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Pulse electrochemical finishing: Modeling and experiment
Journal of Materials Processing Technology 210 (2010) 852–857
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Pulse electrochemical finishing: Modeling and experiment Ning Ma, Wenji Xu ∗ , Xuyue Wang, Bin Tao School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, PR China
a r t i c l e
i n f o
Article history: Received 4 August 2008 Received in revised form 16 November 2009 Accepted 25 January 2010
Keywords: Pulse electrochemical finishing (PECF) Rotational electrode Surface roughness Mathematical model Anodic smoothing
a b s t r a c t Surface quality of the workpiece has great influence on its service performance and lifespan. Pulse electrochemical finishing (PECF) provides an effective method for improving surface quality of the workpiece. In PECF, surface irregularities are removed by electrochemical dissolution rather than by cutting force. Due to non-contact nature of the process, there is no residual stress and thermal effect on the workpiece surface. For successful utilization of PECF, in present manufacturing, it still demands for more intensive research, including the mechanism of anodic smoothing. The anodic smoothing characteristics of PECF are analyzed through a developed mathematical model. The main influencing factors such as the finishing time, the interelectrode gap, the applied voltage and the rotational speed of electrode have been examined. The predictive values based on the developed mathematical model are found to be in reasonable agreement with the experimental values. The surface roughness Rz ranges from 3 m to 1.22 m. The research achievement through various parametric studies can be used as a guideline for the operation of a PECF system. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Surface quality of the workpiece has great influence on their service performance and lifespan. In particular, those workpieces with frictional pair, abrasion resistance, fatigue resistance and the friction force between frictional surfaces rely on the surface quality to a great extent, such as bearing ring and gear. Thus, the surfaces as the frictional pair need to be finished so as to improve the surface quality of the workpiece. Conventional technique such as polishing by hand heavily depends on the operator’s experience. Hand polishing will result in non-uniform residual stress due to the contact between the tool and the workpiece. Surface cracks and depressions can reduce the service life of the part (Hocheng and Pa, 1999). Electrochemical finishing (ECF) and the application of electrochemical machining (ECM), can overcome the above mentioned shortcomings and produce the workpiece with good surface quality efficiently without residual stress or burr (Phillips, 1986; Masuzawa and Sakai, 1987). The ECM process was first patented by Gusseff in 1929. The principle of ECM was presented by Faraday in the 18th century. ECM has many advantages over traditional machining such as its applicability regardless of material hardness, no tool wear, high material removal rate, smooth and bright surface and production of components of complex geometry (Rajurkar et al., 1999). The use of pulsed power and hence the ability to use narrower interelectrode gaps
∗ Corresponding author. Tel.: +86 411 84708422; fax: +86 411 84708422. E-mail address: [email protected] (W. Xu). 0924-0136/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2010.01.016
has yielded the major breakthrough in improving ECM precision (Rajurkar et al., 1993, 1995; Kozak et al., 1994; Rosenkranz et al., 2005). ECM is considered to be a promising method for finishing or polishing due to its micro-removal characteristics (Rajurkar et al., 1999). ECF is the same as ECM with very limited and low removal rate (Mahdavinejad and Hatami, 2008). ECF has a low-level electrochemical dissolution process in which the tool is the cathode and the workpiece is the anode in an electrolytic cell (Ramasawmy and Blunt, 2007). In many applications, a smooth and bright surface is essential and ECF is a better technique for approaching mirrorlike surfaces on many metals (Landolt et al., 2003). Many industrial applications of surface finishing have been reported. Shen (1995) used NaNO3 as the electrolyte for the electropolishing of die surfaces. The results showed that the surface roughness of workpiece decreased with the increase of current density, flow rate and concentration of the electrolyte. Moreover, polishing with pulsed direct current was found better than that of continuous direct current. Sun et al. (2001) developed a new MREF-ECM (modulated reverse electric field electrochemical machining) polishing process for hard passive alloys surface finishing. Hocheng and Pa (2003) presented a new application of electropolishing using a lowcost disc-form electrode offering fast improvement of the surface roughness of SKD61. Ramasawmy and Blunt (2007) studied the effect of parameters of electrochemical polishing on the 3D surface texture parameters of EDM surfaces of tool steel specimens. Pa (2008) investigated an efficient finishing process using a low-cost electrode of end turning surface finishing. Despite the considerable amount of experimental research, there are many fundamental
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
853
to the motion of the cathode. The metal removal thickness of the anodic surface is dS. According to Eq. (1), the reduction in height of the anodic surface in time dt is given by: dS =
e kv (U0 − U) dt S
(2)
where kv is the volumetric electrochemical equivalent and it can be computed as follows: Fig. 1. Principle of PECF of bearing inner ring raceway.
