{Principles of the express method for controlling interelectrode space condition during wire electrochemical processing} http://dx.doi.org/10.5599/jese.660 269 J. Electrochem. Sci. Eng. 9(4) (2019) 269-280; http://dx.doi.org/10.5599/jese.660 Open Access: ISSN 1847-9286 www.jESE-online.org Original scientific paper Principles of the express method for controlling interelectrode space condition during wire electrochemical processing Vasyl Osypenko, Oleksandr Plakhotnyi and Oleksii Timchenko Cherkasy State Technological University, Cherkasy, 18006, Ukraine Corresponding author: o.plakhotny@chdtu.edu.ua Received: February 3, 2019; Revised: June 26, 2019; Accepted: June 27, 2019 Abstract In the practical implementation of the sequential wire electrical discharge machining – pulsed electrochemical machining (WEDM – PECM) technology and in order to perform high quality electrochemical processing, there is a need for the real-time operational control of electrical parameters of inter-electrode space and corresponding adaptive correction of amplitude-frequency power supply parameters (AFPSP). In the context presented by the authors, a mathematical apparatus and an algorithm of operational galvanostatic mode monitoring of anode dissolution using wire electrode-tool are proposed. This will allow adaptive adjustment of AFPSP to ensure controlled passage of electrochemical reactions and significantly increase process stability, dissolved surface layer thickness uniformity along entire electrode tool movement trajectory and resulting surface quality. Keywords Wire electrical discharge machining; pulsed electrochemical machining; current and voltage waveforms; process monitoring; surface finishing. Introduction Wire electrical discharge machining (WEDM) technology fully satisfies the requirements of modern production in terms of miniaturization and precision. However, modern industry and especially instrumental production require electrical discharge wire cutting machines to form surfaces with roughness Ra < 0.1 microns. Obtaining such surface parameters and getting rid of a structurally modified heat affected zone (HAZ) using only material removal by a highly concentrated source of heat having a spark discharge is extremely costly and difficult. In modern machines of the world leader in the field of electrical discharge nanotechnology, Sodick Co. LTD, a mirror-like smoothing of steel blank surfaces of up to 0.08 microns is achieved in 12 passes with a change of working environment. This leads to an unacceptable cost increase of machined parts. http://dx.doi.org/10.5599/jese.660 http://dx.doi.org/10.5599/jese.660 http://www.jese-online.org/ mailto:o.plakhotny@chdtu.edu.ua J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 INTERELECTRODE SPACE CONDITION 270 Pulse electrochemical machining (PECM) principally allows obtaining surfaces with roughness Ra < 0.1 microns with the absence of a structurally altered layer on the workpiece surface. However, implementation of an efficient PECM process by a mobile wire tool electrode (WTE) following to the WEDM technology scheme is currently not sufficiently researched and is challenging in scientific and technical terms. The solution requires complex experimental and theoretical studies, as well as mathematical and physical modelling of basic processes that determine the nature of the electrochemical dissolution of the anode surface obtained by WEDM. Literature review and problem statement For WEDM, the express methods of preliminary determination of power supply parameters and inter-electrode space (IES) condition monitoring in real time are already developed and successfully used on serial machines. The IES resistance is controlled by the hardware. AFPSP and machine drives feed rate have adaptive control. More sophisticated modern schemes are implemented through the continuous supply of low-power diagnostic impulses to IES. By analysing the response, a decision is made to switch on a more powerful source of pulsed technological current, which in fact, carries the electro-discharge destruction of material [1,2]. For wire PECM, such control methods have not been developed. The time of periodic process of double layer charging to the overvoltage activation and its discharge time are very important for nanosecond pulsed electrochemical processing [3-5]. Cylindrical wire electrode causes significant current density