Accepted Manuscript Title: Monitoring and control of the electrochemical machining process under the conditions of a vibrating tool electrode Authors: Tomasz Paczkowski, Jarosław Zdrojewski PII: DOI: Reference:
S0924-0136(17)30023-7 http://dx.doi.org/doi:10.1016/j.jmatprotec.2017.01.023 PROTEC 15098
To appear in:
Journal of Materials Processing Technology
Received date: Revised date: Accepted date:
25-7-2016 28-12-2016 22-1-2017
Please cite this article as: Paczkowski, Tomasz, Zdrojewski, Jarosław, Monitoring and control of the electrochemical machining process under the conditions of a vibrating tool electrode.Journal of Materials Processing Technology http://dx.doi.org/10.1016/j.jmatprotec.2017.01.023 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Tomasz PACZKOWSKI*, Jarosław ZDROJEWSKI** MONITORING AND CONTROL OF THE ELECTROCHEMICAL MACHINING PROCESS UNDER THE CONDITIONS OF A VIBRATING TOOL ELECTRODE Electrochemical machining process of curvilinear surfaces with a shaped electrode is still considered one of basic operations within this technology. In a case of machining such complex surfaces it is difficult to design constant values of this process for the whole of the machining time and additionally ensure high production efficiency. This paper presents a system for controlling and monitoring the electrochemical machining process in a way which allows a suitable modification of parameters related to the kinematics of a tool electrode, including the frequency of its vibrations and tool design stage verification and optimization of machining equipment behavior. The parameters are modified according to designed criteria. The article also presents the research station which was used for verification of the presented system, as well as the effects of this verification. Keywords: computer simulation, tool design, electrochemical machining, process monitoring, process control, equipment behavior
1. INTRODUCTION During electrochemical machining (ECM) the machined item and the tool make up a system of electrodes, in which the machined item is connected with a positive pole of an electric power source. This system creates also an inter-electrode gap in which the electrolyte flows. Material from the machined item is removed through electrochemical processes after applying voltage to the electrodes. Accuracy in electrochemical machining is conditioned by the shape of the tool electrode and thickness of the gap between the tool electrode and the machined item. In standard continuous current electrochemical machining for gaps smaller than 0,2mm continuing this process is rather difficult. It is caused by many factors, among others: due to heating of the electrolyte caused by the flow of electric current, gas phase emission in the electrolyte, creation of solid products in the electrolyte, mainly metal hydroxides, low speed of the electrolyte flow, high changeability of conditions in the inter-electrode gap in case of electrode surfaces with complex curvilinear shapes. Changes in electrical conductivity connected mainly with variable temperature disposition and electrolyte properties in the inter-electrode gap have a significant influence on electrochemical machining accuracy. CAE-ECM system developed by Kozak (1998) allows defining conditions in the inter-electrode gap, including changes in electrical conductivity, which are mainly connected with the changing temperature distribution and properties of the electrolyte. The mechanism of changes in electrical current density distribution were researched by Kunieda and his team with the
*
Department of Production Engineering, Faculty of Mechanical Engineering, University of Technology and Life Sciences in Bydgoszcz ** Department of Digital Technology, Faculty of Telecommunications and Electrical Engineering , University of Technology and Life Sciences in Bydgoszcz
use of transparent tool electrode material (Chu et al, 2016). Studied phenomena have an essential influence on the accuracy of electrochemical machining. Excessive temperature rise in ECM processes is the main factor leading to the incidence of critical states. Knowledge of maximum temperature values is essential for designating machining parameters' boundaries. Another very important factor influencing changes in electrical conductivity in the gap is the gas phase formation. Derogatory influence of a gas phase is reflected not only in conductivity values but also in changes of hydraulic resistance, which causes a drop in electrolyte velocity or the occurrence of lack of flow stationarity. These problems were described by authors studying mathematical modelling of ECM processes, resulting in calculations of electrolyte velocity values' distribution along the inter-electrode