kv =
aspects of PECF process, such as the basic mechanism of the anodic smoothing, which need to be understood further. The PECF is used to reduce the surface roughness of the workpiece. In PECF, with the increase of finishing time, a certain amount of material is removed through the anodic dissolution. In order to maintain the precision of the workpiece, the total removal thickness should not be too large. Thus, it is better to achieve lower surface roughness of the workpiece by removing smaller metal surface thickness. In this work, a mathematical model of the PECF process has been developed for predicting particular important features such as the total removal thickness and the maximum height of the assessed profile. Moreover, this paper emphasizes features of the mathematical model for correlating the interactive and higherorder influences of the various finishing parameters, such as the interelectrode gap, the applied voltage, the finishing time, and the rotational speed of electrode, for achieving of controlled PECF. 2. Theoretical modeling 2.1. Fundamentals of PECF Fig. 1 illustrates the principle of PECF of bearing inner ring raceway. The PECF bases on an anodic dissolution process. Workpiece and tool are respectively anode and cathode, in which two electrodes are separated by electrolyte. When an electric current passes through the electrolyte, the material on the workpiece surface is dissolved. As the tool scans over the surface of the workpiece, the whole surface is finished. According to Faraday’s law and Ohm’s law, the anode recession rate of the workpiece surface can be calculated as follows (McGeough, 1974): r˙ a =
e kv (U0 − U) S
(1)
where is the current efficiency of anodic dissolution, e is the electrolyte conductivity, kv is the volumetric electrochemical equivalent, S is the interelectrode gap, U0 is the applied voltage, U is the over potential value. 2.2. Mathematical modeling of ideal surface in PECF Fig. 2 shows the gap between two electrodes which is filled with electrolyte. The initial interelectrode gap is equal to S0 . During the PECF processing, the initial interelectrode gap increases according
A za F
(3)
where a is the density of anode metal, F is Faraday’s constant, A is the atomic weight, z is the valency. By integrating Eq. (2) over the time from 0 to tp with an initial interelectrode gap S0 , the interelectrode gap equation can be computed as follows: S = (S0 2 + 2e kv (U0 − U)tp )
1/2
(4)
where S0 is the initial interelectrode gap, the electrolyte conductivity e of the multi-phase medium can be estimated by the following Brugeman equation (McGeough, 1974): e = 0 (1 + ˛T )(1 − ˇ)
3/2
(5)
where T = T − T0 is temperature increment, T0 is the inlet electrolyte temperature, ˛ is the electrolyte temperature coefficient, 0 is the inlet electrolyte conductivity and ˇ is the gas void ratio in the electrolyte. The major factors that influence the electrolyte electrical conductivity are the heat generation and gas bubble. However, in this work, the influences can be neglected. On the one hand, since the process is a finishing rather than a forming process, the electrolyte temperature changes do not exceed 1 ◦ C. This is due to the rotation of the electrolyte and the fast rotational speed of electrode. On the other hand, the working area between two electrodes is smaller than the machined area. Therefore, the assumption of constant conductivity is feasible. The following conditions are assumed for one-dimensional twophase homogeneous flow: (1) The current efficiency of anodic dissolution is constant. (2) The total overpotential U is constant. (3) The electrolyte conductivity e is constant. With these conditions and assumptions, the anodic smoothing equation of PECF using a rotational electrode can be described as follows: m
S 2 = S0 2 + 2
j=1
tp
Cj (t)dt
(6)
0
where Cj (t) = e kv (U0j (t) − Uj (t)), and based on above assumptions, Cj (t) can be regarded as constant C. Since relation between the total finishing time t and the total pulse number m is m = t/tp (with being the pulse duty factor tp /(tp + to )), Eq. (6) becomes: S 2 = S0 2 + 2Cmtp = S0 2 + 2Ctef
(7)
where mtp is the effective finishing time. It can be seen that the effective finishing time is influenced by the pulse duty factor , the ratio of Lc to Lp (Lp = d) and the total finishing time t. Thus, the effective finishing time can be described as: tef = ·
Fig. 2. Scheme of PECF on ideal surface.
Lc · nw t dnw
(8)
where Lc is the thickness of the cathode, d is the diameter of the workpiece, nw is the workpiece rotational speed. Taking into
854
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
Fig. 3. Scheme of PECF on real surface.
account the relationships (7) and (8), Eq. (7) can be expressed as: S 2 = S0 2 + 2C
Lc ·t d
(9) Fig. 5. Effect of finishing time on the maximum height of the assessed profile Hn .
Although the PECF process becomes idealized with these assumptions, the developed mathematical model is helpful to understand the PECF processing characteristics.
Hn
2.3. Mathematical modeling of real surface in PECF The real metal surface does not look like that illustrated in Fig. 2. As shown in Fig. 3, it is the uneven and peak-like profile. When the cathode scans over the anodic surface, the dissolution rate of the wave crests of the surface profile is faster than the wave troughs, which results from the concentration of current lines on the crests of surface profile. Proceeding with anodic dissolution, the workpiece surface is gradually smoothed. In order to make further analysis, the real surface profile in Fig. 3 is simplified as shown in Fig. 4. Therefore, according to Eq. (9), the total removal thickness Sn can be expressed as: Sn =
S02 + 2C
Lc ·t d
1/2
− S0
(10)
The Sn is the total removal thickness from the surface of the workpiece after time t in PECF. In Fig. 4, it can be seen that H0 is the initial sum of height of the largest profile peak height and the largest profile valley depth with an evaluation length. It can be expressed as: H0 = ht − hp
(11)
After the cathode scans over the surface of the workpiece one time, the sum of height of the largest profile peak height and the largest profile valley depth with an evaluation length is H1 . It can be calculated as follows: H1
= h1t − h1p =
2
ht + 2C
Lc d
1/2
2
− hp + 2C
Lc d
1/2
Fig. 4. Simplified model of real metal surface.
So, after the cathode scans is over the surface n times, the maximum height of the assessed profile Hn is calculated as follows: = hnt − hnp =
h2t + 2C
Lc ·t d
1/2
− h2p + 2C
Lc ·t d
1/2
(13)
In addition, it can be found that the maximum height of the assessed profile Hn is the Rz from definition of the evaluation parameter of surface roughness (ISO 4287:1997). From above expression, it is clear that the total removal thickness and the maximum height of the assessed profile depend on many factors, such as the interelectrode gap, the finishing time, the applied voltage. Further analysis is to be carried out in the following sections. 3. Parametric analysis of PECF processing Based on the developed mathematical model of PECF process a parametric analysis has been carried out to evaluate the effect of various process parameters on the total removal thickness Sn and the maximum height of the assessed profile Hn . The theoretical calculations have been carried out with initial values U0 = 16 V, U = 0, kv = 1.7 mm3 /A min, e = 13 A/V m, = 0.2. Based on Eq. (13), studies are carried out to analyze the effects of the various process variables on the maximum height of the assessed profile Hn . Fig. 5 shows the relationship between the maximum height of the assessed profile and the finishing time at different interelectrode gap. It is obvious that as the finishing time increases, the maximum height of the assessed profile decreases. Theoretically, it takes an infinite time to remove the surface irregularities completely. In practice, as soon as the Hn goes below a pre-assigned allowable value the process is completed.