distribution on the anode surface. Therefore, even a slight change in electrode potential leads to a significant change in current density and accordingly, to dissolution localization. With a longer duration of microsecond pulses, a diffusion processes becomes a limiting factor in IES. Accordingly, calculation of stationary and transition components of diffusion current, which depend on main parameters of each technological PECM scheme, must be preceded by the choice of current amplitude [6]. For configuration of flat anode and cylindrical cathode with stream electrolyte flow, it is problematic to determine diffusion layer thickness, which depends on velocities distribution of electrolyte in near-anode zone. Consequently, calculated mathematical models of electrochemical processes in IES are complex, require usage of computer-aided design software and significant computational time [7]. These mathematical models are adequate for preliminary calculation of PECM processes parameters but are not suitable for operational monitoring and adaptive real-time correction. Therefore, there is an urgent need for the creation of algorithms and schemes suitable for practical implementation in the existing technological equipment. The proposed approach is based on the determination of magnitude and dynamics change of IES electrical parameters and as a result, process nature of electrochemical dissolution. These can be obtained from analysis of response oscillograms using equivalent electrical circuit substitution scheme. A similar approach was used in [8], using a complex mathematical apparatus not suitable for operative quantitative analysis of response oscillograms. In the subsequent work [9] only a qualitative analysis of oscillograms was conducted. Proper choice of AFPSP according to PECM scheme, can significantly improve surface quality, machining accuracy, material removal rate and overall process controllability [10,11]. The purpose is to increase the technological characteristics of high-performance combined methods of current-conducting materials machining with the help of further development of mathematical apparatus of operational monitoring and adaptive efficiency correction of galvanostatic PECM mode. Vasyl Osypenko et al. J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 http://dx.doi.org/10.5599/jese.660 271 Experimental equipment and methods Technological scheme When using the PECM scheme of unipolar current pulses with moving WTE as a cathode (Figure 1), developed by the authors and implemented in particular experimental technological equipment, the process of anodic dissolution of workpiece material significantly depends on the magnitude and growth dynamics of anode polarization and relaxation of its potential during the pause between current pulses. Figure 1. Machining scheme of sequential wire EDM and wire PECM Replacement of the partition boundary “anode – electrolyte” for equivalent electrical circuit (Randles circuit) is carried out and described in Figure 2 [8,12]. The choice of circuit should be based on electrical properties of IES. Technological parameters during machining process determine dynamics change of electrical properties of IES. Electrolyte flow speed (renewal rate) influences RE – electrolyte resistance. Change of IEG value, a size of interacting surface while moving on intricate- contoured trajectory affects capacity. WTE feed rate along trajectory alters dissolution conditions of EDM-affected surface layers and influences the electrical properties of IES. a b Figure 2. a - Current pulse parameters; b - Electrical equivalent scheme for anode-electrolyte boundary interface of pulse ECM (PECM): RE – electrolyte resistance; C – double layer capacity; RF – Faraday resistance Methods for obtaining oscillograms of anode current pulses are well worked out and have a relatively simple scheme implementation (Figure 3) [8,13]. Research of physical and technological parameters of wire cutting electrical discharge machining and subsequent electrochemical processing by a wire electrode was carried out on SELD-02 (wire-cut http://dx.doi.org/10.5599/jese.660 J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 INTERELECTRODE SPACE CONDITION 272 electrical discharge machine on linear motors, Ukraine). SELD-02 machine has linear motors, granite guides and gas-lubricated supports. This provides minimal displacement error. a b Figure 3. Schemes of measurements: a - flat electrodes, b - flat anode – cylindrical (wire) cathode. 