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Effects of pulsating electrolyte flow in electrochemical machining
Journal of Materials Processing Technology 214 (2014) 36–43
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Effects of pulsating electrolyte flow in electrochemical machining Xiaolong Fang, Ningsong Qu ∗ , Yudong Zhang, Zhengyang Xu, Di Zhu College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China
a r t i c l e
i n f o
Article history: Received 20 April 2013 Received in revised form 15 July 2013 Accepted 17 July 2013 Available online 27 July 2013 Keywords: Electrochemical machining Pulsating flow Heat transfer Material removal rate Surface profile
a b s t r a c t Electrochemical machining (ECM) is a promising and low-cost process for yielding various components of difficult-to-machine materials, and has been well established in diverse applications. Distributions of gas and temperature affect the electrolyte electrical conductivity and determine the machining accuracy in ECM. Attempts have been made to generate the pulsating flow via a servo-valve in the electrolytic supply pipe, which is introduced to improve the heat transfer, material removal rate and surface profile in ECM. A multi-physics model coupling of electric, heat, transport of diluted species and fluid flow is presented. Simulation results indicate that pulsating flow has a significant impact on the distributions of velocity, gas fraction, and temperature near the workpiece surface along the flow direction. Experiments are conducted to verify the feasibility of the proposed process and study the effects of pulsating flow on material removal rate. The experimental results agree well with the simulations. Using optimal pulsating parameters, the material removal rate and surface profile are enhanced. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Electrochemical machining (ECM) removes metal material by controlled anodic dissolution in an electrolytic cell. Compared to other typical machining technologies, ECM has superiority by having a high material removal rate, a good surface integrity, is stress free, and has no tool wear or metallurgical defects. ECM is a promising and low-cost process for yielding various components of difficult-to-machine materials, and has been well established in diverse applications, such as turbine blades, airfoils, and surgical implants (Rajurkar et al., 1999). In ECM, the electrolyte with a velocity of 10–30 m/s is pumped into the inter-electrode gap to remove waste products (gases and metallic hydroxides) and Joule heat. The distributions of gases and Joule heat affect the electrolyte electrical conductivity and determine the machining accuracy. Therefore, many studies have focused on the disposal of metal hydroxide sludge and an efficient process simulation. Various approaches have been developed to modify the electrolyte flow regime and enhance the electrolyte refreshment in the inter-electrode gap. Rajurkar and Zhu (1999) found that orbital electrode movement reduces the flow disrupting phenomena and improves the machining accuracy and machining stability. Hewidy et al.
∗ Corresponding author at: College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, P.O. Box 265, 29 Yudao Street, Nanjing 210016, China. Tel.: +86 25 84893870; fax: +86 25 84895912. E-mail address: [email protected] (N. Qu). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.07.012
(2001) proposed that orbital electrode movement eliminates the presence of the spikes and enhanced the ECM accuracy. Ruszaj et al. (2003) demonstrated that electrode ultrasonic vibration causes heterogeneous cavitation of electrolyte flow in the gap, and significantly improves the removal of heat and products out of the machining gap. Hewidy et al. (2007) shown that low frequency tool vibration provides a positive effect by changing the physical conditions in the inter-electrode gap, and enhances electrolytic renewal and the removal of sludge products. Wang et al. (2010) proposed that reverse electrolyte flow pattern with vacuum-extraction could prevent the occurrence of cavitations and diminishes sparking and formation of striations. Furthermore, abundant computational methods have been used to analyse the characteristics of electrolyte flow, the distributions of gas and temperature, and acknowledge the anodic shaping rules. Analytical solutions (Hopenfeld and Cole, 1969) were obtained to describe the one-dimensional equilibrium-cutting gap along the flow direction. Fujisawa et al. (2008) established a multi-physics model, including multiphase flow, thermal fields and electric fields, to predict the final shape of a three-dimensional compressor blade. Van Tijum and Pajak (2008) used a multi-physics approach to support the design of the ECM process for machining the electric shaver. Lee et al. (2009) applied a multi-physics model, consisting of electric, convection and diffusion, to predict the parametric effects on machining accuracy. Deconinck et al. (2011) proposed the multi-ion transport and reaction model to describe the effects of water depletion, and temperature on the anodic process in ECM. Havemann and Rao (1954) shown that periodic fluctuations of fluid flow create different hydrodynamic characteristics and alter
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2. Theoretical models Nomenclature Notations A pulsating amplitude of electrolyte pressure (MPa) bp Bruggeman’s coefficient Ci concentration of diluted species (mol m−3 ) electrolyte specific heat capacity (J K−1 kg−1 ) Cp Di diffusion coefficient of diluted species (m2 s−1 ) E electric field (V m−1 ) pulsating frequency of electrolyte pressure (Hz) f F Faraday constant (C mol) i current density (A cm−2 ) k electrolyte thermal conductivity mass removed in machining (g) m M molar mass of anodic material (g mol−1 ) N gas flux (mol m−2 s−1 ) p electrolyte pressure (MPa) pa absolute pressure of electrolyte (MPa) average electrolyte pressure (MPa) pav Pbulk Joule heating in the bulk of electrolyte ideal gas constant (J mol−1 K−1 ) R ReMRR relative material removal rate machining time (s) t T electrolyte temperature (K) electrolyte velocity magnitude (m s−1 ) u U applied voltage for ECM (V) ˛ degree of temperature dependence ˇgas gas void fraction in electrolyte electric current efficiency electrolyte electrical conductivity (S m−1 ) electrolyte density (g mm−3 ) n material removal rate (m s−1 ) electrical potential (V) ϕ ω volumetric electrochemical equivalent (mm3 A−1 s−1 ) Subscripts 0 property at the flow inlet i property of diluted species i n property in normal direction constant property at a constant electrolyte pressure
the thickness of the boundary layer; therefore, the pulsating flow of optimised pulsating parameters is beneficial to the transfer process. Pulsating flow has been applied to heat exchange, ramjet combustion, solid fermentation, drip irrigation emitter (Benavides, 2009). Recently, the low-frequency tool vibration has been introduced to ECM, and high precision was obtained. When the electrode vibrates, the gap dimension oscillates in the same amplitude, and an electrolytic fluctuation is observed. However, this pulsating flow generated in an oscillating gap is different from those in a constant gap, which have been well applied in heat and mass transfer. Research shows limited studies on this pulsating flow in electrochemical machining. In this study, attempts have been made to generate the pulsating flow via a servo-valve in the electrolytic supply pipe. This work focuses on the improvement of the heat transfer and material removal rate in ECM. A multi-physics model coupling of electric, heat, transport of diluted species, and fluid flow is presented to study the variations of electrolytic velocity, electrolytic temperature, and ion concentration along the flow direction near the workpiece surface. Moreover, experiments have been conducted to verify the feasibility of the proposed process.