gap (Kozak, 1998), along and across the gap (Paczkowski and Sawicki, 2008) and on a curvilinear surface area (Wołgin, 2001). The influence of electrolyte flow conditions on ECM process stability was also studied by Zhu, who defined its limit values based on theoretical and practical research (Zhu et al, 2016). Simultaneously, to ensure required accuracy, high efficiency and small grittiness of surfaces, ECM process is conducted with high current densities (as much as hundreds amperes per cm2) and inter-electrode gaps as small as tenths of a millimeter. As it was mentioned above, during machining process various incidents take place, such as the emission of significant amounts of heat (which may cause electrolyte boiling), the formation of a gas phase and solid particles, and other processes, such as, for example passivation of the machined surface. These processes may halt machining process, or cause the incidence of ECM critical states, often resulting in electrical short circuit between the electrodes. In ECM with the use of a shaped electrode, products mentioned above are removed by hydrodynamics, through a forced high intensity electrolyte flow with velocities from a few to over a dozen m/sec at pressures of tenths up to several MPa. Positive features of the flow is simultaneously accompanied by negative ones, such as cavitation. The process of electrochemical formation is therefore multidimensional, dynamic, conducted in a multiphase center, with features changing in time and space, and with complex linked physicochemical phenomena. One of the methods of improving the stability and accuracy of this process is the introduction of vibrations to one of the electrodes, what is meant to improve the effectiveness of regeneration of conditions in the IEG. This method was used and studied by Bhattacharyya in micro-ECM conditions (Bhattacharyya et al, 2007), Hewidy, who defined the influence of ECM process input parameters on electrode vibration effectiveness (Hewidy, 2007), and Paczkowski who introduced multidirectional tool electrode vibrations for machining of curvilinear surfaces (Paczkowski, 2012).
Fig. 1. Electrolyte flow area
Multidimensional, dynamic ECM process requires the application of a computer system for design, control and monitoring. Invention of a modern ECM technology should be conditioned by
knowledge of the nature of physical phenomena occurring during machining in the electrolyte flow area (fig. 1) and the limitations of electrochemical process. The necessity of developing methods of ECM process modelling, supervision and control were described by Rajurkar (Rajurkar et al, 1999). Accurate value estimation of these limitations will enable the optimal parameter value to be assigned in a given machining time, which in turn will assure high usage and economic indicators without leading the ECM process to the so-called critical state, in which machining is interrupted and the electrodes damaged, Therefore analysis and control of the process requires ECM mathematical modeling which leads to estimation of thickness of the removed allowance or inter-electrode gap width distribution, both of which change along the gap length in ECM conditions. However, the complexity and dynamic of ECM process requires additional control and monitoring. It makes online corrections of machining parameters obtained earlier through theoretical calculations possible. Attempts at such method of control were made by Brusilovski (2008), where he studied the influence of parameters controlling the process on ECM machining outcome. This research resulted in a method of controlling ECM machining through adjustment of voltage and pressure of the electrolyte feed. The conclusion which stems from aforementioned analysis is that ensuring precision and stability of an ECM process, which are dependant on several factors, can require undertaking adequate steps. The inter-electrode gap width distribution has a significant influence on the process, however, a precise observation of it is impossible during the machining with curvilinear electrode shapes. Therefore a need arises for creation of mechanisms controlling the ECM process. This paper presents elements of such control system. In it we can distinguish two base stages: 1. Mathematical modeling of the ECM process, with regards to electrolyte flow hydrodynamics, which is the basis of computer simulation. Such simulation allows to acquire code steering the machine, with machining parameters that are variables in time. 2. Monitoring ECM process in real time with the use of CCD camera for verification and correction of results acquired from stage 1. The aim of proposed control method is elevating the precision and stability of ECM process.