1 – anode, 2 – cathode, 3 – reference electrode (platinum), 4 – electrolyte, 5 – bridge, 6 – driving pulse generator, 7 – current source, 8 – current transducer, 9 – oscillograph, 10 – computer, software, 11 – computer numerical control unit, 12 – positioner Experimental conditions: anode – stamping steel DIN X155CrVMo12-1, cathode – 0.2 mm diameter Cobra Cut B wire (AGIE, Switzerland), CuZn37 hard brass, 1 M NaCl electrolyte at temperature of 28 °C which was delivered as a jet from the upper chamber of the machine at pressure of 5104 Pa. Height of the part is 11 mm. The machine-tool provided wire electrode movement with a given speed along the trajectory at a given distance (IEG) from the machined surface. Conductivity of the electrolyte was controlled by the Oakton TDS-5/CON-5 with a special electrode which expands measurement scale (cell factor K = 10). Polarization-time and current-time dependencies were recorded by digital Atten ADS1000 dual-channel oscillograph and transmitted to computer in a mathematical software package for processing. Preliminary testing of the proposed method for monitoring IES was carried out in studies of transient processes in electrochemical system. It had fixed flat electrodes and the process was Vasyl Osypenko et al. J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 http://dx.doi.org/10.5599/jese.660 273 conducted by the passing of a sequence of rectangular current pulses. Electrodes 2012.51.5 mm were immersed in a bath with immovable 1 M NaCl electrolyte, so the electrodes interaction area was 2.5 cm2. Anode material – stamping steel DIN X155CrVMo12-1, cathode – brass СuZn37. Mathematical method for calculating parameters of an electric circuit loaded by microsecond current pulses As is known, current i(t) and voltage u(t) at the ends of an electrical circuit element with active resistance R and capacity C are bound by formula [14] = ( ) ( ),u t R i t   = +     1 0 0 1 ( ) ( )du t i t t q C (1) where q0 – initial charge on condenser covers. Using the operational method [14], we introduce an integral transform of Laplace’s "operational current", →( ) ( )i t I p and "operational voltage", →( ) ( )u t U p , where p is a complex number frequency parameter. Then, relation (1) will be converted into operational formulas = ,U RI = 1 U I Cp (2) if we consider q0 = 0. Formulas (2) combine into "operational Ohm’s law " =U ZI (3) where Z is “operational resistance” or impedance, which in the case of active resistance and capacitance has the following form: = , R Z R = 1 C Z Cp (4) Considering rules for adding parallel and serial impedances, we obtain the expression for the overall circuit (Figure 2b) impedance, = + +1 F E F R Z R CpR (5) and the operational equation, respectively:   = +  + 1 F E F R U R I CpR (6) Similarly, it is possible to formulate the operational equation for more complex electric substitution schemes taking into account additional components of inter-electrode space, such as cathode double electrical layer capacitance, resistance of passivating films that can be formed on surface of electrodes, etc. Also, in the substitution scheme, inductivities can be introduced if response oscillograms taken from IES clearly indicate oscillatory attenuation signals and model must reproduce them. It is important to substantiate the conformity of each element of electrical circuit and way of its connection to the real processes occurring in IES during electrochemical machining. To construct a mathematical description of the passage of a rectangular current pulse through a model of an electrochemical cell (Figure 2b), we first consider the problem of DC current i0 activation at time t = 0. http://dx.doi.org/10.5599/jese.660 https://en.wikipedia.org/wiki/Complex_number J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 INTERELECTRODE SPACE CONDITION 274 = 0 ( ) ( ),i t i t   =   0, if 0, ( ) 1, if 0; t t t ( )t – Heaviside function. Operational current is defined as I = i0/p, while the operational voltage according to Eqs. (3) and (6) is defined as:   = +  +  0 1 F E F iR U R CpR p (7) We perform the transition operation to the original ( ) ( )u t U p started using the conclusion of the second expansion theorem [14], according to formula = = → + 1 ( ) (0) ( ) ( ) (0) '( ) k k l p tk k k k A p A