ECM is a field-synergy electrolysis process, which consists of mass transfer, energy transfer, momentum transfer and chemical reactions (McGeough, 1974). When a voltage is applied across the cathode tool and the anodic workpiece, the metallic ions of the anodic dissolution migrate from the anode surface to the electrolyte by an electrical force and are formed to insoluble hydroxides in neutral solutions. At the same time, hydrogen and oxygen is generated on the cathode and anode surface, respectively. Heat generated by the passage of current and electrochemical reactions will heat the electrolyte in the inter-electrode gap. All these occurrences interactively influence the electrolyte electrical conductivity, which would affect the current density distribution and the local material removal rate. The relation between the electrical conductivity , the electrolyte temperature T, and the gas void fraction ˇgas is given as follows (Van Tijum and Pajak, 2008): bp
= 0 (1 − ˇgas ) (1 + ˛(T − T0 ))
(1)
where bp is the Bruggeman’s coefficient. Fig. 1 illustrates the schematic diagram of a typical ECM process with pulsating electrolyte flow. With a pulsating electrolyte, periodic fluctuations of flow create different characteristics of flow and heat transfer along the flow direction. The electrochemical cell consists of a cathode tool (Boundaries 9–11) and an anode workpiece (Boundaries 3–5), with electrolyte pumped through the electrode gap from the left inlet (Boundary 1) to the right outlet (Boundary 7). To simplify the proposed model, several assumptions are made as follows: (1) The electrolyte flow is impressible single-phase flow. The scale of bubbles in the electrolyte is small enough to neglect its impact on fluid flow (Brebbia and Mammoli, 2011). (2) The diffusion coefficient of bubbles is temperature independent and at a constant value of 3.0 × 10−6 m2 /s (Fujisawa et al., 2008). (3) The electrolyte dynamic viscosity is assumed to be a constant value of 1.003 × 10−3 Pa s (Van Tijum and Pajak, 2008). (4) The heat generated in the electrolyte is only Joule heat. 2.1. Impressible fluid model The entire flow channel has dimensions of 1 mm in height, 112 mm in length and 12 mm in width; the distance from the inlet to the workpiece is 60 mm; the workpiece and cathode have a cross section of 12 mm × 12 mm with an initial machining gap of 0.15 mm. The governing equations, which usually describe the turbulent flow in ECM (Fujisawa et al., 2008), are given as follows: −∇ 2 u + (u · ∇ )u + ∇ p = 0
∇ ·u=0
(2)
The electrolyte pressure at the inlet is given as follows: p0 (t) = A sin(2 ft) + pav
Fig. 1. Schematic diagram of ECM with pulsating electrolyte flow.
(3)
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X. Fang et al. / Journal of Materials Processing Technology 214 (2014) 36–43
The diffusion of ion and gases forced by fluid convection will be discussed independently in the following sections.
The temperature distribution in this cell is calculated by solving a convection–diffusion equation with heat sources (Kozak, 2004) as follows:
2.2. Electrical model The electrical potential in the inter-electrode gap, ϕ, can be approximately described by Laplace’s equations as follows:
∇2ϕ = 0
(4)
The boundary conditions are given as follows:
ϕ 3,4,5 = U
(5)
ϕ 10 = 0
(6)
∂ϕ
1,2,6,7,8,9,11,12 = 0 ∂n
(7)
According to Faraday’s law, the material removal rate, n , is described as follows: n = ωin = ωEn = ω
∂ϕ ∂n
(8)
Experiments were conducted to obtain the variation of current efficiency (Bejar and Gutierrez, 1993), , with an increase in current density. Samples and processing conditions for these experiments are identical to those conditions used in practice. The results are plotted in Fig. 2 and are analysed by curve fitting to obtain Eq. (9) as follows: (i) =
0.85 (1 + e(10−i)/6 )
− 0.1
(9)
Gases produced in the ECM process would adversely influence the electrolyte electrical conductivity. The fluxes of the gases generated at each electrode can be described by Faraday’s law (Van Tijum and Pajak, 2008) as follows: NH2
i = 2F
NO2 =
2.3. Thermal model
(10)
i(1 − ) 4F
(11)
Cp
∂T + Cp u · ∇ T = ∇ (k∇ T ) + Pbulk ∂t
(12)
where Cp is the electrolyte specific heat capacity, and k is the electrolyte thermal conductivity. Pbulk denotes the Joule heating in the bulk of electrolyte and can be obtained by Joule’s law as follows: Pbulk = Ui
(13)
In this electrochemical system, the thermal conductivity of electrode material, 81 W/m, is 102 times larger than that of the electrolyte, which is only 0.6 W/m. Consequently, the interfaces between the electrodes and electrolyte can be considered as outer boundaries. That is, the temperature on the electrode surface is set to be the same as the temperature reference. The boundary conditions are given as follows:
T 1,3,4,5,9,10,11 = T0
(14)
∂T
2,6,8,12 = 0 ∂n
(15)
2.4. Reactant transport model Reactants produced in the process are metal ions dissolved from the anode, hydrogen near the cathode surface and oxygen near the anode surface. Transport of species in the gap is driven by migration, convection and diffusion. Diffusion is the main transport mechanism via the anode–electrolyte layer. In areas of electrolyte adjacent to the anode surface, convection is the main role of transport. The governing equation based on diffusion by Fick’s law and convection forced by fluid flow can be shown as follows: ∂Ci + ∇ (Ci u − Di ∇ Ci + Di Ni ) = 0 ∂t
(16)
where Di denotes the diffusion coefficient of diluted species i and Ni denotes the flux of diluted species i. In this system, all of the initial species concentrations are zero. The boundary conditions for the transport equations are as follows: Inlets: At the inlet of H2 :
NH2 =
i 2F
(10)
At the inlet of O2 :
NO2 =
i(1 − ) 4F
(11)
Outlet: ∂Ci
7 = 0 ∂n
(17)
All other boundaries are considered as a no-flux wall. As shown in Eq. (1), gas generated in the process will adversely influence the electrolyte electrical conductivity. From the transport model of H2 and O2 , the gas void fraction can be calculated using Eq. (18) and is given as follows: ˇgas =
Fig. 2. Current efficiency curve from experimental results.
