The computer aided simulation of electrochemical process with universal spherical electrodes when machining sculptured surfaces

Journal of Materials Processing Technology 107 (2000) 283±287

The computer aided simulation of electrochemical process with universal spherical electrodes when machining sculptured surfaces Jerzy Kozaka, Maria Chuchrob,*, Adam Ruszajb, Krzysztof Karbowskic b

a Warsaw University of Technology, Warsaw, Poland The Institut of Metal Cutting, Department of Electrochemical Machining, ul. Wroclawska 37a, 30-011 Cracow, Poland c Cracow University of Technology, Cracow, Poland

Abstract In this paper a mathematical model, the results of computer simulation and experimental investigations of electrochemical machining with a spherical tool-electrode are presented. The experimental investigations were carried out in order to evaluate the in¯uence of working voltage, velocity of electrode displacement, initial interelectrode gap size, tool-electrode cross feed and electrode radius on removed material excess thickness, machined surface height of waviness, surface roughness and metal removal rate. Accuracy of computer simulation evaluated by differences between results of experimental tests and computer simulation depends on accuracy of a priori estimation of electrochemical machining coef®cient, total overpotential of electrode processes, electrical conductivity of electrolyte, etc. The results of application of neural network to prediction of height of surface waviness and thickness of removed allowance which depend on setting parameters of electrochemical machining (ECM) are also presented. The developed software for simulation of the ECM process with universal spherical tool-electrode and trained neural networks are useful for process analysis, machined surface prediction and optimisation. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Material-removal processes; Non-traditional processes; Electrochemical machining

1. Introduction The quality of details depends signi®cantly on surface layer properties and surface layer properties depend on phenomena occurring into machining area. In case of cutting in surface layer there are some changes in metallurgical structure, internal stresses, plastic deformations, and sometimes local defects resulted from mechanical contact between cutting edge and workpiece, accompanied by increase of temperature. In case of electrical discharge machining thickness of changed surface layer can be even about 0.5±1.0 mm. It results from the fact that electrical discharge machining is a thermal process. As a result, the surface layer changes metallurgical structure, hardness, internal stresses and many cracks. In order to create the surface layer without cracks or mechanical defects the electrochemical machining should be applied. Here material allowance is removed as a result of electrochemical dissolution process, which does not introduce any additional

*

Corresponding author. Tel.: ‡48-12-63-17-239; fax: ‡48-12-933-94-90. E-mail address: [email protected] (M. Chuchro).

changes into surface layer [1,2]. In order to solve this problem the investigations of electrochemical machining with universal spherical electrode have been carried out. Basic way of electrochemical machining is machining with pro®led tool-electrode (Fig. 1). During the machining process, the tool-electrode is moving in direction of machined part Ð anode. The gap between tool-electrode and the workpiece is supplied by electrolyte Ð most often water solution of salt (e.g. NaCl, NaNO3). The result of this machining is the tool-electrode shape reproduction in machined material. Accuracy of electrochemical machining is mainly limited by randomness of phenomena occurring in machined space and accuracy of tool-electrode design and stabilisation of machining parameters [1±3]. The fact of accuracy increasing with decreasing of machined area may be utilized in case of using universal electrode [3,4]. Scheme of this type of machining is shown in Fig. 2. 2. Mathematical model of electrochemical machining with universal electrode The most often used universal electrode is electrode with spherical shape, i.e. ball-end electrode. Using this electrode

0924-0136/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 0 ) 0 0 6 9 7 - X

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Fig. 1. Scheme of machining of turbine blades: (1) cassete body; (2) cassete caver; (3) blade; (4) tool-electrode.

it is possible to effectively remove in one pass the allowance a  0:05ÿ1:5 mm, get to roughness Ra  0:2ÿ2 mm and waviness on the border lines of successive electrode passes D < 0:01 mm. Mathematical modelling of electrochemical machining with universal spherical electrode (ECM-CNC) has been developed for given conditions of dissolution, initial shape of workpiece and tool-electrode trajectory. In general case ECM-CNC mathematical model of surface shaping process is described by the following system (Eq. (1)): div…k grad u† ˆ 0;

u…f † ˆ ÿEk …ic †

i…F† ˆ kF jgrad ujF u…F† ˆ U ÿ Ea …ia †; @F ‡ kV …i†i…F†jgrad Fj ˆ 0; F…t ˆ 0† ˆ F0 @t

(1)

where k ˆ k…F† is the speci®c conductivity of electrolyte on the anode F face, u the electrical potential, Ea the anode potential during electrochemical dissolution, Ek the cathode potential, F0 the shape of the workpiece-anode in

Fig. 3. Scheme used for describing machined shape changes in sequence time increment Dt; Dni, anode surface displacement in Dt time.

