A Study on Universal Factor Determining the Evolution of Surface Roughness During Electrochemical Polishing

Electrochemical polishing (ECP) is widely used for scratch- and damage-free finishing of metal components. Though the polishing effect of ECP has been confirmed in many researches, the influence of polishing parameters on evolution of surface roughness is still ambiguous owing to the use of different ECP systems. In this paper, the universal factor determining the evolution of surface roughness during ECP is studied by theoretical analysis as well as experiments. Theoretical analysis based on viscous layer mechanism demonstrates that the material removal thickness is the key parameter governing the roughness evolution of the polished surface regardless of other parameters including the voltage, current and electrolyte concentration and so forth. A series of experiments were designed and carried out to verify the proposed hypothesis. Both the experimental results and already published researches proved the validity and universality of the newly developed hypothesis on surface roughness evolution. This work is of great significance for further understanding the finishing mechanism of ECP and process control for its practical applications.


Introduction
The surface quality can seriously affect the appearance and working performance of metal components. Polishing is an important method to enhance the quality of a surface. Selecting an economical and efficient polishing method is crucial for the processing of high-quality surfaces. At present, chemical mechanical polishing (CMP) [1,2] is the most widely used polishing method. However, CMP is difficult for the finishing of intricate geometries, such as medical implants and optical molds. In addition, the polishing efficiency of CMP is seriously low which is unacceptable for mass production of metal components [3][4][5].
Besides, electrochemical polishing (ECP) [6][7][8] is a widely used metal finishing technique because of its high material removal efficiency, allowance for complex geometries, and no subsurface damage owing to its anodic dissolution mechanism. Since the discovery of ECP technology, relevant material removal mechanisms have been proposed and improved over time. According to the most widely accepted viscous layer theory [9], the dissolved products accumulate on the anode surface and form a highly resistive viscous layer during ECP. The viscous layer thickness determines its electrical resistance and the dissolution rate of the metal. Therefore, surface protrusions with shallow viscous layer are preferentially dissolved, and the rough surface becomes smooth. Later, passive film theory [10], duplex salt film model theory [11] and adsorbate acceptor mechanism [12] were proposed respectively. All these theories believed that the viscous layer is indispensable in the ECP process. Although these theories can explain the polishing phenomenon based on the material removal mechanism, they are ineffective to optimize the ECP parameters.
At present, numerous experiments are required to establish the evolution laws of surface roughness and optimize the polishing parameters of ECP. Some of the fundamental ECP parameters used for optimization are applied voltage/current, electrolyte concentration, electrolyte temperature, and polishing duration, which are also coupled simultaneously. In different researches on ECP, different systems are used by different researchers and it is almost impossible to fully control the amount parameters in the polishing process. Therefore, the literary-reported results are difficult to repeat and their conclusions provide extremely limited guidance about the process. And the reason is all the above conclusions are obtained based on specific polishing parameters. In summary, the current researches have not broken through the premise of experimental conditions or polishing parameters, and this means the governing parameter of the evolution of surface roughness in ECP is still undiscovered.
In this study, a novel understanding about the roughness evolution in ECP is proposed.
Based on theoretical analysis and experimental validation, it is proved that the material removal thickness is the universal factor determining the evolution of surface roughness during ECP.

Experimental
Tungsten samples (Xin Ji Metal Materials Co., Ltd. China) used in experiments are more than 99.99% pure and taken from the same batch to ensure the uniformity of the samples. The size of the workpiece is 3×13×13 mm 3 . The samples were grounded for 30 s on a new 180 grit sandpaper. Later, the samples were further ground for another 10 s with 600 grit sandpaper.
The roughness of the surface obtained by this process is about 200 nm, which is nearly uniform throughout the workpiece surface. All the samples in this paper, unless otherwise specified, are prepared following the same surface treatment to obtain similar initial roughness and micro-morphology.
Experiments were conducted in a 1000 ml glass beaker containing the NaOH electrolyte.
The workpiece was connected to the anode of the DC power supply. During polishing, only the front face (13×13 mm 2 ) of the workpiece was exposed to the electrolyte, while an insulating clamp covered the rest of the substrate. The cathode was a platinum sheet with an area of 20×20 mm 2 . The polishing voltage was provided by the Keysight E3649A dual-channel DC power supply. The analytical grade NaOH electrolyte used in this study was provided by Merck, Germany.
The surface roughness before and after polishing was measured by white light interferometer (WLI, Taylor Hobson) with a 10X objective lens. The obtained image area was 1.66×1.66 mm 2 , with a total of 2048×2048 pixels. The parameter of average surface roughness Sa (ISO25178) was used to evaluate surface quality. Besides, the power spectral density (PSD) function [13,14] calculated by the Fourier transform of the discrete measured data was also used to analyze the roughness on specific spatial frequencies. A scanning electron microscope (SEM, Hitachi s-4800) was used to investigate the surface morphologies.
The material removed after polishing was determined by a precision electronic balance (Mettler Toledo, ME203).

