error E (YJ
21.05
24.68
21.20
24.78
0.92 14
0.5443
0.8236
0.4449
Multiple correlation coefficient
Sparking
at cathode
tools during electrochemical
IO. J. A. McGeough, Principles of Electrochemical Marhining, p. 175. Chapman and Hall, London (1974). 11. Ya. Z. Agroskin, A. I. Zhemovoy, V. V. Zhukov, V. A. Zyuzin, A. A. Karpov and V. I. Podlovilin, El&&on. Obrab. Mater. No. 5, p. 14 (1979). 12. B. R. Lazarenko and N. 1. Lazarenko, Elektron. Obrab. Mater. No. 1, p_ 14 (1978). 13. P. Novdk, I. Roukr, V. Cezner and V. Mejta, Coil. Czech. them. Commun. 44, 2788 (1981). 14. Spranochnik Khimiko, Vol. III. Khimiya, Moscow (1964). 15. T. H. Drake and J. A. McCcough, Proceedings ofMachine Tool L&sip and Research Co@rence, Manchester, p. 361. Macmillan (1981). I 6. 1. M. Crichton, J. A. McGeough, E. Munro E. and C. White, Precision Engineering, July (1981) (cited in [15])
drilling
49
where y = In [(j~d1L/K~1E)P~0.4], x, = ln Re,
(A3) (A4)
xI = In (d, /L),
(A5)
k, = In AT;
(‘46)
For testing the hypothesis removed from Equations (A7)-(Al2):
that the (d,/L) values can be (13a,b) we used Equation
In [ ( j~L2/K,L,)/Pro.4j
= In AT&., + P In (Lv&/~~)
or in a more condensed
form as
YM = k,,
+Px,,,
(A7)
(Ag)
where y, APPENDIX The evaluation of AT?, P and Q or AT;. R, S by a least squares method is based on Equations (lOa, b). From Equation (lOa), after some rearrangement, we obtain In [( j:d,L/rc&E)/Pr0,4]
= In ATT*+ P In Re + Q In K/O-
Equation
(Al) can be written in a more condensed y=k,+Px,+Qx,,
(Al) form as (-42)
= In [ (j~Lz/xE1E)/P+4],
(A9)
xIM = ln (%&/P,),
(Alo)
k ,M = InAT&.
(Al 1)
Multiple regression analysis give values of k,, P, Q or k,, and P, for both the laminar.and the turbulent regimes of electrolyte flow (See TabIe 5). The residual standard error in % (E) is based on the residual standard error (8) calculated by Equation (Ala); the calculated E values are given for Equations (A2) or (A8). E=(e’--1)x100.
(Al2)
SPARKING AT CATHODE ELECTROCHEMICAL
TOOLS DURING DRILLING
P. NOVAK,* 3. SAJDL and I. Department
of Inorganic
Technology,
ROU~R
Prague Institute of Chemical Czechoslovakia
(Receiued 26 August 1983; in revisedform
Technology,
166 28 Prague 6,
16 May 1984)
Abstract-The current density used in electrochemical machining can be increased only up to a certain value, above which the formation of electric sparks on the cathode (tool) is observed, whereby the latter and its insulation arc damaged. The present work is devoted to the measurement of this critical current density for metal capillaries provided with an external insulation. Experiments are given for the cases of turbulent and laminar flow of the electrolyte inside the cathode tool. The results are correlated by criterion equations which gave the values of the limiting (cathodic) current densities, jr, with an average error of f 12%.
LIST
OF
SYMBOLS
during the process and if the working conditions are kept constant the accuracy in the shape of the workpiece is very high. By increasing the rate of removal, not only the process can be accelerated but the machined surface becomes smoother[2]. However, the current density on the tool (cathode) can be increased only up to a certain limiting value given by the shape of the tool and hydrodynamic conditions. A further increase of the current density causes the formation of electric sparks on the cathode[3-6], whereby the latter and its insulation are damaged. Sparking during electrochemical machining was studied also by Drake and McGeough[ 151 who elaborated a very efficient method for drilling by simultaneous ECM and electrochemical arc machining (ECAM). They used an oscillating anode fed with pulsed direct current; the appiied peak voltage was 25-55 V. They also studied the cathode tool wear during ECAM. The electrolyte flow rate depended on the hole depth and changed from a nominal value at the beginning of the drilling to about one half at the end of drilling.