the initial time of machining, F the actual shape of anode surface, f0 the cathode surface, ic and ia the current density on the cathode-tool and anode-workpiece, respectively, kV the coef®cient of electrochemical machinability which is de®ned as the volume of material dissolved per unit electrical charge. This system of equations (Eq. (1)) was solved for displacement of machined surface according to the normal to machined surface. In this case modelling resolves itself to determine following intervals Dn with which machined surface is displaced in time Dt (Fig. 3). To ®nd the current density on the surface of anode-workpiece approximation using linearisation of electrical potential along distance between a given point the anode and the closet point on the cathode can be applied [1]. In this case the changes of workpiece shape during ECM by using the spherical electrode are described by system (Eq. (2)) [5]: k‰U ÿ E…iA †Š i ˆ q …xA ÿ xe †2 ‡ …yA ÿ ye †2 ‡ …zA ÿ ze †2 ÿ R xe ˆ xe …t†;

ye ˆ ye …t†;

ze ˆ ze …t† DnA ˆ kV …iA †iA Dt (2)

Using the above mathematical model, software was developed for computer simulation of machining process. This software allows for the following established process parameters: working voltage U, feed rate of tool-electrode vp , frontal interelectrode gap thickness in the beginning of machining S0, cross-feed per electrode stroke c, to determine the surface after machining and calculate surface geometrical structure indicators (D, a). The simulation was done for ¯at, internal and external cylindrical surfaces. As a simulation result the spatial view of machined surface or parts intersection by perpendicular to machined surface plane was obtained. In Figs. 4 and 5 the examples of simulation results for machining of internal and external cylindrical surface are shown. Fig. 2. Scheme of machining internal cylindrical surface by means of toolelectrode in shape of spherical cup: (1) universal electrode; (2) machined surface, a is the thickness of material excess removed, r the radius of machined surface, S0 the distance of tool-electrode face to machining surface, vp the tool-electrode feed rate and R the radius of tool-electrode.

3. Experimental tests For verifying the model and the simulation results, experimental tests were done. The tests were done for the

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following cases:  machining of flat surface;  machining of external cylindrical surface;  machining of internal cylindrical surface. In the presented tests the following parameters were taken into account: tool-electrode feed rate vp , working voltage U, distance of electrode face from machine surface S0, radius of electrode R, radius of machined surface r, tool-electrode cross-feed c. It can be stated from the mathematical model that these parameters in¯uence on the basic technological parameters like: thickness of removed allowance, machining ef®ciency, waviness of machined surface. As an electrolyte water solution of NaNO3 was used with concentration 15%, tool-electrode was done from brass and samples from NC6 steel. The investigations were carried out on electrochemical machine-tool type EOCA 40 with control system PRONUM 640 FC, equipped with specially designed tooling, samples and electrodes. The investigation results were elaborated using the neural network as an object investigation function. 4. Analyses of investigation results and computer simulation Fig. 4. Results of simulation for machining external cylindrical surface: U ˆ 14 V; vp ˆ 1 mm=min; S0 ˆ 0:5 mm; R ˆ 5 mm, 2r ˆ 140 mm; c=R ˆ 0:5; k ˆ 0:0124 1=O mm; kV ˆ 0:00685 mm3 =AS, sp ˆ 2:6 mm; t ˆ 0:5 s. (a) Spatial view; (b) intersection.

Fig. 5. Results of simulation for machining internal cylindrical surface: U ˆ 14 V; vp ˆ 30 mm=min; S0 ˆ 0:9 mm; R ˆ 5 mm, 2r ˆ 150 mm; c=R ˆ 0:5; k ˆ 0:01937 1=O mm; kV ˆ 0:02329 mm3 =AS, sp ˆ 2:6 mm; t ˆ 0:5 s. (a) Spatial view; (b) intersection.

Based on the trained neural network data, the analysis of in¯uence of machining parameters on thickness of removal allowance and waviness on the border line between successive tool-electrode passes was [6] done. In Figs. 6 and 7 the examples of dependencies obtained from the neural network for the ¯at surface machining are shown. The in¯uence of cross-feed per electrode pass c on technological parameters can be explained in this manner. Thickness of removed allowance a (Fig. 7) is decreasing with increasing S0 and c/R. This results from the decreasing intensity of dissolution process. With vp increasing, D is decreasing (Fig. 7). It results from the fact that removed allowance a decreases when vp

Fig. 6. Relationships between thickness of removed allowance a, frontal interelectrode gap S0 and ratio of the cross-feed to electrode radius c/R, for: U ˆ 14 V; vp ˆ 30 mm=min; R ˆ 5 mm.

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Fig. 7. Relationships between waviness D, tool-electrode velocity vp and thickness initial gap S0, for: U ˆ 14 V; c=R ˆ 0:5; R ˆ 5 mm.

Fig. 8. Relationships between thickness of removed allowance a and frontal interelectrode gap S0 and ratio cross-feed to tool-electrode radius c/R, for: U ˆ 14 V; vp ˆ 30 mm=min; R ˆ 5 mm.

increases (c ˆ const:). In case of cylindrical surface machining, essential will be the in¯uence of machined surface radius. The in¯uence of machined surface radius depends on the type of cylindrical surface (internal or external). In Figs. 8 and 9 examples of relationships received for machining of external cylindrical surface, and in Figs. 10 and 11 for machining of internal cylindrical surface are shown.