(12)
Fig. 6. Effect of finishing time on total removal thickness Sn .
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
855
Table 3 Components of workpiece materials. Element
C
Si
Mn
Cr
Fe
wt%
0.95–1.05
0.15–0.35
0.20–0.40
1.3–1.65
Others
Fig. 7. Experimental set-up.
Table 1 Experimental parameters. Parameters
Value
Pulse frequency Pulse on-time (tp ) Maximal current Applied voltage (U0 ) Interelectrode gap (S0 ) Cathode thickness (Lc ) Duty factor () Electrolyte
5–20 kHz 10–200 s 400 A 0–20 V 0.1, 0.2, 0.3 mm 0.5 mm 0.2 NaNO3 (15 wt%)
Fig. 6 shows that the total removal thickness increases with the increase of the finishing time. It is clear that as the interelectrode gap decreases, the total metal removal thickness increases. This is due to the increase of current density as the interelectrode gap decreases, but too small gap should be avoided because it causes electric sparks and shorts. If the current density is too high it may cause the formation of heat-affected zones, and it finally results in improper surface finish and low accuracy. 4. Experimental tests Fig. 7 shows the set-up of the PECF system for carrying out finishing operations on the bearing inner ring raceway. The operation has been shown schematically. The workpiece and the tool are being securely held by a three-jaw chuck and a clamp respectively. Both the workpiece and the tool are insulated from the main body in order to only focus an electrochemical reaction between the workpiece and the tool. For using a rotational electrode in PECF, the working area between two electrodes is smaller than the machined area which shortens the distance to expel the dissolution products. The electrolyte, which is generally a concentrated salty solution, is pumped at high velocities through the machining gap in order to remove the reaction products and to dissipate the heat generated. The electrolyte flow system consists of a filter, pump, electrolyte tank, throttleer and flowmeter. The function of this system is to ensure adequate amount of clean electrolyte flow in the gap. The tank, pipe lines, valves are made of PVC. The pump is corrosion resistant centrifugal type pump. The pulse DC power supply is adopted in this system. The experimental and workpiece parameters are shown in Tables 1 and 2.
Fig. 8. Comparison of the maximum height of the assessed profile Hn (Rz) between experimental results and calculated results.
The workpiece material is GCr15 with hardness 60 HRC, the tool electrode is made of copper and the main component of the electrolyte is NaNO3 . Passive electrolytes are known to give better machining precision. This is due to the formation of oxide films and oxygen evolution in the stray current region (Bhattacharyya et al., 2005). The workpiece material composition is shown in Table 3. 5. Results and discussion Experimental results are graphically represented to show the influence of various finishing parameters on the maximum height of the assessed profile Hn and total removal thickness Sn . Fig. 8 shows that the maximum height of the assessed profile Hn , namely Rz, decreases with the increase of the finishing time. The decrease of the maximum height Hn reflects the decrease of the surface roughness and the improvement of the surface quality. It has been observed from Fig. 8 that the reduction rate of the maximum height Hn decreases with the increase of finishing time. The slope change is well-known to be the result of changes in the interelectrode gap. For applied voltage equal to 16 V, nw = 200 r/min, S0 = 0.2 mm, the calculated results can be obtained from Eq. (13) and the experimental results are measured by Talysurf profilometer. The measured Rz decreases from 3 m to 1.22 m while the finishing time increases from 0 min to 4 min. As illustrated in Fig. 8, the calculated and experimental results show the same trend.
Table 2 Workpiece parameters. Parameters
Value
Initial surface roughness (Rz) Materials Surface hardness Size Rotational speed (nw )
3 m GCr15 60 HRC Ø70 × 20 mm 120–380 r/min
Fig. 9. Comparison of total removal thickness Sn between experimental results and calculated results.
856
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
Fig. 10. Comparison of the surface micro-topography of workpiece before and after PECF (S0 = 0.2 mm, nw = 200 r/min): (a) before PECF, Rz = 3 m; (b) after PECF, Rz = 1.22 m.