2. ECM MATHEMATICAL MODELING Due to lack of possibility to physically observe and register the processes which take place in the inter-electrode gap, one of the most successful methods for estimation of inter-electrode gap conditions is process modeling. Physical conditions in machined area are described by distribution in time and space of such values as temperature within the gap T, gas phase concentration , electrical potential , electrical conductivity of the , pressure p, and electrolyte velocity w. It also needs to be mentioned that these physical values are directly linked, which is shown, among others, in works by Kozak (1998) and Pajak (2010). Component processes of electrochemical machining and their reciprocal links create an internal structure constituting of: electrode processes on the surfaces of the electrodes (E), processes of moving electric charge (electrical potentials field ), processes of mass exchange (products concentration field: gas ; hydroxides Cm), heat exchange processes (temperatures field T), electrolyte flow hydrodynamics (pressure field p and electrolyte velocity v), characteristics in the inter-electrode gap (electrolyte electrical conductivity ), processes of machined surface shape changes (machining velocity Vn).
The equation of electrochemical machining of a surface in the direction of feed motion for the examined case was described as follows were defined by Kozak (1998) with a relation: √
[∫
(
(
))(
(
)
)
(
)
(1)
]
(2)
where: kv - electrochemical machinability factor, U - operating voltage between the electrodes, E – potential decrease in electrode-adjacent layers, h - inter-electrode gap width, - electrical conductivity temperature factor, - gas phase volume concentration, o - specific electrolyte conductivity. In a case when the initial machined surface differs significantly from the end one, that is the tool electrode shape, it is advisable to conduct the modeling in two phases. In the initial machining changes in electrolyte conductivity can be ignored, which results in omission of equations describing electrolyte flow and IEG temperature distribution. It stems from the fact that fresh electrolyte is easy to deliver to an unshaped yet gap. A set of equations describing ECM process in such case comes down to equations mentioned earlier (1, 2). During the time of machining, the machined surface shape becomes more similar to the tool electrode, and the interelectrode area becomes a narrow gap with a changing width. Physical conditions vary as well from the ones which existed at the beginning of the machining, and we can talk about having finished first phase of calculations. During the second phase of calculations, due to its precision, it is important to take into account hydrodynamic conditions in the IEG. For calculations of electrolyte flow in the inter-electrode gap a curvilinear orthogonal system of coordinates is introduced, for which coordinates system axes x and z lie on given surface and y axis with its perpendicular (fig.2). Lame coefficients for this system of coordinates are as follows: ,
,
(3)
where: R1, R2 - curvature radii of the curvilinear surface.
Fig. 2. Curvilinear, locally orthogonal coordinate system
Coordinate system describing a two-dimensional flow of electrolyte and hydrogen mixture in the inter-electrode gap was adopted, which results from the principles of mass and momentum conservation. Taking into account assumptions that: the electrolyte flow is fixed, two-dimensional, homogenic, pressure pe = pH = p, gas phase volume concentration =(x), inter-electrode gap width is small compared to gap length (h << L ). The resulting system of equations was obtained: (
)
(
(
)
(
)
(4) )
(
(5) )
( *(
)
)
+
(6) (7)
where: vx, vy - components of the velocity vector, j - current density, - current efficiency of the gas emission, - electrochemical equivalent of the hydrogen, coefficient of thermal diffusivity in the laminar flow conditions, (
)
coefficient of thermal diffusivity in the turbulent flow conditions,
thermal conductivity coefficient, e, H - electrolyte and hydrogen densities, T - electrolyte temperature, cp - specific heat at a constant pressure - electrolyte conductivity.
Presented system of equations was solved in part analytically and numerically with the use of finite difference method. Detailed assumptions and the mathematical model solving method are presented in papers were presented by Paczkowski and Sawicki (2008), where mathematical modeling of ECM processes was described, and Paczkowski and Zdrojewski (2010), where a computer simulation of the process was presented. Solving the aforementioned mathematical model allowed to compile a program simulating the ECM process. This program became the starting point for machining control with the use of a numerically controlled device.