specific heat of electrolyte,
J kg-’ K-r inner diameter of cathode, m outer diameter of cathode without insulation, &iting current for sparking, A limiting current density for sparking, A mm2 multiplicative constants in Equations (la) and (lb) characteristic length, Equation (6), m Nusselt number, Equation (4) see Equation (11) exponents, Equations (la) and (lb) Prandtl number, Equation (9) density of heat flow, Wm-’ Reynolds number, Equation (8) electrolyte density, Lam-’ characteristic temperature diflerence, K
see Equation (7), K linear velocity of electrolyte
flow through cathode, ms-’ specific conductivity of electrolyte, !X r m- 1 heat conductivity of electrolyte, W m-’ K-r dynamic viscosity of electrolyte, kg m-’ s- ’
The subscript o! refers to the cathode located 10 mm from the anode, j7 to the cathode 0.2 mm apart from the insulator plate, C to a value calculated from Equation (12), L to a value for laminar fiow,T to avalue for turbulent flow (Re 2 2300), M to a modified quantity,
ELECTRIC
SPARKS IN ELECTROCHEMICAL DRILLING
We shall consider electric discharges in an apparatus (described elsewhere[7]) for drilling small holes. The tool (cathode) is a metal capillary provided with a good external insulation; its end is ground in a plane perpendicular to the capillary axis. An electrolyte flows through the capillary into the gap between the workpiece and the tool. The electric quantities (current, voltage) were measured to an accuracy of 1%- The average electrolyte flow rate setting accurate to 2%. The maximum pulse deviations abaut this setpoint (caused by the metering pump) did not exceed f 5 %. When the voltage of the electrolyser is gradually increased, the current flowing through it attains a limiting value, which is approximately maintained during further increase of the voltage. In this phase,
INTRODUCTION
principle of electrochemical machining[l] is the anodic dissolution of a workpiece in the medium of a flowing electrolyte. The shape of the tool as cathode is copied into the workpiece as anode with relatively small deviations given by the width of the gap between the material and the tool. The tool is not consumed The
l The J. Heyrovsk~ Institute of Physical Chemistry and Electrochemistry, Cxechoslovak Academy of Sciences, U tov&ren 254, 102 ODPrague 10, Czechoslovakia.
43
44
P.NOVAK,
B.SAJDL AND
occasional electric sparks are observed on the surface of the cathode. When the voltage attains 45-55 V, the current increases abruptly by lQ-2Ct”~ and begins to oscillate around a mean value which remains practically constant whilst increasing the voltage further. At the same time, acoustical and optical effects are observed; yellow-orange sparks or flames are visible on the cathode (Fig. 1). Its metallic surface does not change in form, only black. If the insulation of the cathode is from an organic compound it also turns black and is damaged (peels off under the action of the streaming electrolyte). This is illustrated in Fig. 2. If the electrolyte flow through the capillary is very slow (hence bad cooling) the metal at the orifice of the cathode melts and a deformation takes place. Only an alumina ceramic insulation withstands the mentioned conditions. An insulation made of inorganic enamels lasts for a limited time. The mentioned phenomena are observed not only in oxidising media (NaN03, NaC103 or their mixture) but also in a neutral solution of NaCl. A typical dependence of current on time during sparking is shown in Fig. 3, and thisat constant voltage. It follows from the observed j-r curves that the discharge has the character of sparks. The form of the dependence does not change with hydrodynamic conditions and is the same regardless of whether the electrode is in the free electrolyte or in the hole formed by drilling; and the same applies for the limiting
I. ROLJ~AR
current of sparking, I,, which is constant to within * 20 ;4. To explain this phenomenon, the following mechanism was proposed in accordance with experimente reported in[8] and[I6]. With respect to the distribution of current density on the cathode[9] (the current density in the capillary is negligible), the electrochemical process is concentrated on the tip of the insulated capillary. The quantity of the evolved gas increases with the current density. At the same time, a considerable amount of heat is evolved at the electrode. Since the latter is thermally insulated by the applied ceramic or enamel, the heat is transferred to the electrolyte mainly by convection, Finally, the temperature of the electrolyte layer at the electrode attains the boiling point. Thus, together with the gas evolved electrolytically, a large number of bubbles appear on the electrode surface, and eventually at a certain current density a continuous layer of gas is formed[S, lo]. The resistivity of the gas-electrolyte mixture on the cathode surface rises abruptly, while the current density remains practically constant regardless of the increasing voltage. For these conditions the fluorescence of bubbles is visible[ll]. When the voitage attains a certain value, s&rking takes place between the electrode and the electrolvterl2-l. The high temperature of the sparks causes the &&age of the cathode tool and its insulation.