(CO2 + CH2 )RT (CO2 + CH2 ) + u · pa
(18)
where R is the ideal gas constant, T is the local present temperature, pa is the local absolute pressure, and u is the local electrolyte velocity.
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Table 1 Parameters in calculation. Electrolyte concentration Electrolyte temperature Pulsating frequency (Hz) Pulsating amplitude (MPa)
120 g/L, NaNO3 293 K 1, 2, 5, 10, 20, 40 0.1, 0.2, 0.3, 0.4
2.5. Moving mesh To study the time dependent response of periodic pulsating flow on the material removal process, the geometry should be suitably realigned with the new position of the electrodes. The arbitrary Lagrangian–Eulerian formulation is chosen to track the cathode feed movement and anodic shaping process. All models are coupled and analysed using COMSOL software version 4.3. The parameters used in the calculations are listed in Table 1.
Fig. 4. Variations of gas fraction with pulsating pressure in a period.
3. Simulation results The evolution procedures of process variables, such as gas void fraction and temperature, were simulated in the ECM process with pulsating electrolyte flow. Furthermore, the effects of pulsating parameters on the transfer of heat, material anodic dissolution rate and surface profile were studied. Simulations were performed in transient mode with initial expressions of zero. 3.1. Variations of velocity and gas fraction The electrolyte was pumped into the machining gap at a pulsating pressure of 0.2 MPa in amplitude and 10 Hz in frequency. A probe, marked by the dashed line in Fig. 1, was set to obtain the response of the electrolyte velocity and gas fraction to the pulsating pressure. Figs. 3 and 4 present the averaged values of the electrolyte flow velocity and gas void fraction, respectively. These values change with the oscillation of the pulsating pressure. When the pulsating phase is at 90◦ , the pressure and flow velocity are at a maximum while the gas void fraction is minimal. When the flow velocity reaches the lowest point, the void fraction is at a maximum. 3.2. Influence on heat transfer Fig. 5 presents the changes of the averaged temperature at the probe. When the pulsating pressure is at a maximum, the temperature is minimal. When the pulsating pressure is minimal, the temperature is at a maximum.
Fig. 3. Variations of velocity with pulsating pressure in a period.
Fig. 5. Variations of temperature with electrolyte pressure in a period.
Fig. 6 shows the periodic variations of the averaged temperature gradient on the anode surface, which reveals the speed of heat transfer from electrolyte to electrode. The pulsation of electrolyte pressure leads to an obvious jump of temperature gradient, which varies 180◦ out of phase to the electrolyte pressure. When the pulsating amplitude increases to 0.4 MPa, the fluctuation of temperature gradient increase approximately 100%. When a pulsating
Fig. 6. Variations of the averaged temperature gradient in time-scale; f = 5 Hz.
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Fig. 8. Variations of the anodic removal rate in a time-scale.
Fig. 9, large pulsating amplitude is adverse to anodic dissolution, and the optimal pulsating frequency for material removal is 10 Hz. When the pulsating amplitude is 0.4 MPa, the electrolyte pressure at the inlet would be zero. Hence, zero pressure difference existed between the electrolyte inlet and outlet, and the forced convention driven by the electrolyte flow ceased. Additionally, anodic dissolution occurred in an instant static flow, which is adverse to the renewal of heat and products. Fig. 10 shows the predicted surface profiles after machining for 30 s. As shown in Fig. 10(a), when the pulsating pressure is less than 0.3 MPa, the pulsating flow is beneficial to the anodic dissolution process. When A increases to 0.4 MPa, the dissolution slows down. The results shown in Fig. 10(b) indicate that when the pulsating amplitude is 0.2 MPa, all frequencies are advantageous to the process. Additionally, the optimal frequency in this case is 10 Hz. Fig. 7. Effects of pulsating flow on the time-averaged temperature gradient. (a) Variation curves of the time-averaged temperature gradient with pulsating amplitude A; f = 5 Hz. (b) Variation curves of the time-averaged temperature gradient with pulsating frequency f; A = 0.2 MPa.
electrolyte is applied, flow separation occurs and creates regions of reverse flow, where regions of high mixing and turbulence are generated. The boundaries of this reverse flow are characterised by the creation and destruction of eddies of large turbulence energy and vortex shedding, which are expected to increase the heat transfer rates. Fig. 7 presents the variations of the time-averaged temperature gradients with different pulsating parameters. As the pulsating amplitude increases from 0.1 MPa to 0.4 MPa, the time-averaged gradient increases approximately 7%. As the pulsating amplitude frequency increases, the temperature gradient initially increases and then decreases to a constant. The optimal pulsating frequency for this electrolyte flow model is 10 Hz. 3.3. Influence on material removal rate and surface profile The changes of flow field, temperature and gas distribution finally determine the material anodic removal rate and surface profile. The foreground of this effect is the intersection point between the anode surface and flow outlet. Fig. 8 shows the variations of material removal rate at this point, which changes in synchronisation with the pressure fluctuation. As the pulsating amplitude increases, the fluctuation range of the anodic removal rate increases. Fig. 9 presents the variations of the time-averaged material removal rate with different pulsating parameters. As shown in
4. Experimental results and discussion 4.1. Experimental procedures An ECM system, as shown in Fig. 11, was constructed to study the effects of pulsating electrolyte flow on material removal and surface profile in the ECM process. The pulsating flow is modulated by a Get-type electro-hydraulic servo valve (RT6615E, Radk-Tech, China), which can quickly respond to a broadband signal ranging from 0 to 100 Hz. A specific full feedback control system was established to control the pressure and obtain the machining voltage and current. Samples of SS304, with dimensions of 12 mm × 12 mm × 10 mm, are ultrasonically cleaned and weighted by analytical balance (AE240, METTLER, China) before and after the experiments. Furthermore, the relative material removal rate is defined as follows: m ReMRR = (19) mcosntant where m denotes the mass removed in the ECM process with pulsating flow, and mconstant denotes the mass removed when the electrolyte pressure is at a constant value. Surface profiles along the flow direction were measured by a coordinate measure machine (TESA Micro-Hite 3D, HEXAGON, Switzerland). Table 2 shows the machining conditions. 4.2. Effects of pulsating parameters on material removal rate Fig. 12(a) shows the change of the relative material removal rate with pulsating amplitude A. As the pulsating amplitude increases,
X. Fang et al. / Journal of Materials Processing Technology 214 (2014) 36–43
Fig. 9. Effects of pulsating flow on the averaged material removal rate on the anode surface. (a) Variation curves of the averaged material removal rate with pulsating amplitude A; f = 5 Hz. (b) Variation curves of the averaged material removal rate with pulsating frequency f; A = 0.2 MPa.