ECP of tungsten
The following experiment verified the performance of the polishing system. The polishing voltage used in the experiment was 15 V, the electrolyte concentration was 1wt%, the interelectrode gap was 40 mm, and the polishing time was 90 min. Since the surface roughness largely depends on the selected measurement position. The repeated positioning analysis method was adopted to eliminate the error caused by the random measurement positions and accurately evaluate the polishing ability of ECP. The details about the repeated positioning method and the analysis of positioning accuracy can be found in Ref. [15]. The surface quality before and after ECP is shown in Fig. 1. Tungsten substrate images before and after polishing are shown in Fig. 1(a), where a dull surface is transformed into a mirror-like glossy surface after ECP. As shown by the SEM images in Fig. 1 Wang et al. [16] found that surface polishing strongly depends on the applied voltage.
According to the results, surface polishing was realized when the polishing voltage was greater than 5 V. However, the viscous layer did not develop, and the surface polishing was not realized below 5 V; it was defined as the etching stage of ECP. The set of ECP parameters that can achieve surface polishing are defined as polishable parameters. Accordingly, it is essential to study the fundamental factors affecting the surface roughness evolution in the range of polishable parameters of ECP. Therefore, in Section 4, factors affecting the surface roughness evolution in ECP are theoretically analyzed based on the viscous layer theory.

Theoretical analysis
The viscous layer theory is the most widely accepted electrochemical polishing mechanism, according to which a viscous layer with electrical resistance much higher than the electrolyte is formed on the anode surface during ECP. The schematic diagram of viscous layer theory is shown in Figure 2(a). The viscous layer at the convex position of the surface is relatively thinner and less resistive, allowing higher current flow and a higher material removal rate; on the contrary, the material removal rate at the concave position is lower. As the polishing progresses, the surface is gradually smoothed, and the surface roughness is reduced. The current flowing through point A can be expressed as follows:

Viscous layer
Anode Surface profile before ECP Surface profile after ECP where U is the applied voltage, k is the resistivity of the viscous layer, S is the unit area, and l A is the viscous layer thickness at position A.
It should be noted that when material removes from the surface, two possible changes may occur in the viscous layer: (i) the upper surface of the viscous layer remains unchanged and viscous layer becomes thicker, (ii) the upper surface of the viscous layer moves downward and the viscous layer remains unchanged. The first case is adopted in this paper mainly due to two reasons. As direct evidence, the thickness evolution of the viscous layer during ECP has been observed by using the in-situ X-ray nano-tomography, which shows an increase in the viscous layer thickness [17]. Secondly, current evolution (Fig. 3) during ECP also provides evidence of an increase in the viscous layer thickness. According to Fig. 3, the current continuously fluctuates during the ECP process. The gradually decreasing current means the viscous layer gradually thickens. A sudden fluctuation may be caused by the local breakdown or shedding of the viscous layer. An abrupt but minute change in current has little impact on the material removal process, therefore, in general, the viscous layer thickens during ECP.
During the polishing time t, the total removal volume at position A is as follows： , then K is a constant and represents the material properties in the formula.
The material removal thickness d A during the polishing time t at position A can be expressed as: Further solving equation (4), we get: According to equation (5), the removal thickness positively correlates with voltage and processing time, which is consistent with the experimental results. The height difference between A and B positions after machining is given as follows: According to equations (5) and (6), if the removal thickness d A at position A is the same in different processes, ηUt/k will be the same, then Δh also remains the same. If A is the highest point on the surface, its height difference from a random point on the surface after polishing depends on the removal thickness d, which also determines the surface roughness after polishing.
Based on the above theoretical analysis, the ECP processed surface roughness is closely related to the removal thickness. However, the removal thickness itself is determined by ECP voltage, duration, and electrolyte concentration. According to the author's knowledge, this study is the first to propose variation in the surface roughness based on the material removal thickness. Previous studies have investigated surface roughness as a function of the polishing parameters, such as voltage and electrolyte concentration, while completely ignored the role of material removal thickness.