Fig. 1%Electric discharge on the cathode.
Sparking at cathode tools during electrochemical drilling
45
Fig. 2. Electrodes damaged by electricdischarges it6electrolyte. An electrode before use is shown on the right for comparison. Insulation made by an eiectrophoretical enamel (CSSR No. S-2201/0625).
Table
1. Characteristics of electrodes used
Symbol
d,, mm
dl. mm
Insulation
A B C D E F
1.07 0.66 0.28 0.21 0.71 0.30
1.50 0.99 0.5 1 0.43 1.03 0.52
Enamel 0.06 mm Ceramics 0.3 mm Enamel 0.06 mm Ceramics 0.2 mm Ceramics 0.3 mm Ceramics 0.2 mm
Fig. 3. Dependence of current on time of sparking. Vertical division corresponds to 0.34 A, horizontal division to 0.5 rns, sparking frequency 68 kHz.
EXPERIMENTAL During electrochemical ensure that the current
drilling,
it is necessary
to
does not surpass the limiting value above which the sparking begins, I,. Since this depends on hydrodynamic conditions, we measured the dependence of Is on the Reynolds number Re, and this for six electrodes whose outer diameters (without insulation) were in the range 0:43-1.50 mm. The insulation was made either of alumina ceramics or inorganic enamel. The description of the electrodes is apparent from Table i and Fig. 4. The velocity of electrolyte flow was raising from the laminar to the turbulent region, its upper limit was given by the maximum pressure of 10MPa in the apparatus. Physical data about the electrolytes used are given in Table 2; the temperature of the electrolyte at the inlet was 20°C. The method ofwork was the following. First the rate of flow of the electrolyte through the cathode
Fig. 4. Scheme of the cathode. K. metal capillary; P, insulation; arrow denotes direction of electrolyte flow; v,, velocity of electrolyte flow; d,, d,, inner and outer diameter of metal capillary: L, thickness of the metal capillary. was set as desired; the attainment of the stationary state was indicated by a record of the pressure in the apparatus. Then the electric current was switched on and the voltage was gradually raised. The instant when the sparks began to form on the cathode was determined visually in a dimmed light. The value of I, was determined as the current which passed at a
46
P.Nov.k,
B.
SAJDL
AND
I. ROUSAR
Table 2. Characteristicsof electrolytesused (20°C)[14] Symbol
fiE x lo3
1, W m-l K-’
Composition
5.5 kJ kg-l K-’
kg m-is-L
1
15 % NaNO, 20 % NaClO,
18.0
1329
0.550
1.60
3.40
2 3 4 5 6
25 % 20 % 15% 10% 5%
21.4 19.6 16.4 12.1 6.7
1191 1148 1109 1071 1034
0.572 0.578 0.584 0.590 0.594
1.81 1.58 1.28 1.14 1.09
2.73 3.06 3.39 3.72 4.05
Nail NaCl Nail NaCl Nacl
voltage lower by 1 V than that at which the sparking began. Two dependences of I, on Ra were measured For various electrode-electrolyte combinations. The the cathode was placed either 10 mm from anode (case a) or an insulating plate was placed at a distance 0.2 mm from the orifice perpendicular to the capillary axis (ease fi), in which case the outflowing electrolyte was forced to change its direction abruptly. Since no dependence of the value of I, on the character of flow near the capillary orifice was observed, the results for both cases GC and p were evaluated together. In total, 365 data (cases (z and 8) were measured for various electrode-electrolyte combinations; some of them are given in Tables 3 and 4.