41
Fig. 10. Effects of pulsating flow on predicted surface profiles after 30 s of ECM. (a) Variation curves of predicted surface profiles with pulsating amplitude A; f = 5 Hz. (b) Variation curves of predicted surface profiles with pulsating frequency f; A = 0.2 MPa.
Fig. 11. Experimental set-up schematic diagram.
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Table 2 Experimental conditions. Electrolyte concentration Electrolyte temperature Pulsating frequency (Hz) Pulsating amplitude (MPa) Averaged pressure (MPa) Machining time (s)
120 g/L, NaNO3 293 K 1, 2, 5, 10, 20, 40 0.1, 0.2, 0.3, 0.4 0.4 30
the relative material removal rate obtained from the experiments first increases and then decreases. When A is 0.2 MPa, the maximum relative removal rate of 1.02 is achieved. When A is 0.4 MPa, the relative removal rate is less than one. In this case, a moment of zero pressure difference exists between the electrolyte inlet and outlet, and anodic dissolution occurs in an instant static flow. A decrease in the material removal rate adversely affected the timeaveraged value. The experimental optimised value is 0.2 MPa and the optimised simulation value is 0.1 MPa. But their difference in material removal rate is less than 1%. Both the results show that when A is larger than 0.2 MPa, the material removal rate decreases. So we chose the pulsating amplitude as 0.2 MPa in the following experiments. Fig. 12(b) shows the variation of relative material removal rate with pulsating frequency. As the pulsating frequency increases, the relative material removal rate obtained from the experiments first
Fig. 13. Effects of pulsating flow on surface profiles in the flow direction after 30 s of ECM. (a) Variation curves of surface profiles with pulsating amplitude A; f = 5 Hz. (b) Variation curves of surface profiles with pulsating frequency f; A = 0.2 MPa.
increases and then decreases. When f is 10 Hz, the maximum relative removal rate of 1.03 is achieved. Higher frequency would not induce the response of electrolyte pressure because of the inertia of the electrolyte. The experimental results agree well with the simulation results in trend, but all the simulation results are smaller than the experimental. This difference most likely occurs because of the estimation of heat generated in electrochemical reactions, which should warm up the electrolyte and increase the electrolyte electrical conductivity. 4.3. Effects of pulsating parameters on surface profile
Fig. 12. Effects of pulsating flow on ReMRR. (a) Variation curves of relative material removal rate with pulsating amplitude A; f = 5 Hz. (b) Variation curves of relative material removal rate with pulsating frequency f; A = 0.2 MPa.
Fig. 13 presents the surface profiles along the flow direction. As shown in Fig. 13(a), the pulsating amplitude plays an advantageous role when the amplitude is less than 0.3 MPa. The result becomes unfavourable when the amplitude is 0.4 MPa. The pulsating frequency has less of an effect on the surface profile than the amplitude. Additionally, as shown in Fig. 13(a), the predicted profile agrees well with the experiment result, but differs at some points. This variation is mostly because of the errors from computation and measurement of start points. Furthermore, the sampling points were analysed with Range and Deviation analysis. As shown in Fig. 14, the range and standard deviation of height difference both change in a concave trend. At the optimal conditions of 10 Hz and 0.2 MPa, the range of the surface
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5. Conclusions Pulsating electrolyte flow was introduced to enhance heat and mass transfer for ECM by a modified electrolyte flow approach. The conclusions can be summarised as follows: 1. A multiple physics model was established to study the distribution of several physical variables along the flow direction, which were critical to ECM. The simulation results indicate that proper pulsating parameters would enhance the heat transfer and material removal rate. The predicted profiles agreed well in trend with the experimental results. 2. Experiments verified that with an optimal pulsating parameter of 10 Hz in frequency and 0.2 MPa in amplitude, the range and standard deviation of the surface height difference would decrease to 19.8 m and 5.2 m, respectively. Acknowledgements The authors wish to acknowledge the financial support provided by the China Natural Science Foundation (51175258) and the Funding of Jiangsu Innovation Programme for Graduate Education (CXZZ11 0195). References
Fig. 14. Effects of pulsating flow on range and standard deviation of surface height difference. (a) Variation curves of range and standard deviation of surface height difference with pulsating amplitude A; f = 5 Hz. (b) Variation curves of range and standard deviation of surface height difference with pulsating frequency f; A = 0.2 MPa.
profile is 19.8 m, which is quite lower than the value at constant pressure, 67.3 m. Furthermore, the standard deviation of the height difference is 5.2 m, which is still lower than the 28.2 m value at constant pressure. According to Eq. (1), the local electrolyte electrical conductivity is closely related to the gas void fraction and local electrolyte temperature. The bubbles and Joule heat generated in the interelectrode gap cause varying local electrolyte electrical conductivity. When a pulsating electrolyte is applied, flow separation occurs and creates regions of reverse flow, where regions of high mixing and turbulence are generated. Therefore, the difference in electrolyte electrical conductivity and electrical potential in the inter-electrode is smaller, which may lead to a more homogeneous machined surface profile. It has been shown that a better surface profile may be acquired with the correct pulsating electrolyte.