Experimental validation
A series of experiments were carried out to verify the previously discussed theoretical hypothesis. By adjusting the polishing duration, the same material removal thickness was achieved under different polishing parameters, and then the surface roughness after polishing was measured. In experiment set 1, the effect of different voltages (10 V, 15 V, 20 V) was investigated under the same electrolyte concentration (1%). In experiment set 2, the effect of different electrolyte concentrations (0.5%, 1%, 1.5%) was investigated under the same polishing voltage (15 V). The material removal thickness under different working conditions was calculated by combining the mass reduction with tungsten density and the workpiece geometry. The detailed experimental parameters and results are given in Table 1.  Figure 4 shows the PSD curves and WLI topographies obtained after experiment set 1 (see Fig. 4(a)) and experiment set 2 (see Fig. 4(b)). It should be noted that the PSD curves before polishing are coincident, which describe similar features of the substrate obtained after initial grounding. After both sets of polishing experiments, the PSD curves decreased significantly due to the reduction in surface roughness. Besides, PSD curves after polishing are also coincident, which is attributed to the similar surface roughness. The WLI topographies of workpieces after polishing also endorsed the PSD results. In conclusion, if the initial surfaces are identical, comparable final surface roughness values can be achieved by removing the same thickness regardless of the applied voltage and electrolyte concentration. Following the procedure outlined in Section 2, a series of surfaces with similar roughness (~200 nm) were prepared. All the workpieces were marked to specify the surface measurement position before and after polishing. Subsequently, the workpieces were polished for the different durations by randomly selecting applied voltage and electrolyte concentrations while keeping the rest of the parameters fixed. According to the results shown in Fig. 5, similar removal thickness on the abscissa finds no significant difference in the surface roughness. It means, as long as the material removal thickness is identical, post-processing surface roughness remains similar regardless of the polishing parameters.

Fig. 5 Evolution of surface roughness with material removal thickness in ECP technology
The proposed conclusion is further verified by the ECP experiments on stainless steel and copper, the most widely used industrial metals. The electrolyte used for polishing stainless steel is phosphoric acid and sulfuric acid with a volume ratio of 2:1, and the electrolyte used for polishing copper is phosphoric acid and deionized water with a volume ratio of 4:1. The initial surface roughness of all the samples was ~200 nm. Figure 6 shows the surface roughness of stainless steel (Figs. 6(a-c)) and copper (Figs. 6(d-f)) after ECP at different applied currents (1, 2, and 3 A) while keeping the material removal thickness constant. As evident from Fig. 6, the surface roughness values for each material are comparative after ECP when the material removal thickness is similar. In addition, it can be stated that the proposed mechanism is independent of the applied current and nature of electrolytes when material removal thickness is constant, which is also in agreement with the theoretical analysis given in Section 4.  Fig. 7(a). However, a fundamental in-depth analysis was not performed. Similarly, stainless steel 316L was processed in phosphoric acid and sulphuric acid electrolyte by using the Taguchi method [19].
According to the results shown in Fig. 7(b) , under the same electrode gap, the polished surface roughness is comparable when the product of applied current and machining time is constant. In addition, the higher the value Q, the better the roughness, that means the roughness is not determined by the voltage or current, but by the material removal thickness.
Such results are in good agreement with formula derivation in Section 4. Compared with the experimental results and the results reported by literature, it is easy to conclude that the hypothesis we proposed is generic, regardless of the polished material or working electrolyte.
Furthermore, these results agree with the theoretical analysis since the parameter K representing material properties is like a coefficient. Regardless of the changes in the value of K, the conclusion remains valid.  A key comparison have been presented between the conventional approach and the universal factor approach in Fig. 8. Since the discovery of ECP technology, much research work on the surface roughness evolution during ECP has been conducted. Conventional approach usually obtained the evolution laws of surface roughness at the premise of specific experimental conditions or polishing parameters, which leads to extremely limited guidance for the practical application of ECP. In contrast, our work reveals the decisive factors affecting surface roughness evolution during ECP and obtains the essential evolution law of surface roughness independent of polishing parameters. The theoretical derivation, experimental results, and results reported by researchers all strongly support the correctness and universality of these conclusions.

Conclusions
Due to the material removal nature of anodic dissolution, ECP has many advantages and is a

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Availability of data and materials
All data generated or analyzed during this study are included in this published article.

Declaration of Competing Interest
The authors declare that there are no conflicts of interest.