3. ECM PROCESS CONTROL Designing an electrochemical machining process control consists of two basic modules. In the first one calculations simulating ECM process are conducted. During the calculations selected process parameters are analyzed for achieving critical states for which the process would be interrupted during real machining. Under the term ‘critical state’ for an ECM process fall states
described by a set of machining parameters in which suddenly grows the probability of the occurrence of electric discharge and an electrical short (which can be called borderline states for ECM). The studied machining parameters in ECM process control system are presented in table 1. Correct selection and modification of these should especially ensure avoidance of disadvantageous phenomena that lead to critical states. In a case when the initial machining surface differs significantly from tool electrode shape, the system analyzes only the occurrence of a critical IEG width. Tab. 1. Parameters of the first control system module Examined parameter Graphical symbol
System reaction
IG height
Reduce feed rate Vf, Temporary stop of TE, Retract TE
Velocity of IG electrolyte flow
Reduce feed rate Vf, Temporary stop of TE, Retract TE
Negative velocity of the electrolyte
Reducing the frequency w, Reducing the frequency p
Temperature of electrolyte
Reduce feed rate Vf, Temporary stop of TE, Retract TE
Gas phase concentration
Reduce feed rate Vf, Temporary stop of TE, Retract TE
In case of occurrence of such states, system reaction algorithms have been devised to correct selected process parameters. Correction of parameters takes place in specified control points (tk) on time axis which are before the critical state. Through such analysis we obtain ECM process parameters changing in time which allow to avoid critical states. It is especially important during machining complex curvilinear shapes. The end result of such simulation is a control code for the machining device. Fig. 3, portrays a diagram of the first control module.
Fig. 3. Diagram of the first control module and control code
These assumptions allowed to design an algorithm for the first control module (fig. 4), which became a basis for devising controlling programs.
Start
Read CAM files to define TE, WP, WPk
Read parameters of machining process
Ts – time to save shape of WP and MCP values MSI – machining status indicators, Dmin – minmal gap, Tmax – maximal temperature, Vxmax – max speed of elctrolyte flow, Vxmin - min speed of elctrolyte flow, Bmax -max of beta
Set electrode tool designing parameters WSko,TOLte
Ts :=Ts + Dts
Yes
t := 0 Ts := t + Dts
t >= Ts
Calculate values of MSI: Dmin, Tmax, Vxmax, Vxmin, Bmax
MSI in the range
Stop
Save current shape of WP and MCP values
No
k := 1
ECM calculations for k couple curves
Yes
k := k + 1
Modify and apply new values of MCP
Yes
k <= K Yes
Save results
Restore last saved shape of WP t := t - Dts
t <= T
Save ECM gcode
Prepare ECM process gcode
Restore MCP history
No t := t + Dt
Where: MCP – machining control parameters, Dts – time between storing a state of simulation, t – current time, T – total simulation time, Dts – step for the simulation time, K –number of curves on the WP and TE surface,
Fig. 4. First control module algorithm
Fig. 5 presents a program enabling a machining control with the use of changeable process parameters. In the first tab of the program initial process parameters are entered, which are also reference parameters for modification processes. At the same time, in the tab 'Control' links of process parameters with system reactions should be described, as well as the strength of their influence. The final result of the calculations is a controlling code for the machining device (research station).