Bejar, M.A., Gutierrez, F., 1993. On the determination of current efficiency in electrochemical machining with a variable gap. J. Mater. Process. Technol. 37, 691–699. Benavides, E.M., 2009. Heat transfer enhancement by using pulsating flows. J. Appl. Phys. 105, 094907. Brebbia, C.A., Mammoli, A.A., 2011. Computational Methods in Multiphase Flow, 6th ed. WIT Press, Southampton. Deconinck, D., Van Damme, S., Albu, C., Hotoiu, L., Deconinck, J., 2011. Study of the effects of heat removal on the copying accuracy of the electrochemical machining process. Electrochim. Acta 56, 5642–5649. Fujisawa, T., Inaba, K., Yamamoto, M., 2008. Multiphysics simulation of electrochemical machining process for three-dimensional compressor blade. J. Fluids Eng. 130 (8), 081602. Havemann, H.A., Rao, N.N., 1954. Heat transfer in pulsating flow. Nature 174, 41. Hewidy, M.S., Ebeid, S.J., El Taweel, T.A., Youssef, A.H., 2007. Modelling the performance of ECM assisted by low frequency vibrations. J. Mater. Process. Technol. 189, 466–472. Hewidy, M.S., Ebeid, S.J., Rajurkar, K.P., El Safti, M.F., 2001. Electrochemical machining under orbital motion conditions. J. Mater. Process. Technol. 109, 339–346. Hopenfeld, J., Cole, R.R., 1969. Prediction of the one-dimensional equilibrium cutting gap in electrochemical machining. J. Manuf. Sci. Eng. 91, 755–763. Kozak, J., 2004. Thermal models of pulse electrochemical machining. Bull. Pol. Acad. Sci. Tech. 52, 313–320. Lee, Y.M., Lee, S.J., Lee, C.Y., Chang, D.Y., 2009. The multiphysics analysis of the metallic bipolar plate by the electrochemical micro-machining fabrication process. J. Power Sources 193, 227–232. McGeough, J.A., 1974. Principle of Electrochemical Machining. Chapman & Hall, London. Rajurkar, K.P., Zhu, D., 1999. Improvement of electrochemical machining accuracy by using orbital electrode movement. Ann. CIRP 48, 139–142. Rajurkar, K.P., Zhu, D., McGeough, J.A., Kozak, J., DeSilva, A., 1999. New developments in electrochemical machining. Ann. CIRP 48, 567–579. Ruszaj, A., Zybura, M., Zurek, R., Skrabalak, G., 2003. Some aspects of the electrochemical machining process supported by electrode ultrasonic vibrations optimization. Proc. IMechE B: J. Eng. Manuf. 217, 1365–1371. Van Tijum, R., Pajak, P.T., 2008. Simulation of production processes using the multiphysics approach: the electrochemical machining process. In: Proceedings of the European COMSOL Conference, Hannover, Germany. Wang, W., Zhu, D., Qu, N.S., Huang, S.F., Fang, X.L., 2010. Electrochemical drilling with vacuum extraction of electrolyte. J. Mater. Process. Technol. 210, 238–244.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Effects of pulsating electrolyte flow in electrochemical machining Xiaolong Fang, Ningsong Qu ∗ , Yudong Zhang, Zhengyang Xu, Di Zhu College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China
a r t i c l e
i n f o
Article history: Received 20 April 2013 Received in revised form 15 July 2013 Accepted 17 July 2013 Available online 27 July 2013 Keywords: Electrochemical machining Pulsating flow Heat transfer Material removal rate Surface profile
a b s t r a c t Electrochemical machining (ECM) is a promising and low-cost process for yielding various components of difficult-to-machine materials, and has been well established in diverse applications. Distributions of gas and temperature affect the electrolyte electrical conductivity and determine the machining accuracy in ECM. Attempts have been made to generate the pulsating flow via a servo-valve in the electrolytic supply pipe, which is introduced to improve the heat transfer, material removal rate and surface profile in ECM. A multi-physics model coupling of electric, heat, transport of diluted species and fluid flow is presented. Simulation results indicate that pulsating flow has a significant impact on the distributions of velocity, gas fraction, and temperature near the workpiece surface along the flow direction. Experiments are conducted to verify the feasibility of the proposed process and study the effects of pulsating flow on material removal rate. The experimental results agree well with the simulations. Using optimal pulsating parameters, the material removal rate and surface profile are enhanced. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Electrochemical machining (ECM) removes metal material by controlled anodic dissolution in an electrolytic cell. Compared to other typical machining technologies, ECM has superiority by having a high material removal rate, a good surface integrity, is stress free, and has no tool wear or metallurgical defects. ECM is a promising and low-cost process for yielding various components of difficult-to-machine materials, and has been well established in diverse applications, such as turbine blades, airfoils, and surgical implants (Rajurkar et al., 1999). In ECM, the electrolyte with a velocity of 10–30 m/s is pumped into the inter-electrode gap to remove waste products (gases and metallic hydroxides) and Joule heat. The distributions of gases and Joule heat affect the electrolyte electrical conductivity and determine the machining accuracy. Therefore, many studies have focused on the disposal of metal hydroxide sludge and an efficient process simulation. Various approaches have been developed to modify the electrolyte flow regime and enhance the electrolyte refreshment in the inter-electrode gap. Rajurkar and Zhu (1999) found that orbital electrode movement reduces the flow disrupting phenomena and improves the machining accuracy and machining stability. Hewidy et al.
∗ Corresponding author at: College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, P.O. Box 265, 29 Yudao Street, Nanjing 210016, China. Tel.: +86 25 84893870; fax: +86 25 84895912. E-mail address: [email protected] (N. Qu). 0924-0136/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2013.07.012
(2001) proposed that orbital electrode movement eliminates the presence of the spikes and enhanced the ECM accuracy. Ruszaj et al. (2003) demonstrated that electrode ultrasonic vibration causes heterogeneous cavitation of electrolyte flow in the gap, and significantly improves the removal of heat and products out of the machining gap. Hewidy et al. (2007) shown that low frequency tool vibration provides a positive effect by changing the physical conditions in the inter-electrode gap, and enhances electrolytic renewal and the removal of sludge products. Wang et al. (2010) proposed that reverse electrolyte flow pattern with vacuum-extraction could prevent the occurrence of cavitations and diminishes sparking and formation of striations. Furthermore, abundant computational methods have been used to analyse the characteristics of electrolyte flow, the distributions of gas and temperature, and acknowledge the anodic shaping rules. Analytical solutions (Hopenfeld and Cole, 1969) were obtained to describe the one-dimensional equilibrium-cutting gap along the flow direction. Fujisawa et al. (2008) established a multi-physics model, including multiphase flow, thermal fields and electric fields, to predict the final shape of a three-dimensional compressor blade. Van Tijum and Pajak (2008) used a multi-physics approach to support the design of the ECM process for machining the electric shaver. Lee et al. (2009) applied a multi-physics model, consisting of electric, convection and diffusion, to predict the parametric effects on machining accuracy. Deconinck et al. (2011) proposed the multi-ion transport and reaction model to describe the effects of water depletion, and temperature on the anodic process in ECM. Havemann and Rao (1954) shown that periodic fluctuations of fluid flow create different hydrodynamic characteristics and alter
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2. Theoretical models Nomenclature Notations A pulsating amplitude of electrolyte pressure (MPa) bp Bruggeman’s coefficient Ci concentration of diluted species (mol m−3 ) electrolyte specific heat capacity (J K−1 kg−1 ) Cp Di diffusion coefficient of diluted species (m2 s−1 ) E electric field (V m−1 ) pulsating frequency of electrolyte pressure (Hz) f F Faraday constant (C mol) i current density (A cm−2 ) k electrolyte thermal conductivity mass removed in machining (g) m M molar mass of anodic material (g mol−1 ) N gas flux (mol m−2 s−1 ) p electrolyte pressure (MPa) pa absolute pressure of electrolyte (MPa) average electrolyte pressure (MPa) pav Pbulk Joule heating in the bulk of electrolyte ideal gas constant (J mol−1 K−1 ) R ReMRR relative material removal rate machining time (s) t T electrolyte temperature (K) electrolyte velocity magnitude (m s−1 ) u U applied voltage for ECM (V) ˛ degree of temperature dependence ˇgas gas void fraction in electrolyte electric current efficiency electrolyte electrical conductivity (S m−1 ) electrolyte density (g mm−3 ) n material removal rate (m s−1 ) electrical potential (V) ϕ ω volumetric electrochemical equivalent (mm3 A−1 s−1 ) Subscripts 0 property at the flow inlet i property of diluted species i n property in normal direction constant property at a constant electrolyte pressure
the thickness of the boundary layer; therefore, the pulsating flow of optimised pulsating parameters is beneficial to the transfer process. Pulsating flow has been applied to heat exchange, ramjet combustion, solid fermentation, drip irrigation emitter (Benavides, 2009). Recently, the low-frequency tool vibration has been introduced to ECM, and high precision was obtained. When the electrode vibrates, the gap dimension oscillates in the same amplitude, and an electrolytic fluctuation is observed. However, this pulsating flow generated in an oscillating gap is different from those in a constant gap, which have been well applied in heat and mass transfer. Research shows limited studies on this pulsating flow in electrochemical machining. In this study, attempts have been made to generate the pulsating flow via a servo-valve in the electrolytic supply pipe. This work focuses on the improvement of the heat transfer and material removal rate in ECM. A multi-physics model coupling of electric, heat, transport of diluted species, and fluid flow is presented to study the variations of electrolytic velocity, electrolytic temperature, and ion concentration along the flow direction near the workpiece surface. Moreover, experiments have been conducted to verify the feasibility of the proposed process.