Fig. 9 gives the comparison of the calculated values of total removal thickness Sn and those measured values from experiments. The total removal thickness Sn is equal to about 210 m while the finishing time increases from 0 min to 4 min. Their agreement is quite clear for t < 2 min, but discrepancies occur when t > 2 min. This is mainly due to the reduction rate of Hn decreases. At the beginning of PECF, the interelectrode gap between the two electrodes is small. During the process of PECF, the gap becomes larger, which will slow down the finishing process by decreasing the electric field intensity as shown by Eq. (1). It can be seen from Eq. (10) that the total removal thickness Sn is not influenced by the rotational speed of workpiece. However, it has been obtained form the experiments that there exists an optimal rotational speed for the surface quality of workpiece. It is not good for the surface quality of workpiece while the rotational speed too fast or too slow than the optimal rotational speed nw = 200 r/min. The gap has a great effect on the anodic dissolution. When the gap is set small, the reaction will be acute. If the gap is set smaller than 0.1 mm, the undesired electric discharge will happen. If the current density is set larger than 100 A/cm2 , it may cause the formation of heat-affected zones. Several reasons account for the errors between calculated and experimental results. Firstly, the anode consists of multiple metal and nonmetal elements. However, it has been considered as simple metal in the mathematical model. Secondly, the machining traces in pre-machined surface influence the measurement results. Thirdly, some parameters in mathematical model have been idealized. The average percent error (APE) is calculated with a modified equation from Beamish and Fournier (1981): 1 APE = N N
i=1
Xi − Yi Xi
× 100%
(14)
where N is the number of data points, Xi is the calculated values and Yi are the experimental values. In this paper, the APE between the experimental values and calculated values of the maximum height of assessed profile Hn in Fig. 8 is 8.77%. The APE between the experimental values and calculated values of total removal thickness Sn in Fig. 9 is 25.49%. Fig. 10 shows the surface micro-topography of workpiece before and after PECF. It can be found that the surface micro-topography finished by PECF is much different from original mechanically machined surface profile. As shown in Fig. 10, wave crests of original mechanically machined surface profile disappear quickly after PECF. This is mainly due to the concentration of current lines on wave crests of a surface profile thus leading to a locally higher dissolution rate (Landlot, 1987), which is popularly considered as an
explanation for the finishing mechanism. It can be also verified by the following analysis. In Fig. 3, the rate of reduction of the point P in the wave crests of surface profile is: r˙ p =
C Sp
(15)
The rate of reduction of point T in the wave troughs of surface profile is: r˙ t =
C St
(16)
Therefore, the ratio of Eqs. (15) and (16) is: r˙ p ıp + ıt C St = · =1+ Sp C Sp r˙ t
(17)
Thus, it can be seen from Eq. (17) that r˙ p /r˙ t > 1, that is r˙ p > r˙ t . The rate of anodic smoothing equals to the difference in dissolution rate between wave crests and wave troughs. After the period of finishing time, the anodic surface is gradually smoothed. 6. Conclusions In the present work, an idealized mathematical model has been developed and verified experiments have been performed with different finishing parameters. Some key findings both the theoretical modeling and the experimental investigation are listed as follows: (1) PECF proves an effective method to reduce the surface roughness Rz from 3 m to 1.22 m in 4 min. (2) The mathematical model is capable of explaining the mechanism of anodic smoothing and predicting the results with reasonable accuracy. The model can be utilized for controlled PECF operation. (3) From the developed mathematical model, in order to reduce several microns of the maximum height of the profile, it needs to remove a few hundred of microns from the workpiece surface. For example, the total removal thickness is equal to 210 m in order to reduce the maximum height of the profile Hn from 3 m to 1.22 m. (4) The experimental results show that the surface microtopography finished by PECF is much different from original mechanically machined surface. The wave crests of original mechanically machined surface profile disappear quickly after PECF.
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
Acknowledgements The authors are grateful to the financial aid to this projects supplied by National Natural Science Foundation of China (Grant No. 90923022). Appendix A. The purpose of this appendix is to indicate step by step how to calculate the total removal thickness Sn and the maximum height of the assessed profile Hn . Giving initial values: Applied voltage U0 , over potential U, the volumetric electrochemical equivalent kv , electrolyte conductivity e , duty factor , initial interelectrode gap S0 , cathode thickness Lc , the diameter of the workpiece d, initial surface roughness Rz. A.1. Calculation of Sn The total removal thickness Sn is determined by Eq. (A1) Sn =
S02 + 2C
Lc ·t d
1/2
− S0
(A1)
where C = e kv (U0 − U) The total removal thickness Sn can be obtained by substituting above initial values into Eq. (A1). A.2. Calculation of Hn The maximum height of the assessed profile Hn is determined by Eq. (A2) Hn
= hnt − hnp =
h2t + 2C
Lc ·t d
1/2
− h2p + 2C
Lc ·t d
1/2
(A2)
According to Fig. 4, the distance between the cathode and the largest profile valley is ht = S0 +
Rz 2
(A3)
The distance between the cathode and the largest profile peak height is hp = S0 −
Rz 2
(A4)
857
Substituting both Eqs. (A3) and (A4) into Eq. (A2) the maximum height of the assessed profile Hn can be obtained by substituting the above initial values. References Beamish, R.J., Fournier, D.A., 1981. A method for comparing the precision of a set of age determinations. Can. J. Fish. Aquat. Sci. 38, 982–983. Bhattacharyya, B., Malapati, M., Munda, J., 2005. Experimental study on electrochemical micromachining. J. Mater. Process. Technol. 169, 485– 492. Hocheng, H., Pa, P.S., 1999. Electropolishing and electrobrightening of holes using different feeding electrodes. J. Mater. Process. Technol. 89-90, 440– 446. Hocheng, H., Pa, P.S., 2003. Electropolishing of cylindrical workpiece of tool materials using disc-form electrodes. J. Mater. Process. Technol. 142, 203–212. ISO 4287, 1997. Geometrical product specifications (GPS)—surface texture: profile method—terms, definitions and surface texture parameters. Kozak, J., Rajukar, K.P., Wei, B., 1994. Modelling and analysis of pulse electrochemical machining. Trans. ASME J. Eng. Ind. 116 (3), 316–323. Landlot, D., 1987. Fundamental aspects of electropolishing. Electrochem. Acta 32 (1), 1–11. Landolt, D., Chauvy, P.F., Zinger, O., 2003. Electrochemical micromachining, polishing and surface structuring of metals: fundamental aspects and new developments. Electrochem. Acta 48, 3185–3201. Mahdavinejad, R., Hatami, M., 2008. On the application of electrochemical machining for inner surface polishing of gun barrel chamber. J. Mater. Process. Technol. 