a)
b)
Fig. 5. Machining control program a) initial machining parameters b) adaptive control module
In the Graphs tab, there is a possibility to view distributions along and across the interelectrode gap for computed physical values, which include: flow velocity, pressure, temperature, viscosity, electrolyte conductivity and gas phase concentration in the electrolyte, as well as interelectrode gap width and current density. Fig. 6a presents examples of distribution along interelectrode gap for its width h and current density j. Cross-section for which the calculations were made is presented in fig 6b. a)
b)
Fig. 6. a) IEG thickness and current density distribution b) Section of conducted calculations with discretization points marked on the curve
The distribution of IEG width has a vital influence on ECM process analysis. It decides indirectly the intensity of dissolution on the anode surface. Indirectly, because calculated physical variables are strongly linked, and the change of one triggers rapidly the changes of the others. For example, lowering the value of IEG width distribution causes an increase in the intensity of the ECM process which results in an increase of electrolyte contamination, increase in hydrodynamic resistance which changes the electrolyte flow velocity and in consequence raises the temperature and electrolyte conductivity, which in turn influences current density distribution, that is the intensity of dissolution process of the anode surface. The dissolution process of the anode surface juxtaposed with cathode surface and its kinematics returns information about IEG width
distribution. Knowledge of this distribution is crucial for estimating the precision of machining process, and linked with monitoring the removed surplus gives a possibility for controlling and steering the ECM process. Second control stage is realized during machining process and is connected with width examination of the removed allowance. The measurement is conducted for tk machining time specified in the simulation process. Correction of tool electrode position is obtained through comparative analysis, in a way which equates the inter-electrode width value with values obtained from the simulation. Fig. 7 presents an algorithm for the second module of the control system.
Fig. 7. Second control module algorithm
Fundamental functions of this module are as follows: controlling the device, periodic examination of removed allowance width, and monitoring the process. These functions are conducted by a second program, ExECM, which is show on fig.8.
Fig. 8. ExECM program controlling the process
In it we can distinguish panels responsible for referencing the electrodes, set values of the initial process parameters and control code loading, measurements and analysis of obtained data from temperature and electrolyte pressure sensors, and the panel responsible for analyzing the image from the CCD camera. Details of the image analysis panel are shown in fig. 9.
Fig. 9. Image analysis panel
Edges creating shape of the tool electrode and the machined item, which create the inter-electrode gap, are searched for in the analyzed image. Result geometric elements of the electrodes are shown in green color on the left-hand side of fig. 9. A juxtaposition of these elements with a calculation of distance value between them is shown on the right-hand side of fig. 9. As an effect we obtain a real distribution of inter-electrode fragments' width, which are compared with distributions obtained
from computer simulation. As it was aforementioned, through these calculations a correction of tool electrode position is executed by an adequate entry in the control code. Modules described above produce an ECM process control system (fig. 10).
Fig. 10. Process parameters control system
4. ECM PROCESS MONITORING Besides control and examination in selected tk points in time of the ECM process, on-line monitoring procedures were designed. Process parameters which are controlled in a continuous way include: servo drives operating parameters, electrolyte pressure at the inlet and outlet of the machining area, electrolyte temperature at the inlet and outlet of the machining area, parameters connected with tool electrode movement dynamics (velocity, location, vibrations). CCD camera image analysis was used for the control of parameters connected with tool electrode dynamics. Due to high tool electrode movement velocity resulting from vibrations, control and measurement procedures were devised based on image analysis and video input of the control system. This solutions makes evaluation of movement type correctness and compatibility of primary parameters with the ones obtained from control process possible. Monitored parameters are directly linked with initial conditions set in the first control module. Maintaining them in a specific tolerance range guarantees an accurate reflection of the conditions assumed in the machining simulation process. Process parameters control system was built based on a Mitsubishi FX 3U driver and a PC-class computer. Interrelationships in the system are shown in fig. 11.
Fig. 11. Elements of the control system
The system includes (fig. 4) : PC-class computer with an implemented ExECM program - 1, Mitsubishi FX 3U driver with an FX 3U-232-BD I/O module - 2, DC motors (servo) - 3, limit switches - 4, optical sensors - 5, electrolyte pressure sensors- 6, electrolyte temperature sensors - 7, CCD video camera - 8.
5. RESEARCH STATION In ECM process research, which is inherently a complex and multidimensional process, research, both theoretical, conducted with the use of developed mathematical and numerical models, and experimental, conducted on model stands is of great significance. Both allow for a verification of designed mathematical models and designed methods of control and machining. The ECM control and monitoring system presented in the article was tested on a research stand pictured in fig. 12. We can distinguish a body consisting of boards places on slides, and drive systems which realize designated process kinematics. A machining cell was attached in the middle of the body. It was assumed that machining process will be realized in so-called machining cells, which form a separate structural unit (fig. 13). Such approach makes machining area modeling much simpler.