ECM is a field-synergy electrolysis process, which consists of mass transfer, energy transfer, momentum transfer and chemical reactions (McGeough, 1974). When a voltage is applied across the cathode tool and the anodic workpiece, the metallic ions of the anodic dissolution migrate from the anode surface to the electrolyte by an electrical force and are formed to insoluble hydroxides in neutral solutions. At the same time, hydrogen and oxygen is generated on the cathode and anode surface, respectively. Heat generated by the passage of current and electrochemical reactions will heat the electrolyte in the inter-electrode gap. All these occurrences interactively influence the electrolyte electrical conductivity, which would affect the current density distribution and the local material removal rate. The relation between the electrical conductivity , the electrolyte temperature T, and the gas void fraction ˇgas is given as follows (Van Tijum and Pajak, 2008): bp
= 0 (1 − ˇgas ) (1 + ˛(T − T0 ))
(1)
where bp is the Bruggeman’s coefficient. Fig. 1 illustrates the schematic diagram of a typical ECM process with pulsating electrolyte flow. With a pulsating electrolyte, periodic fluctuations of flow create different characteristics of flow and heat transfer along the flow direction. The electrochemical cell consists of a cathode tool (Boundaries 9–11) and an anode workpiece (Boundaries 3–5), with electrolyte pumped through the electrode gap from the left inlet (Boundary 1) to the right outlet (Boundary 7). To simplify the proposed model, several assumptions are made as follows: (1) The electrolyte flow is impressible single-phase flow. The scale of bubbles in the electrolyte is small enough to neglect its impact on fluid flow (Brebbia and Mammoli, 2011). (2) The diffusion coefficient of bubbles is temperature independent and at a constant value of 3.0 × 10−6 m2 /s (Fujisawa et al., 2008). (3) The electrolyte dynamic viscosity is assumed to be a constant value of 1.003 × 10−3 Pa s (Van Tijum and Pajak, 2008). (4) The heat generated in the electrolyte is only Joule heat. 2.1. Impressible fluid model The entire flow channel has dimensions of 1 mm in height, 112 mm in length and 12 mm in width; the distance from the inlet to the workpiece is 60 mm; the workpiece and cathode have a cross section of 12 mm × 12 mm with an initial machining gap of 0.15 mm. The governing equations, which usually describe the turbulent flow in ECM (Fujisawa et al., 2008), are given as follows: −∇ 2 u + (u · ∇ )u + ∇ p = 0
∇ ·u=0
(2)
The electrolyte pressure at the inlet is given as follows: p0 (t) = A sin(2 ft) + pav
Fig. 1. Schematic diagram of ECM with pulsating electrolyte flow.
(3)
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The diffusion of ion and gases forced by fluid convection will be discussed independently in the following sections.
The temperature distribution in this cell is calculated by solving a convection–diffusion equation with heat sources (Kozak, 2004) as follows:
2.2. Electrical model The electrical potential in the inter-electrode gap, ϕ, can be approximately described by Laplace’s equations as follows:
∇2ϕ = 0
(4)
The boundary conditions are given as follows:
ϕ 3,4,5 = U
(5)
ϕ 10 = 0
(6)
∂ϕ
1,2,6,7,8,9,11,12 = 0 ∂n
(7)
According to Faraday’s law, the material removal rate, n , is described as follows: n = ωin = ωEn = ω
∂ϕ ∂n
(8)
Experiments were conducted to obtain the variation of current efficiency (Bejar and Gutierrez, 1993), , with an increase in current density. Samples and processing conditions for these experiments are identical to those conditions used in practice. The results are plotted in Fig. 2 and are analysed by curve fitting to obtain Eq. (9) as follows: (i) =
0.85 (1 + e(10−i)/6 )
− 0.1
(9)
Gases produced in the ECM process would adversely influence the electrolyte electrical conductivity. The fluxes of the gases generated at each electrode can be described by Faraday’s law (Van Tijum and Pajak, 2008) as follows: NH2
i = 2F
NO2 =
2.3. Thermal model
(10)
i(1 − ) 4F
(11)
Cp
∂T + Cp u · ∇ T = ∇ (k∇ T ) + Pbulk ∂t
(12)
where Cp is the electrolyte specific heat capacity, and k is the electrolyte thermal conductivity. Pbulk denotes the Joule heating in the bulk of electrolyte and can be obtained by Joule’s law as follows: Pbulk = Ui
(13)
In this electrochemical system, the thermal conductivity of electrode material, 81 W/m, is 102 times larger than that of the electrolyte, which is only 0.6 W/m. Consequently, the interfaces between the electrodes and electrolyte can be considered as outer boundaries. That is, the temperature on the electrode surface is set to be the same as the temperature reference. The boundary conditions are given as follows:
T 1,3,4,5,9,10,11 = T0
(14)
∂T
2,6,8,12 = 0 ∂n
(15)
2.4. Reactant transport model Reactants produced in the process are metal ions dissolved from the anode, hydrogen near the cathode surface and oxygen near the anode surface. Transport of species in the gap is driven by migration, convection and diffusion. Diffusion is the main transport mechanism via the anode–electrolyte layer. In areas of electrolyte adjacent to the anode surface, convection is the main role of transport. The governing equation based on diffusion by Fick’s law and convection forced by fluid flow can be shown as follows: ∂Ci + ∇ (Ci u − Di ∇ Ci + Di Ni ) = 0 ∂t
(16)
where Di denotes the diffusion coefficient of diluted species i and Ni denotes the flux of diluted species i. In this system, all of the initial species concentrations are zero. The boundary conditions for the transport equations are as follows: Inlets: At the inlet of H2 :
NH2 =
i 2F
(10)
At the inlet of O2 :
NO2 =
i(1 − ) 4F
(11)
Outlet: ∂Ci
7 = 0 ∂n
(17)
All other boundaries are considered as a no-flux wall. As shown in Eq. (1), gas generated in the process will adversely influence the electrolyte electrical conductivity. From the transport model of H2 and O2 , the gas void fraction can be calculated using Eq. (18) and is given as follows: ˇgas =
Fig. 2. Current efficiency curve from experimental results.