202, 307–315. Masuzawa, T., Sakai, S., 1987. Quick finishing of WEDM products by ECM using a mate-electrode. Ann. CIRP 36 (1), 123–126. McGeough, J.A., 1974. Principles of Electrochemical Machining. Chapman and Hall, London. Pa, P.S., 2008. Effective form design of electrode in electrochemical smoothing of end turning surface finishing. J. Mater. Process. Technol. 195, 44–52. Phillips, R.E., 1986. What is electrochemical grinding and how does it work. Carbide Tool J. 18 (6), 12–14. Rajurkar, K.P., Kozak, J., Wei, B., McGeough, J.A., 1993. Study of pulse electrochemical machining characteristics. Ann. CIRP 42 (1), 231–234. Rajurkar, K.P., Wei, B., Kozak, J., McGeough, J.A., 1995. Modelling and monitoring interelectrode gap in pulse electrochemical machining. Ann. CIRP 44 (1), 177–180. Rajurkar, K.P., Zhu, D., McGeough, J.A., Kozak, J., De Silva, A., 1999. New developments in electro-chemical machining. Ann. CIRP 48 (2), 567–579. Ramasawmy, H., Blunt, L., 2007. Investigation of the effect of electrochemical polishing on EDM surfaces. Int. J. Adv. Manuf. Technol. 31, 1135– 1147. Rosenkranz, C., Lohrengel, M.M., Schultze, J.W., 2005. The surface structure during pulsed ECM of iron in NaNO3 . Electrochim. Acta 50, 2009– 2016. Sun, J.J., Taylor, E.J., Srinivasan, R., 2001. MREF-ECM process for hard passive materials surface finishing. J. Mater. Process. Technol. 108, 356– 368. Shen, W.M., 1995. The study of polishing of electric discharge-machined mold with ECM, MSc Thesis, National Yunlin Institute of Techndogy, Taiwan, pp. 11–30.
Contents lists available at ScienceDirect
Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Pulse electrochemical finishing: Modeling and experiment Ning Ma, Wenji Xu ∗ , Xuyue Wang, Bin Tao School of Mechanical Engineering, Dalian University of Technology, Dalian 116024, PR China
a r t i c l e
i n f o
Article history: Received 4 August 2008 Received in revised form 16 November 2009 Accepted 25 January 2010
Keywords: Pulse electrochemical finishing (PECF) Rotational electrode Surface roughness Mathematical model Anodic smoothing
a b s t r a c t Surface quality of the workpiece has great influence on its service performance and lifespan. Pulse electrochemical finishing (PECF) provides an effective method for improving surface quality of the workpiece. In PECF, surface irregularities are removed by electrochemical dissolution rather than by cutting force. Due to non-contact nature of the process, there is no residual stress and thermal effect on the workpiece surface. For successful utilization of PECF, in present manufacturing, it still demands for more intensive research, including the mechanism of anodic smoothing. The anodic smoothing characteristics of PECF are analyzed through a developed mathematical model. The main influencing factors such as the finishing time, the interelectrode gap, the applied voltage and the rotational speed of electrode have been examined. The predictive values based on the developed mathematical model are found to be in reasonable agreement with the experimental values. The surface roughness Rz ranges from 3 m to 1.22 m. The research achievement through various parametric studies can be used as a guideline for the operation of a PECF system. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Surface quality of the workpiece has great influence on their service performance and lifespan. In particular, those workpieces with frictional pair, abrasion resistance, fatigue resistance and the friction force between frictional surfaces rely on the surface quality to a great extent, such as bearing ring and gear. Thus, the surfaces as the frictional pair need to be finished so as to improve the surface quality of the workpiece. Conventional technique such as polishing by hand heavily depends on the operator’s experience. Hand polishing will result in non-uniform residual stress due to the contact between the tool and the workpiece. Surface cracks and depressions can reduce the service life of the part (Hocheng and Pa, 1999). Electrochemical finishing (ECF) and the application of electrochemical machining (ECM), can overcome the above mentioned shortcomings and produce the workpiece with good surface quality efficiently without residual stress or burr (Phillips, 1986; Masuzawa and Sakai, 1987). The ECM process was first patented by Gusseff in 1929. The principle of ECM was presented by Faraday in the 18th century. ECM has many advantages over traditional machining such as its applicability regardless of material hardness, no tool wear, high material removal rate, smooth and bright surface and production of components of complex geometry (Rajurkar et al., 1999). The use of pulsed power and hence the ability to use narrower interelectrode gaps
∗ Corresponding author. Tel.: +86 411 84708422; fax: +86 411 84708422. E-mail address: [email protected] (W. Xu). 0924-0136/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2010.01.016
has yielded the major breakthrough in improving ECM precision (Rajurkar et al., 1993, 1995; Kozak et al., 1994; Rosenkranz et al., 2005). ECM is considered to be a promising method for finishing or polishing due to its micro-removal characteristics (Rajurkar et al., 1999). ECF is the same as ECM with very limited and low removal rate (Mahdavinejad and Hatami, 2008). ECF has a low-level electrochemical dissolution process in which the tool is the cathode and the workpiece is the anode in an electrolytic cell (Ramasawmy and Blunt, 2007). In many applications, a smooth and bright surface is essential and ECF is a better technique for approaching mirrorlike surfaces on many metals (Landolt et al., 2003). Many industrial applications of surface finishing have been reported. Shen (1995) used NaNO3 as the electrolyte for the electropolishing of die surfaces. The results showed that the surface roughness of workpiece decreased with the increase of current density, flow rate and concentration of the electrolyte. Moreover, polishing with pulsed direct current was found better than that of continuous direct current. Sun et al. (2001) developed a new MREF-ECM (modulated reverse electric field electrochemical machining) polishing process for hard passive alloys surface finishing. Hocheng and Pa (2003) presented a new application of electropolishing using a lowcost disc-form electrode offering fast improvement of the surface roughness of SKD61. Ramasawmy and Blunt (2007) studied the effect of parameters of electrochemical polishing on the 3D surface texture parameters of EDM surfaces of tool steel specimens. Pa (2008) investigated an efficient finishing process using a low-cost electrode of end turning surface finishing. Despite the considerable amount of experimental research, there are many fundamental
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
853
to the motion of the cathode. The metal removal thickness of the anodic surface is dS. According to Eq. (1), the reduction in height of the anodic surface in time dt is given by: dS =
e kv (U0 − U) dt S
(2)
where kv is the volumetric electrochemical equivalent and it can be computed as follows: Fig. 1. Principle of PECF of bearing inner ring raceway.