Fig. 12. Body of the research station with a mounted machining cell
Fig. 13 presents a CCD camera, which monitors machining area through a machining cell wall made from a transparent material.
Fig. 13. Machining cell with a CCD camera
6. VERIFYING TESTS The aim of experimental research was to verify the developed control and monitoring system of ECM processes. The experiments were conducted on a constructed electrochemical machining machine (fig. 12). Tests were run on samples of alloy tool steel for hot work, with symbol 2312, heat treated to the hardness of 32 HRC. The measurement of shape after the ECM treatment was done by active scanning on a Mitutoyo Crysta-Apex CNC coordinate measuring machine with a Renishaw probe. Verifying tests of ECM process were conducted for two types of machining control: machining with a vibrating tool electrode with machining parameters changing in time and an active system of control and monitoring,
machining with a vibrating tool electrode with machining parameters constant in time. Geometrical form of electrodes used in tests is shown in fig. 14.
Fig. 14. Dimensional layout and geometrical form for tool electrode and machined item a) isometric view, b) projections
Table 2 presents values for initial parameters assumed in ECM process simulation. These parameters are at the same time initial setpoins on the workstation. Parameter values marked (*) are possible to monito and modify according to procedures resulting from monitoring and controlling an ECM process. Parameter values marked (**) are possible to monitor and they influence modifications of controllable parameters.
Tab. 2. Initial parameters assumed in ECM process Factor
Value
Inter-electrode voltage
15 V
Electrolyte type
NaNO3 15%
Machining time Inter-electrode gap width*
180 s 0.2 mm
Feed movement velocity*
Vf = 1 mm/min
Longitudinal vibrations*
f = 30 Hz, A = 0,1 mm
Transverse vibrations*
f = 30 Hz, A = 0,05 mm
Electrolyte temperature**
293 K
Electrolyte feed**
Q = 2 l/min, pz = 0.01 MPa
In tests an assumed reference area was being compared with the area obtained from the machining process.
Tables 3 and 4 present: shape deviation distribution (blue line) along the section length L shown in the image (red line), accuracy indicators adopted for evaluation S - standard deviation of shape deviation, max - maximum deviation.
Tab. 3. Distributions of shape deviation for a system with an active adaptive control 0.014 mm
max
0.021 mm
0.05 0.025
[ mm ]
S
0 -0.025 -0.05
0
0.019 mm
max
0.026 mm
10
15
20
25 30 L [ mm ]
35
40
45
0.05 0.025
[ mm ]
S
5
0 -0.025 -0.05
0
5
10
15
20
25 30 L [ mm ]
35
40
45
Tab. 4. Shape deviation distribution for a system without an active adaptive control 0.023 mm
max
0.029 mm
0.05 0.025
[ mm ]
S
0 -0.025 -0.05
0
0.029 mm
max
0.041 mm
10
15
20
25 30 L [ mm ]
35
40
45
0.05 0.025
[ mm ]
S
5
0 -0.025 -0.05
0
5
10
15
20 25 L [ mm ]
30
35
40
45
7. SUMMARY This paper presents a method for machining process control orientated on tool design stage verification and optimization of machining equipment behavior. The presented control method allows an increase in stability and precision of machining, most particularly for machining areas with complex shapes. During tests with machining parameters constant in time, in over 20% cases the so-called borderline states have occurred. The most often occurring ones were as follows: cavitation (fig. 15a), a single short circuit (fig. 15b), process instability (fig. 15c). The occurring borderline states are presented against a so-called current line. Current lines in fluid mechanics are lines tangent in every point to the velocity vector of a fluid particle. In a stationary flow they
visualize the assumptive character of the flow and in large depend on the shape of the surface, in this case of the electrodes, and also from the kind of IEG feed. We can therefore observe that sizeable instabilities of ECM process appear in places where the flow is less intensive. a)
b)
c)
Fig. 15. Item area image after the incidence of critical machining states: a) cavitation, b) single short circuit, c) process instability
However, the reasons for the occurrence of critical - and then in turn borderline - states are usually connected with badly chosen machining parameters. It is most often related to changes in physical characteristics, especially with a decrease in electrical conductivity - resulting from products of ECM and emitted gases, mainly hydrogen, gathering in the IEG, - which inevitably leads to short circuits and process instability. Another important factor is the changing electrolyte flow in the inter-electrode gap in the range of: 2300 < Re < 50000 [8, 9]. A changing flow character causes sudden changes in electrolyte flow velocity, which is caused by varying distribution of IEG width. In consequence, this causes an unfavorable increase in temperature and leads to singular electric discharges. Fig. 16 presents a photo of a machined surface with an active control system.