(CO2 + CH2 )RT (CO2 + CH2 ) + u · pa
(18)
where R is the ideal gas constant, T is the local present temperature, pa is the local absolute pressure, and u is the local electrolyte velocity.
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Table 1 Parameters in calculation. Electrolyte concentration Electrolyte temperature Pulsating frequency (Hz) Pulsating amplitude (MPa)
120 g/L, NaNO3 293 K 1, 2, 5, 10, 20, 40 0.1, 0.2, 0.3, 0.4
2.5. Moving mesh To study the time dependent response of periodic pulsating flow on the material removal process, the geometry should be suitably realigned with the new position of the electrodes. The arbitrary Lagrangian–Eulerian formulation is chosen to track the cathode feed movement and anodic shaping process. All models are coupled and analysed using COMSOL software version 4.3. The parameters used in the calculations are listed in Table 1.
Fig. 4. Variations of gas fraction with pulsating pressure in a period.
3. Simulation results The evolution procedures of process variables, such as gas void fraction and temperature, were simulated in the ECM process with pulsating electrolyte flow. Furthermore, the effects of pulsating parameters on the transfer of heat, material anodic dissolution rate and surface profile were studied. Simulations were performed in transient mode with initial expressions of zero. 3.1. Variations of velocity and gas fraction The electrolyte was pumped into the machining gap at a pulsating pressure of 0.2 MPa in amplitude and 10 Hz in frequency. A probe, marked by the dashed line in Fig. 1, was set to obtain the response of the electrolyte velocity and gas fraction to the pulsating pressure. Figs. 3 and 4 present the averaged values of the electrolyte flow velocity and gas void fraction, respectively. These values change with the oscillation of the pulsating pressure. When the pulsating phase is at 90◦ , the pressure and flow velocity are at a maximum while the gas void fraction is minimal. When the flow velocity reaches the lowest point, the void fraction is at a maximum. 3.2. Influence on heat transfer Fig. 5 presents the changes of the averaged temperature at the probe. When the pulsating pressure is at a maximum, the temperature is minimal. When the pulsating pressure is minimal, the temperature is at a maximum.
Fig. 3. Variations of velocity with pulsating pressure in a period.
Fig. 5. Variations of temperature with electrolyte pressure in a period.
Fig. 6 shows the periodic variations of the averaged temperature gradient on the anode surface, which reveals the speed of heat transfer from electrolyte to electrode. The pulsation of electrolyte pressure leads to an obvious jump of temperature gradient, which varies 180◦ out of phase to the electrolyte pressure. When the pulsating amplitude increases to 0.4 MPa, the fluctuation of temperature gradient increase approximately 100%. When a pulsating
Fig. 6. Variations of the averaged temperature gradient in time-scale; f = 5 Hz.
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Fig. 8. Variations of the anodic removal rate in a time-scale.
Fig. 9, large pulsating amplitude is adverse to anodic dissolution, and the optimal pulsating frequency for material removal is 10 Hz. When the pulsating amplitude is 0.4 MPa, the electrolyte pressure at the inlet would be zero. Hence, zero pressure difference existed between the electrolyte inlet and outlet, and the forced convention driven by the electrolyte flow ceased. Additionally, anodic dissolution occurred in an instant static flow, which is adverse to the renewal of heat and products. Fig. 10 shows the predicted surface profiles after machining for 30 s. As shown in Fig. 10(a), when the pulsating pressure is less than 0.3 MPa, the pulsating flow is beneficial to the anodic dissolution process. When A increases to 0.4 MPa, the dissolution slows down. The results shown in Fig. 10(b) indicate that when the pulsating amplitude is 0.2 MPa, all frequencies are advantageous to the process. Additionally, the optimal frequency in this case is 10 Hz. Fig. 7. Effects of pulsating flow on the time-averaged temperature gradient. (a) Variation curves of the time-averaged temperature gradient with pulsating amplitude A; f = 5 Hz. (b) Variation curves of the time-averaged temperature gradient with pulsating frequency f; A = 0.2 MPa.