kv =
aspects of PECF process, such as the basic mechanism of the anodic smoothing, which need to be understood further. The PECF is used to reduce the surface roughness of the workpiece. In PECF, with the increase of finishing time, a certain amount of material is removed through the anodic dissolution. In order to maintain the precision of the workpiece, the total removal thickness should not be too large. Thus, it is better to achieve lower surface roughness of the workpiece by removing smaller metal surface thickness. In this work, a mathematical model of the PECF process has been developed for predicting particular important features such as the total removal thickness and the maximum height of the assessed profile. Moreover, this paper emphasizes features of the mathematical model for correlating the interactive and higherorder influences of the various finishing parameters, such as the interelectrode gap, the applied voltage, the finishing time, and the rotational speed of electrode, for achieving of controlled PECF. 2. Theoretical modeling 2.1. Fundamentals of PECF Fig. 1 illustrates the principle of PECF of bearing inner ring raceway. The PECF bases on an anodic dissolution process. Workpiece and tool are respectively anode and cathode, in which two electrodes are separated by electrolyte. When an electric current passes through the electrolyte, the material on the workpiece surface is dissolved. As the tool scans over the surface of the workpiece, the whole surface is finished. According to Faraday’s law and Ohm’s law, the anode recession rate of the workpiece surface can be calculated as follows (McGeough, 1974): r˙ a =
e kv (U0 − U) S
(1)
where is the current efficiency of anodic dissolution, e is the electrolyte conductivity, kv is the volumetric electrochemical equivalent, S is the interelectrode gap, U0 is the applied voltage, U is the over potential value. 2.2. Mathematical modeling of ideal surface in PECF Fig. 2 shows the gap between two electrodes which is filled with electrolyte. The initial interelectrode gap is equal to S0 . During the PECF processing, the initial interelectrode gap increases according
A za F
(3)
where a is the density of anode metal, F is Faraday’s constant, A is the atomic weight, z is the valency. By integrating Eq. (2) over the time from 0 to tp with an initial interelectrode gap S0 , the interelectrode gap equation can be computed as follows: S = (S0 2 + 2e kv (U0 − U)tp )
1/2
(4)
where S0 is the initial interelectrode gap, the electrolyte conductivity e of the multi-phase medium can be estimated by the following Brugeman equation (McGeough, 1974): e = 0 (1 + ˛T )(1 − ˇ)
3/2
(5)
where T = T − T0 is temperature increment, T0 is the inlet electrolyte temperature, ˛ is the electrolyte temperature coefficient, 0 is the inlet electrolyte conductivity and ˇ is the gas void ratio in the electrolyte. The major factors that influence the electrolyte electrical conductivity are the heat generation and gas bubble. However, in this work, the influences can be neglected. On the one hand, since the process is a finishing rather than a forming process, the electrolyte temperature changes do not exceed 1 ◦ C. This is due to the rotation of the electrolyte and the fast rotational speed of electrode. On the other hand, the working area between two electrodes is smaller than the machined area. Therefore, the assumption of constant conductivity is feasible. The following conditions are assumed for one-dimensional twophase homogeneous flow: (1) The current efficiency of anodic dissolution is constant. (2) The total overpotential U is constant. (3) The electrolyte conductivity e is constant. With these conditions and assumptions, the anodic smoothing equation of PECF using a rotational electrode can be described as follows: m
S 2 = S0 2 + 2
j=1
tp
Cj (t)dt
(6)
0
where Cj (t) = e kv (U0j (t) − Uj (t)), and based on above assumptions, Cj (t) can be regarded as constant C. Since relation between the total finishing time t and the total pulse number m is m = t/tp (with being the pulse duty factor tp /(tp + to )), Eq. (6) becomes: S 2 = S0 2 + 2Cmtp = S0 2 + 2Ctef
(7)
where mtp is the effective finishing time. It can be seen that the effective finishing time is influenced by the pulse duty factor , the ratio of Lc to Lp (Lp = d) and the total finishing time t. Thus, the effective finishing time can be described as: tef = ·
Fig. 2. Scheme of PECF on ideal surface.
Lc · nw t dnw
(8)
where Lc is the thickness of the cathode, d is the diameter of the workpiece, nw is the workpiece rotational speed. Taking into
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Fig. 3. Scheme of PECF on real surface.
account the relationships (7) and (8), Eq. (7) can be expressed as: S 2 = S0 2 + 2C
Lc ·t d
(9) Fig. 5. Effect of finishing time on the maximum height of the assessed profile Hn .
Although the PECF process becomes idealized with these assumptions, the developed mathematical model is helpful to understand the PECF processing characteristics.