A p e pB p B p B p (8) where pk – kth equation root of B(p) = 0. In our case, using Eq. (7) we have only one root, p1 = 1/CRF. Then using Eq. (8) → + − 1 0 0 ( ) ( ) ( ) p t E F F A p R R i R i e pB p u(t) becomes defined as: = + − 1 0 ( ) [ (1 )] p t E F u t i R R e (9) Next, to get response function to the rectangular shape current pulse passage,   = − − 0 0 ( ) ( ) ( ) i i t i t i t , where  i is pulse duration, the lag theorem [14] was used and we get:     − = + − − + − −1 1 ( ) 0( ) {[ (1 )] ( ) [ (1 )] ( )} ip t p t E F E F iu t i R R e t R R e t (10) Here it is assumed that electrochemical cell parameters RE, RF, C have not changed during pulse duration. Figure 4. Sequence of current pulses with arbitrary parameters of duration and on-off time For a series of current pulses with an arbitrary time duration and on-off time parameters (Figure 4), it is suitable to use the following form of the response function       − − − − − = + − − + − − + + + − − − + − − + + + − − − + − − + + 1 2 1 3 2 4 3 5 4 6 5 ( ) 0 1 1 2 2 1 ( ) ( ) 3 3 2 4 4 3 ( ) ( ) 5 5 4 6 6 5 ( ) {[ (1 )] ( ) [ (1 )] ( ) [ (1 )] ( ) [ (1 )] ( ) [ (1 )] ( ) [ (1 )] ( ) ...}, p t p t t E F E F p t t p t t E F E F p t t p t t E F E F u t i R R e t R R e t t R R e t t R R e t t R R e t t R R e t t (11) where according to the trend of parameters changing from RE1, RF1, C1 to RE2, RF2, C2, then to RE3, RF3, C3, etc, it is possible to clearly observe dynamics of IES condition indicators for an electrochemical cell during pulsed current workload in the galvanostatic mode. Vasyl Osypenko et al. J. Electrochem. Sci. Eng. 9(4) (2019) 269-280 http://dx.doi.org/10.5599/jese.660 275 Results and discussion Flat electrodes Figure 5(a) presents the results of dynamic measurements of anode polarization at given amplitude-time parameters of current. It should be noted that amplitude of current pulses and interaction area of electrodes in this experiment do not correspond to the operating modes of current density of electrochemical dissolution using wire WEDM + PECM technology. Duration and amplitude of pulse current, area of interaction of electrodes, IEG value were selected in such a way to maximize manifestation of IES resistance and capacity in anodic polarization curves. In addition, oscillograms were recorded at the beginning of dissolution process in order to minimize influence of external factors such as electrochemical reaction products saturation (slag) and IES gas pollution or formation of various films on electrodes, which had not yet appeared in a short time. a b Figure 5. Oscillograms and their mathematical processing: a - rectangular current pulses (red curve); increase and decrease of anode polarization (blue curve); b - approximation by response function of areas with transient processes Then, the inverse mathematical problem was solved using the experimentally obtained plot of polarization-time dependence, and selecting coefficients in the response function (Eq. (10)), i.e. parameters RE, RF, C of the electrical equivalent substitution scheme of an electrochemical cell. Polarization growth area (Figure 5b) was approximated by the least squares method using function (9), which is a response function when passing the front edge of current pulse through an electrochemical cell. The decrease of area which corresponds to the back edge of the switch-off of current pulse, was approximated by the function represented in the second term Eq. (10). According to oscillogram processing results (Figure 5b), it was found that at the moment of passing the forward front of current pulse, IES parameters had following values: RE = 0.12 Ohm, RF = 0.33 Ohm, C = 1.2·10-4 F. At the moment of passing rear front, these values were: RE = 0.12 Ohm, RF = 0.4 Ohm, C = 3.9·10-4 F. Estimated total IES resistance, R, according to the Ohm’s law   =R S (12) using values of electrolyte conductivity,  = 8.61 S m-1, electrodes interaction area, S = 2.5·10-4 m2 and IEG,  = 0.8·10-3 m, was 0.37 Ohm. Specific capacity of double electric layer i.e. capacity according to the equivalent interaction area of electrodes is 0.48 F/m2 and 1.6 F/m2 in the first and second case, respectively. According to the literature data, specific capacity values should be within 0.2-0.4 F/m2 [15, Helmholtz model, 0.6-0.8 F/m2] [15, or 0.4-0.5 F/m2 [16, measured at the boundary between mercury anode and 1М NaCl solution at 25 °С, 0