electrolyte is applied, flow separation occurs and creates regions of reverse flow, where regions of high mixing and turbulence are generated. The boundaries of this reverse flow are characterised by the creation and destruction of eddies of large turbulence energy and vortex shedding, which are expected to increase the heat transfer rates. Fig. 7 presents the variations of the time-averaged temperature gradients with different pulsating parameters. As the pulsating amplitude increases from 0.1 MPa to 0.4 MPa, the time-averaged gradient increases approximately 7%. As the pulsating amplitude frequency increases, the temperature gradient initially increases and then decreases to a constant. The optimal pulsating frequency for this electrolyte flow model is 10 Hz. 3.3. Influence on material removal rate and surface profile The changes of flow field, temperature and gas distribution finally determine the material anodic removal rate and surface profile. The foreground of this effect is the intersection point between the anode surface and flow outlet. Fig. 8 shows the variations of material removal rate at this point, which changes in synchronisation with the pressure fluctuation. As the pulsating amplitude increases, the fluctuation range of the anodic removal rate increases. Fig. 9 presents the variations of the time-averaged material removal rate with different pulsating parameters. As shown in
4. Experimental results and discussion 4.1. Experimental procedures An ECM system, as shown in Fig. 11, was constructed to study the effects of pulsating electrolyte flow on material removal and surface profile in the ECM process. The pulsating flow is modulated by a Get-type electro-hydraulic servo valve (RT6615E, Radk-Tech, China), which can quickly respond to a broadband signal ranging from 0 to 100 Hz. A specific full feedback control system was established to control the pressure and obtain the machining voltage and current. Samples of SS304, with dimensions of 12 mm × 12 mm × 10 mm, are ultrasonically cleaned and weighted by analytical balance (AE240, METTLER, China) before and after the experiments. Furthermore, the relative material removal rate is defined as follows: m ReMRR = (19) mcosntant where m denotes the mass removed in the ECM process with pulsating flow, and mconstant denotes the mass removed when the electrolyte pressure is at a constant value. Surface profiles along the flow direction were measured by a coordinate measure machine (TESA Micro-Hite 3D, HEXAGON, Switzerland). Table 2 shows the machining conditions. 4.2. Effects of pulsating parameters on material removal rate Fig. 12(a) shows the change of the relative material removal rate with pulsating amplitude A. As the pulsating amplitude increases,
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Fig. 9. Effects of pulsating flow on the averaged material removal rate on the anode surface. (a) Variation curves of the averaged material removal rate with pulsating amplitude A; f = 5 Hz. (b) Variation curves of the averaged material removal rate with pulsating frequency f; A = 0.2 MPa.
41
Fig. 10. Effects of pulsating flow on predicted surface profiles after 30 s of ECM. (a) Variation curves of predicted surface profiles with pulsating amplitude A; f = 5 Hz. (b) Variation curves of predicted surface profiles with pulsating frequency f; A = 0.2 MPa.
Fig. 11. Experimental set-up schematic diagram.
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Table 2 Experimental conditions. Electrolyte concentration Electrolyte temperature Pulsating frequency (Hz) Pulsating amplitude (MPa) Averaged pressure (MPa) Machining time (s)
120 g/L, NaNO3 293 K 1, 2, 5, 10, 20, 40 0.1, 0.2, 0.3, 0.4 0.4 30
the relative material removal rate obtained from the experiments first increases and then decreases. When A is 0.2 MPa, the maximum relative removal rate of 1.02 is achieved. When A is 0.4 MPa, the relative removal rate is less than one. In this case, a moment of zero pressure difference exists between the electrolyte inlet and outlet, and anodic dissolution occurs in an instant static flow. A decrease in the material removal rate adversely affected the timeaveraged value. The experimental optimised value is 0.2 MPa and the optimised simulation value is 0.1 MPa. But their difference in material removal rate is less than 1%. Both the results show that when A is larger than 0.2 MPa, the material removal rate decreases. So we chose the pulsating amplitude as 0.2 MPa in the following experiments. Fig. 12(b) shows the variation of relative material removal rate with pulsating frequency. As the pulsating frequency increases, the relative material removal rate obtained from the experiments first
Fig. 13. Effects of pulsating flow on surface profiles in the flow direction after 30 s of ECM. (a) Variation curves of surface profiles with pulsating amplitude A; f = 5 Hz. (b) Variation curves of surface profiles with pulsating frequency f; A = 0.2 MPa.
increases and then decreases. When f is 10 Hz, the maximum relative removal rate of 1.03 is achieved. Higher frequency would not induce the response of electrolyte pressure because of the inertia of the electrolyte. The experimental results agree well with the simulation results in trend, but all the simulation results are smaller than the experimental. This difference most likely occurs because of the estimation of heat generated in electrochemical reactions, which should warm up the electrolyte and increase the electrolyte electrical conductivity. 4.3. Effects of pulsating parameters on surface profile
Fig. 12. Effects of pulsating flow on ReMRR. (a) Variation curves of relative material removal rate with pulsating amplitude A; f = 5 Hz. (b) Variation curves of relative material removal rate with pulsating frequency f; A = 0.2 MPa.
Fig. 13 presents the surface profiles along the flow direction. As shown in Fig. 13(a), the pulsating amplitude plays an advantageous role when the amplitude is less than 0.3 MPa. The result becomes unfavourable when the amplitude is 0.4 MPa. The pulsating frequency has less of an effect on the surface profile than the amplitude. Additionally, as shown in Fig. 13(a), the predicted profile agrees well with the experiment result, but differs at some points. This variation is mostly because of the errors from computation and measurement of start points. Furthermore, the sampling points were analysed with Range and Deviation analysis. As shown in Fig. 14, the range and standard deviation of height difference both change in a concave trend. At the optimal conditions of 10 Hz and 0.2 MPa, the range of the surface
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5. Conclusions Pulsating electrolyte flow was introduced to enhance heat and mass transfer for ECM by a modified electrolyte flow approach. The conclusions can be summarised as follows: 1. A multiple physics model was established to study the distribution of several physical variables along the flow direction, which were critical to ECM. The simulation results indicate that proper pulsating parameters would enhance the heat transfer and material removal rate. The predicted profiles agreed well in trend with the experimental results. 2. Experiments verified that with an optimal pulsating parameter of 10 Hz in frequency and 0.2 MPa in amplitude, the range and standard deviation of the surface height difference would decrease to 19.8 m and 5.2 m, respectively. Acknowledgements The authors wish to acknowledge the financial support provided by the China Natural Science Foundation (51175258) and the Funding of Jiangsu Innovation Programme for Graduate Education (CXZZ11 0195). References
Fig. 14. Effects of pulsating flow on range and standard deviation of surface height difference. (a) Variation curves of range and standard deviation of surface height difference with pulsating amplitude A; f = 5 Hz. (b) Variation curves of range and standard deviation of surface height difference with pulsating frequency f; A = 0.2 MPa.
profile is 19.8 m, which is quite lower than the value at constant pressure, 67.3 m. Furthermore, the standard deviation of the height difference is 5.2 m, which is still lower than the 28.2 m value at constant pressure. According to Eq. (1), the local electrolyte electrical conductivity is closely related to the gas void fraction and local electrolyte temperature. The bubbles and Joule heat generated in the interelectrode gap cause varying local electrolyte electrical conductivity. When a pulsating electrolyte is applied, flow separation occurs and creates regions of reverse flow, where regions of high mixing and turbulence are generated. Therefore, the difference in electrolyte electrical conductivity and electrical potential in the inter-electrode is smaller, which may lead to a more homogeneous machined surface profile. It has been shown that a better surface profile may be acquired with the correct pulsating electrolyte.
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