Hn
2.3. Mathematical modeling of real surface in PECF The real metal surface does not look like that illustrated in Fig. 2. As shown in Fig. 3, it is the uneven and peak-like profile. When the cathode scans over the anodic surface, the dissolution rate of the wave crests of the surface profile is faster than the wave troughs, which results from the concentration of current lines on the crests of surface profile. Proceeding with anodic dissolution, the workpiece surface is gradually smoothed. In order to make further analysis, the real surface profile in Fig. 3 is simplified as shown in Fig. 4. Therefore, according to Eq. (9), the total removal thickness Sn can be expressed as: Sn =
S02 + 2C
Lc ·t d
1/2
− S0
(10)
The Sn is the total removal thickness from the surface of the workpiece after time t in PECF. In Fig. 4, it can be seen that H0 is the initial sum of height of the largest profile peak height and the largest profile valley depth with an evaluation length. It can be expressed as: H0 = ht − hp
(11)
After the cathode scans over the surface of the workpiece one time, the sum of height of the largest profile peak height and the largest profile valley depth with an evaluation length is H1 . It can be calculated as follows: H1
= h1t − h1p =
2
ht + 2C
Lc d
1/2
2
− hp + 2C
Lc d
1/2
Fig. 4. Simplified model of real metal surface.
So, after the cathode scans is over the surface n times, the maximum height of the assessed profile Hn is calculated as follows: = hnt − hnp =
h2t + 2C
Lc ·t d
1/2
− h2p + 2C
Lc ·t d
1/2
(13)
In addition, it can be found that the maximum height of the assessed profile Hn is the Rz from definition of the evaluation parameter of surface roughness (ISO 4287:1997). From above expression, it is clear that the total removal thickness and the maximum height of the assessed profile depend on many factors, such as the interelectrode gap, the finishing time, the applied voltage. Further analysis is to be carried out in the following sections. 3. Parametric analysis of PECF processing Based on the developed mathematical model of PECF process a parametric analysis has been carried out to evaluate the effect of various process parameters on the total removal thickness Sn and the maximum height of the assessed profile Hn . The theoretical calculations have been carried out with initial values U0 = 16 V, U = 0, kv = 1.7 mm3 /A min, e = 13 A/V m, = 0.2. Based on Eq. (13), studies are carried out to analyze the effects of the various process variables on the maximum height of the assessed profile Hn . Fig. 5 shows the relationship between the maximum height of the assessed profile and the finishing time at different interelectrode gap. It is obvious that as the finishing time increases, the maximum height of the assessed profile decreases. Theoretically, it takes an infinite time to remove the surface irregularities completely. In practice, as soon as the Hn goes below a pre-assigned allowable value the process is completed.
(12)
Fig. 6. Effect of finishing time on total removal thickness Sn .
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
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Table 3 Components of workpiece materials. Element
C
Si
Mn
Cr
Fe
wt%
0.95–1.05
0.15–0.35
0.20–0.40
1.3–1.65
Others
Fig. 7. Experimental set-up.
Table 1 Experimental parameters. Parameters
Value
Pulse frequency Pulse on-time (tp ) Maximal current Applied voltage (U0 ) Interelectrode gap (S0 ) Cathode thickness (Lc ) Duty factor () Electrolyte
5–20 kHz 10–200 s 400 A 0–20 V 0.1, 0.2, 0.3 mm 0.5 mm 0.2 NaNO3 (15 wt%)
Fig. 6 shows that the total removal thickness increases with the increase of the finishing time. It is clear that as the interelectrode gap decreases, the total metal removal thickness increases. This is due to the increase of current density as the interelectrode gap decreases, but too small gap should be avoided because it causes electric sparks and shorts. If the current density is too high it may cause the formation of heat-affected zones, and it finally results in improper surface finish and low accuracy. 4. Experimental tests Fig. 7 shows the set-up of the PECF system for carrying out finishing operations on the bearing inner ring raceway. The operation has been shown schematically. The workpiece and the tool are being securely held by a three-jaw chuck and a clamp respectively. Both the workpiece and the tool are insulated from the main body in order to only focus an electrochemical reaction between the workpiece and the tool. For using a rotational electrode in PECF, the working area between two electrodes is smaller than the machined area which shortens the distance to expel the dissolution products. The electrolyte, which is generally a concentrated salty solution, is pumped at high velocities through the machining gap in order to remove the reaction products and to dissipate the heat generated. The electrolyte flow system consists of a filter, pump, electrolyte tank, throttleer and flowmeter. The function of this system is to ensure adequate amount of clean electrolyte flow in the gap. The tank, pipe lines, valves are made of PVC. The pump is corrosion resistant centrifugal type pump. The pulse DC power supply is adopted in this system. The experimental and workpiece parameters are shown in Tables 1 and 2.
Fig. 8. Comparison of the maximum height of the assessed profile Hn (Rz) between experimental results and calculated results.
The workpiece material is GCr15 with hardness 60 HRC, the tool electrode is made of copper and the main component of the electrolyte is NaNO3 . Passive electrolytes are known to give better machining precision. This is due to the formation of oxide films and oxygen evolution in the stray current region (Bhattacharyya et al., 2005). The workpiece material composition is shown in Table 3. 5. Results and discussion Experimental results are graphically represented to show the influence of various finishing parameters on the maximum height of the assessed profile Hn and total removal thickness Sn . Fig. 8 shows that the maximum height of the assessed profile Hn , namely Rz, decreases with the increase of the finishing time. The decrease of the maximum height Hn reflects the decrease of the surface roughness and the improvement of the surface quality. It has been observed from Fig. 8 that the reduction rate of the maximum height Hn decreases with the increase of finishing time. The slope change is well-known to be the result of changes in the interelectrode gap. For applied voltage equal to 16 V, nw = 200 r/min, S0 = 0.2 mm, the calculated results can be obtained from Eq. (13) and the experimental results are measured by Talysurf profilometer. The measured Rz decreases from 3 m to 1.22 m while the finishing time increases from 0 min to 4 min. As illustrated in Fig. 8, the calculated and experimental results show the same trend.