Fig. 16. A correctly machined sample surface
Using process control presented in this paper caused a significant increase in its stability. Critical states occurred only in 3% of machined surfaces. The reason for this is the simplification of modeling and simulation of the process. In the proposed control method a subjective parameter choice by a human operator was reduced to a minimum. It mainly amounts to choosing initial parameters of a simulation and coefficients of mutual interaction of parameters evaluated for critical states. It needs to be stressed that badly chosen initial parameters will be quickly corrected in the simulation process from the first module of the control system. An adverse effect of introduction of such control is a decrease in efficiency of the process. Aforementioned problems are the subject of further research of the authors. They are concerned with the optimization of measurement points amount, inclusion of more parameters of the process in the analysis, and increase in online data collection during the process.
REFERENCES
Bhattacharyya, B., Malapati, M., Munda, J., Sarkar, A., 2007. Influence of tool vibration on machining performance in electrochemical micro-machining of copper. International J. of Machine Tools & Manufacture. 47, 335-342. Brusilovski, Z., 2008. Adjustment and readjustment of electrochemical machinesand control of the process parameters in machining shaped surfaces. Journal of Materials Processing Technology, 196, 311-320. Chu, F., Shimasaki, T., Kunieda, M., 2016. Characteristics of different transparent and conductive materials applied for observation of ECM gap phenomena. Procedia Cirp, 42, 362-366. Hewidy, M. S., Ebeid, S. J., El-Taweel, T. A., Youssef, A. H., 2007. Modelling the performance of ECM assisted by low frequency vibrations. Journal of Materials Processing Technology, 189, 466-472. Kozak, J., 1998. Mathematical Models for Computer Simulation of Electrochemical Machining Processes. Journal of Materials Processing Technology.76,1-3, 170-175. Paczkowski, T., 2012. Computer simulation of curvilinear surfaces electrochemical machining with a complex translation movement work electrode. Publishing University of Technology and Life Sciences in Bydgoszcz, 158. Paczkowski, T., Sawicki, J., 2008. Electrochemical machining of curvilinear surfaces. Journal of Machining Science and Technology, 12, 33-52. Paczkowski, T., Zdrojewski, J., 2010. Electrode tool designing in the ECM machining for curvilinear surfaces. Journal of Machine Engineering, 10, 58-69. Pajak, P. T., van Tijum, R., Altena, H., Visser, C. R., 2010. Virtual Design of the Shaving Cap ECM Process by Multiphysics Simulation Approach. Proceedings of the 16th International Symposium on Electromachining, 693-697. Rajurkar, K. P., McGeough, J. A., Kozak, J., De Silva, A., 1999. New Developments in Electro-Chemical Machining. Annals of the CIRP, 48, 567-579. Wołgin, V. M., Lyubimov, V. V., 2001. Numerical simulation of the electrolyte flow at three-dimensional electrochemical machining. International Conference APE’2001, 299-308. Zhu, D., Gu, Z., Xue, T., Zhu, D., 2016. Flow Field Design in Electrochemical Machining of Diffuser. Procedia Cirp, 42, 121-124.