Fig. 9. Relationships between waviness D and frontal interelectrode gap S0 and ratio cross-feed to electrode radius c/R, for: U ˆ 14 V; vp ˆ 30 mm=min; R ˆ 5 mm.

Fig. 10. Relationships between thickness of removal allowance a and frontal interelectrode gap S0 and ratio of cross-feed to electrode radius c/R, for: U ˆ 14 V; vp ˆ 30 mm=min; R ˆ 5 mm; r ˆ 150 mm.

Fig. 11. Relationships between waviness D and d (2r) and electrode radius R, for: U ˆ 14 V; vp ˆ 30 mm=min; S0 ˆ 0:1 mm; c=R ˆ 0:5.

As shown in Fig. 8, a decreases with S0 and c/R increases. This is caused by decreasing dissolution intensity (S0) and decreasing of machining time in analysed point (c/R). Only for bigger S0 value insigni®cant increase of removed allowance is observed when c/R increases. D also increases

Fig. 12. Relationships a ˆ f …vp † for electrode with radius R ˆ 5 mm; U ˆ 14 V; 2r ˆ 140 mm; c=R ˆ 0:5; S0 ˆ 0:5 mm. Curve determined from: (1) computer simulation data; (2) experimental tests; (3) neural network data.

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can be ¯ow break-away of electrolyte stream which caused decrease of electrode reaction area. Thickness of removed allowance decreases. S0, the removed allowance taken from experimental tests is smaller than that received from simulation. 5. Conclusions

Fig. 13. Relationships D ˆ f …vp † for electrode with radius R ˆ 5 mm; U ˆ 14 V; 2r ˆ 140 mm; c=R ˆ 0:5; S0 ˆ 0:5 mm. Curves 1±3 as in Fig. 12.

signi®cantly as c/R increases (Fig. 9). Increasing S0 process dissolution intensity decreases and thickness of removed allowance also decreases which is the reason for D decreases (Fig. 9). Further increase of S0 is a reason of decrease of area of electrode in¯uence on area machined in former passes, which caused waviness of D to increase. In the range S0 ˆ 0:75ÿ0:9 mm, once more the in¯uence of decrease of thickness removed allowance predominates and D decreases. With c/R increase, time of electrode in¯uence on machined surface is decreased, and a decreases too (Fig. 10). With increase of S0 intensity of dissolution decreases and this is why thickness of removed allowance is decreased. With R increase waviness D also increases (Fig. 11). It is connected with deterioration of electrolyte ¯ow conditions. In the range R ˆ 5ÿ9 mm the D value increases because of electrode in¯uence area increases which caused light decrease of D value. D increase with R increase can be explained by increase of hydrogen concentration causing ``better'' electrode shape reproduction. Increase of r for bigger R value ®rst caused hydrogen concentration decrease, which caused the waviness decrease. With further r increase electrode in¯uence range decreases, which causes again D increase. A comparison between the results got from simulation and experimental tests was done. In Figs. 12 and 13 examples for machining external cylindrical surface are shown. In considered case (Fig. 12) in the real conditions an electrolyte shows trend for ¯owing out of machined area. It

Accuracy of computer simulation, as shown by the agreement between the modelling and experimental test results, depends on the accuracy of determination of the following parameters: electrochemical machinability kV, total overpotential of electrode processes E and electrolyte electrical conductivity k. The investigations con®rm that because of relatively small effectiveness in comparison to classical sinking, electrochemical machining with universal electrode should be used in ®nishing machining surfaces initially machined by other methods like classical milling or electrical discharge machining. It can be stated that presented investigations enable to develop guidelines for practical use of this method of machining. The results of these investigations can be used in designing of ECM process when using universal spherical electrode for ®nishing curvilinear surfaces after rough machining (milling or electrical discharge machining). References [1] A. Davydov, J. Kozak, High Rate of Electrochemical Shaping, Izd. Nauka, Moskva, 1990 (in Russian). [2] J.A. McGeough, Principles of Electrochemical Machining, Chapman & Hall, London, 1979. [3] A. Ruszaj, M. Chuchro, M. Zybura-Skrabalak, The in¯uence of phenomena occurring into interelectrode gap on accuracy of electrochemical machining, in: Proceedings of the 31st International MATADOR Conference, Manchester, UK, 1995, pp. 421±425. [4] M. Chuchro, A. Ruszaj, M. Zybura-Skrabalak, The investigations of electrochemical milling of curvilinear surfaces, in: Proceedings of the Ninth International Precision Engineering Seminar, Braunschweig, Germany, 1997, pp. 600±602. [5] J. Kozak, L. Dabrowski, A. Ruszaj, R. Slawinski, Computer simulation of numerical controlled electrochemical machining (ECM-NC) with a spherical tool-electrode, in: Proceedings of the 11th International Conference on CAPE, London, UK, 1995, pp. 205±210. [6] M. Chuchro, The modelling of electrochemical machining with an universal spherical electrode, Ph.D. Thesis, Cracow University of Technology, Cracow, Poland, 1998.