Table 2 Workpiece parameters. Parameters
Value
Initial surface roughness (Rz) Materials Surface hardness Size Rotational speed (nw )
3 m GCr15 60 HRC Ø70 × 20 mm 120–380 r/min
Fig. 9. Comparison of total removal thickness Sn between experimental results and calculated results.
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N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
Fig. 10. Comparison of the surface micro-topography of workpiece before and after PECF (S0 = 0.2 mm, nw = 200 r/min): (a) before PECF, Rz = 3 m; (b) after PECF, Rz = 1.22 m.
Fig. 9 gives the comparison of the calculated values of total removal thickness Sn and those measured values from experiments. The total removal thickness Sn is equal to about 210 m while the finishing time increases from 0 min to 4 min. Their agreement is quite clear for t < 2 min, but discrepancies occur when t > 2 min. This is mainly due to the reduction rate of Hn decreases. At the beginning of PECF, the interelectrode gap between the two electrodes is small. During the process of PECF, the gap becomes larger, which will slow down the finishing process by decreasing the electric field intensity as shown by Eq. (1). It can be seen from Eq. (10) that the total removal thickness Sn is not influenced by the rotational speed of workpiece. However, it has been obtained form the experiments that there exists an optimal rotational speed for the surface quality of workpiece. It is not good for the surface quality of workpiece while the rotational speed too fast or too slow than the optimal rotational speed nw = 200 r/min. The gap has a great effect on the anodic dissolution. When the gap is set small, the reaction will be acute. If the gap is set smaller than 0.1 mm, the undesired electric discharge will happen. If the current density is set larger than 100 A/cm2 , it may cause the formation of heat-affected zones. Several reasons account for the errors between calculated and experimental results. Firstly, the anode consists of multiple metal and nonmetal elements. However, it has been considered as simple metal in the mathematical model. Secondly, the machining traces in pre-machined surface influence the measurement results. Thirdly, some parameters in mathematical model have been idealized. The average percent error (APE) is calculated with a modified equation from Beamish and Fournier (1981): 1 APE = N N
i=1
Xi − Yi Xi
× 100%
(14)
where N is the number of data points, Xi is the calculated values and Yi are the experimental values. In this paper, the APE between the experimental values and calculated values of the maximum height of assessed profile Hn in Fig. 8 is 8.77%. The APE between the experimental values and calculated values of total removal thickness Sn in Fig. 9 is 25.49%. Fig. 10 shows the surface micro-topography of workpiece before and after PECF. It can be found that the surface micro-topography finished by PECF is much different from original mechanically machined surface profile. As shown in Fig. 10, wave crests of original mechanically machined surface profile disappear quickly after PECF. This is mainly due to the concentration of current lines on wave crests of a surface profile thus leading to a locally higher dissolution rate (Landlot, 1987), which is popularly considered as an
explanation for the finishing mechanism. It can be also verified by the following analysis. In Fig. 3, the rate of reduction of the point P in the wave crests of surface profile is: r˙ p =
C Sp
(15)
The rate of reduction of point T in the wave troughs of surface profile is: r˙ t =
C St
(16)
Therefore, the ratio of Eqs. (15) and (16) is: r˙ p ıp + ıt C St = · =1+ Sp C Sp r˙ t
(17)
Thus, it can be seen from Eq. (17) that r˙ p /r˙ t > 1, that is r˙ p > r˙ t . The rate of anodic smoothing equals to the difference in dissolution rate between wave crests and wave troughs. After the period of finishing time, the anodic surface is gradually smoothed. 6. Conclusions In the present work, an idealized mathematical model has been developed and verified experiments have been performed with different finishing parameters. Some key findings both the theoretical modeling and the experimental investigation are listed as follows: (1) PECF proves an effective method to reduce the surface roughness Rz from 3 m to 1.22 m in 4 min. (2) The mathematical model is capable of explaining the mechanism of anodic smoothing and predicting the results with reasonable accuracy. The model can be utilized for controlled PECF operation. (3) From the developed mathematical model, in order to reduce several microns of the maximum height of the profile, it needs to remove a few hundred of microns from the workpiece surface. For example, the total removal thickness is equal to 210 m in order to reduce the maximum height of the profile Hn from 3 m to 1.22 m. (4) The experimental results show that the surface microtopography finished by PECF is much different from original mechanically machined surface. The wave crests of original mechanically machined surface profile disappear quickly after PECF.
N. Ma et al. / Journal of Materials Processing Technology 210 (2010) 852–857
Acknowledgements The authors are grateful to the financial aid to this projects supplied by National Natural Science Foundation of China (Grant No. 90923022). Appendix A. The purpose of this appendix is to indicate step by step how to calculate the total removal thickness Sn and the maximum height of the assessed profile Hn . Giving initial values: Applied voltage U0 , over potential U, the volumetric electrochemical equivalent kv , electrolyte conductivity e , duty factor , initial interelectrode gap S0 , cathode thickness Lc , the diameter of the workpiece d, initial surface roughness Rz. A.1. Calculation of Sn The total removal thickness Sn is determined by Eq. (A1) Sn =
S02 + 2C
Lc ·t d
1/2
− S0
(A1)
where C = e kv (U0 − U) The total removal thickness Sn can be obtained by substituting above initial values into Eq. (A1). A.2. Calculation of Hn The maximum height of the assessed profile Hn is determined by Eq. (A2) Hn
= hnt − hnp =
h2t + 2C
Lc ·t d
1/2
− h2p + 2C
Lc ·t d
1/2
(A2)
According to Fig. 4, the distance between the cathode and the largest profile valley is ht = S0 +
Rz 2
(A3)
The distance between the cathode and the largest profile peak height is hp = S0 −
Rz 2
(A4)
857
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