Table 3. Measured
RESULTS
In evaluating the measured data, we assume that the whole process is governed by heat transfer from the bubble-electrolyte layer formed on thecathode tip. For the turbulent electrolyte flow, we assume the validity of the equation Nu = KTRePPro-4(d, ,/I#: Re & 2300 (la) and for the laminar flow regime Nu = K LR e RFr”.333(dl/L)S: The Nusselt number is given as
Al4
B/1
C/2
J-V5
l Symbols and 2.
Nu = qd, /&AT,
and calculated limiting current sparking. Turbulent regime
Fxperimental Symbol*
Rt?
2900 4670 6580 8420 10240 12050 13880 15700 17530 19360 4510 7260 10230 13090 15920 18720 3140 4030 4910 5780 6660 7530 2670 4370 5980
correspond
AND DISCUSSION
(*‘!-*) 126 150 180 191 196 203 212 219 224 226 220 241 299 318 360 374 385 392 392 413 448 526 289 407 434 443
to electrodes
data
densities
for
Theory Equation (12~1)
@‘6T;Is_2) 142 173 184 191 212 214 217
220 225 227 215 241 297 311 355 377 371 392 399 413 427 427 298 298 307 353
an& electrolytes
is c
(A &I-‘) 136 156 172 IS4 196 205 213 221 228
235 229 262 290 311 330 346 :z 413 434 448 470 280 325 362 389
in Tables 1
Re < 2300.
(lb)
(2)
Sparking at cathode tools during electrachemicat
Table 4. Measured and cakulated limiting current for sparking Laminar regime Experimental data
Symbol*
Re 1806 1204 602 1921 1281 640 1913 1793 896 2023 1348 674 1672 836 2260 1507 7.53 21% 1464 732
* Syxnbols correspond
and 2.where express in unit on the length,
is. c (Arm-“)
231 229 201 222 217 202 305 345
209 201 199 200 201 202 293 295 331 1.57 149 143 141 174 166 185 182 178
220 214 203 216 209 199 299 305 290 168 163 154 124 118 196 190 180 210 203 193
;z 209 222 167
to electrodes and electrolytes
q = j$L/KE.
(3) The characteristic length, L, should be equal to or should depend on the thickness of the bubbleelectrolyte layer. This quantity is unknown, but we can suppose its dependence on the Reynoids number in the capillary and on the electrode thickness (d2 -d,)/2. Both quantities should be inserted as variables in the heat transfer [Equations (la, b)]. Hence,
The limiting
current
density
j, = 41,/r@:
for sparking -d:).
(6)
The quantity AT in Equation (2) is the characteristic temperature difference related to the given phenomenon; in our case it is constant. This quantity involves also the change of the electrolyticconductivity rcr with temperature and gas evolution in the boundary layer, as well as the change of other properties of the electrolyte with temperature. For the evaluation of our experiments it was necessary to introduce a new quantity AT* defined as AT.+ = &AT:
Re 2 2300
(Ta)
AT: = K,AT:
Re -z 2300.
(7b)
and
in Equation
Re = vBdrP;l~c,,
(1)are (8)
Pr = CpEPJ&.
(9) We denote rcr the specific conductivity of the electrolyte, A, its heat conductivity, p; its density, pE its dynamic viscosity, and cPE its specific heat. AI1 quantities refer to the temperature of the bulk of the electrolyte. Finally, ur is the linear velocity of the electrolyte flowing through the cathode (the hollow needle). The measured data were correlated by Equations {la) and (lb) rearranged by introducing AT*, Equation (7) in the form:
(4)
(5)
in Tables 1
The ReynoIdsand Prandtl numbers defined in the usual way as
is defined as
The symbol dl denotes the inner diameter of the cathode, d, its outer diameter (without insulation). We set the value of L equal to L = (d3 - d,)/2.
Theory Equation (12b)
js.8 (A cm-‘)
for the case of the formation of sparks we the heat Bow density as the formation of heat volume of the bubble-electrolyte layer formed cathode tip multiplied by the characteristic L:
Nu = jidlL/KE&AT.
densities
Js.01 (A cm-‘)
188 184 176 148
47
drilling
Nu,* = RePPro~4(dl/L)Q:
Re 2 2300,
(l&a)
Nu: = ReRPr0~J33(dl/L)S:
Re < 2300,
(lob)
where Nu; = jid,
L./u&ATT,
Nur = j,’ d, LIKE&AT,+.
(1 la) (1 lb)
The exponents P, Q, R, S and the characteristic temperature difference AT,*, AT,* are considered as unknowns, whose values were determined from 356 experiments by using the least squares method with modified Equations (lOa, b) as fohows (see Appendix): (1) for turbulent regime: ATT = 88.3 K, P = 0.58, Q = 0.49. (2) for laminar regime: AT,+ = 2723 K, R = 0.15, S = 0.67. Hence for Re 2 2300 we have in accordance withE 131 Nu,* = Re0.58Pr0.4(d, /L)“.4g (I&) and for Re < 2300 we have NuZ = Re”~‘5Pr0~“3(d,/~)0~67,
II2b)
48
B.
P.NovAK,
SMDLAND
The calculated limiting current densities for sparking j, c from Equations (12a, b) are given with an averaie error of f 12 y0 (See Tables 3 and 4, also Fig 5.) It can be concluded that Equations (12a, b) are suitable for proposing the working conditions for electrochemical drilling of small holes. The limits of applicability of calculating js according to Equations (12a, b) are as follows: (a} ECM drilling with electrolytes dissolved in water; (b) the anode metals form no firmly adherent passive films in given electrolyte; (c) the process of sparking for (a) and (b) is governed by heat transfer from the bubble-electrolyte layer formed on the cathode tip. The most interesting question arising from Equations (l&t) and {12b) is whether the characteristic length for the Reynolds number should be L or d,. Rearranging Equations &!a, b) we obtain j.$ L’/K&,AT,
= (L~~p~/p~)“.~~ x Pr0.4(di/L)0.07,
ji L’ju,J,AT
(13a)
p’ /G E)‘-I5 L = (Lv BE x Pr”.333(d,/L)-o.‘6.
(13b)
For all our experiments, the values of (dl/LjO.” or (d, /L)-0.16 can be put approximately equal to 1.08 or 0.85, with an error of about + 4 % or + 7 %, respectively. Thus it was necessary to test the hypothesis that the geometrical simplex (d, / L1 ) can be removed from
LROUSAR
Equations (13a, b) giving Nu& Nz&
,
h (A tern*] 300
-
h
Re,
2.104
Re
Equation of observations
P error of P
Q Standard
error of Q constant
Residual
standard
[U*
J. F. Wilson.
Practice and Theory of Electrochemical Machining, p. II. Wiley-Interscience, New York (1971). H. Degenhardt, Elekwochemische Senkarbeit metaliischer W’erkstofe, p. 92. Thesis, Technische Hochschule Aachen, Aachen (1972). R. A. Mirzoev, Colhode Process During ECM. Collected papers on ECM, Schtiinca, Kischinev (197 I) (in Russian). A. D. Davydov, V. D. Kaschtscheev and B. N. Kabanov, Elekrron. Obrab. Mater. No. 6, p. 13 (1969). M. Datta and D. Landolt, Electrochim. Acta 26, 899
Elecrrochim. Acta 27, 385 (1982). 7. P. Novak, 1. RouSar, R. Stefcc and V. &al, Mater. Cheat. Plays. 10, 155 (1984). 8. D. landoh, R. Acosta, R. H. Muller, C. W. Tobias, J. electrochem. Sac. 117, 839 (1970). 9. P. Novdlt, 1. Rot&u, A. Kit&a V. Mejta and V. Cezner, Coil. Czech. them. Commun. 46, 2949 (I 981).
Table 5. Results of multiple regression
Regression
(16)
= L~w&IIL~-
(1981). 5. M. Datta and D. Landolt,
Fig. 5. Mcasurcd and calculated limiting current densities for sparking. Electrode B, electrolyte 1 (see Tables 1 and 2). a, case ce o, case ~3;solid line Equations (12a, b).
Standard
(15a) (15b)
Using the least squares method we obtained AT& = lOI.SK, P = 0.57 and &TTM = 1642IC and R = 0.20. Multiple regression analysis was run on an ICL 4-72 computer using the MREG statistical procedure. All results are given in Table 5. On the basis of Table 5 we can conclude that the Equations (I 2a, b) can be recommended for the calculation of the sparking current densities. The calculated values for the turbulent regime are rendered with a high degree of probability because the multiple correlation coefficient is 0.92; less satisfactory is the situation for laminar flow where the multiple correlation coefficient is only 0.54. The simplex (d,/L) cannot be removed from Equations (13a, b) as this would cause a remarkable decrease in the multiple correlation coefficients for Equations (14a, b). At the F level of 2.75, all variables were significant in Equations (12a, b) and Equations (14a, b).
5.
10'
Number
=j~Lz/~E~,rAT&,
and
4.
-*
-
(14b)
Nu TM= j,’ La /K_&AT&
3.
00
100
(14a)
Re < 2300,
Nu;t,
2.
l
0
200
o
b
Re > 2300,
for
REFERENCES
I
I
for
where
1. 400
= Re: P? = Re$Pr0.333
(12a)
analysis
Equation
using Equations (l2b)
(12) and (14)
Equation
(14a)
Equation
(14b)
270
86
270
86
0.5806
0.1504
0.5732
0.1966
0.0238
0.0563 0.6689
0.0237 -
0.0431
0.4872 0.0366
0.1144
(K)]
88.25
2723
101.53
1642
error E (YJ
21.05
24.68
21.20
24.78
0.92 14
0.5443
0.8236
0.4449
Multiple correlation coefficient
Sparking
at cathode
tools during electrochemical
IO. J. A. McGeough, Principles of Electrochemical Marhining, p. 175. Chapman and Hall, London (1974). 11. Ya. Z. Agroskin, A. I. Zhemovoy, V. V. Zhukov, V. A. Zyuzin, A. A. Karpov and V. I. Podlovilin, El&&on. Obrab. Mater. No. 5, p. 14 (1979). 12. B. R. Lazarenko and N. 1. Lazarenko, Elektron. Obrab. Mater. No. 1, p_ 14 (1978). 13. P. Novdk, I. Roukr, V. Cezner and V. Mejta, Coil. Czech. them. Commun. 44, 2788 (1981). 14. Spranochnik Khimiko, Vol. III. Khimiya, Moscow (1964). 15. T. H. Drake and J. A. McCcough, Proceedings ofMachine Tool L&sip and Research Co@rence, Manchester, p. 361. Macmillan (1981). I 6. 1. M. Crichton, J. A. McGeough, E. Munro E. and C. White, Precision Engineering, July (1981) (cited in [15])
drilling
49
where y = In [(j~d1L/K~1E)P~0.4], x, = ln Re,
(A3) (A4)
xI = In (d, /L),
(A5)
k, = In AT;
(‘46)
For testing the hypothesis removed from Equations (A7)-(Al2):
that the (d,/L) values can be (13a,b) we used Equation
In [ ( j~L2/K,L,)/Pro.4j
= In AT&., + P In (Lv&/~~)
or in a more condensed
form as
YM = k,,
+Px,,,
(A7)
(Ag)
where y, APPENDIX The evaluation of AT?, P and Q or AT;. R, S by a least squares method is based on Equations (lOa, b). From Equation (lOa), after some rearrangement, we obtain In [( j:d,L/rc&E)/Pr0,4]
= In ATT*+ P In Re + Q In K/O-
Equation
(Al) can be written in a more condensed y=k,+Px,+Qx,,
(Al) form as (-42)
= In [ (j~Lz/xE1E)/P+4],
(A9)
xIM = ln (%&/P,),
(Alo)
k ,M = InAT&.
(Al 1)
Multiple regression analysis give values of k,, P, Q or k,, and P, for both the laminar.and the turbulent regimes of electrolyte flow (See TabIe 5). The residual standard error in % (E) is based on the residual standard error (8) calculated by Equation (Ala); the calculated E values are given for Equations (A2) or (A8). E=(e’--1)x100.
(Al2)