*Article* **Numerical Study on the Cavitation Characteristics of Micro Automotive Electronic Pumps under Thermodynamic Effect**

**Kaipeng Wu 1,†, Asad Ali 1,† , Changhong Feng 2,\*, Qiaorui Si <sup>1</sup> , Qian Chen <sup>3</sup> and Chunhao Shen <sup>1</sup>**


**Abstract:** In order to study the influence of thermodynamic effects on the cavitation performance of hydromechanics, the Singhal cavitation model was modified considering the influence of the thermo-dynamic effects, and the modified cavitation model was written into CFX using the CEL language. Numerical simulation of the cavitation full flow field at different temperatures (25 ◦C, 50 ◦C and 70 ◦C) was carried out with the automotive electronic water pump as the research object. The results show that the variation trend of the external characteristic simulation and experimental values is the same at all flow rates, and the calculation accuracy meets the subsequent cavitation demand. With the increase in temperature, the low-pressure area inside the automotive electronic pump's impeller decreases. NPSHr decreases and the cavitation resistance is enhanced. During the process of no cavitation to cavitation, the maximum pressure pulsation amplitude in the impeller channel gradually increases. The generation and collapse of cavitations cause the change of pressure pulsation in the internal flow field, causing pump vibration.

**Keywords:** micro automotive electronic pump; computational fluid dynamics; numerical simulation; experimental techniques; cavitation; thermodynamic effects

## **1. Introduction**

Automotive electronic pumps are core components of internal combustion engine cooling systems for drainage and irrigation products, which need to be operated at a high temperature and high speed for a long time. Because the physical parameters of coolant change with temperature, it is easy to induce cavitation of the pump and then affect the stable operation of the system. Cavitation is a flow phenomenon involving a phase change process in which the thermodynamic effect exists during the occurrence, development, and collapse of the bubble [1–5]. As the vaporization medium needs to absorb heat from the surrounding liquid, the temperature will have a certain effect on the physical parameters of the medium, which in turn affects the process of heat exchange during the vaporization process. Therefore, the existing cavitation model should be appropriately modified to predict the cavitation phenomenon accurately, and the source term considering the thermodynamic effect should be added.

Many scholars have studied cavitation flow under thermodynamic effects. In terms of experiments, Fruman et al. [6] proposed a cavitation correction model considering cavity heat transfer by analyzing the heat transfer process in the cavitation process, using R114 as the test object, and found that the cavitation performance improved with the increase of temperature. Franc et al. [7] made a cavitation test of Freon R-114 flowing through the induced wheel at different temperatures and investigated the effect of temperature on

**Citation:** Wu, K.; Ali, A.; Feng, C.; Si, Q.; Chen, Q.; Shen, C. Numerical Study on the Cavitation Characteristics of Micro Automotive Electronic Pumps under Thermodynamic Effect. *Micromachines* **2022**, *13*, 1063. https://doi.org/10.3390/mi13071063

Academic Editor: Stelios K. Georgantzinos

Received: 3 June 2022 Accepted: 29 June 2022 Published: 1 July 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the thermodynamic effect of significant fluid cavitation. By comparing the experimental phenomena of different temperature water around NACA0015 hydrofoil at the same cavitation number, Cervone [8] found that the difference in the water vacuole size was not significant at 293 K and 323 K; however, the vacuole length decreased significantly at 343 K and gave a reasonable explanation for this phenomenon. Yoshida et al. [9,10] systematically investigated the thermal effect on the cavitation performance and cavitation instability of the induced wheel by using liquid nitrogen as the working medium. Gustavsson et al. [11,12] carried out a cavitation flow test of water and fluorinated ketone around NACA0015 hydrofoil separately and found that the cavitation length of fluorinated ketone was shorter than that of water at the same cavitation number and the cavitation thermal inhibition effect was more obvious.

With the development of computer technology and computational fluid dynamics [13–15], numerical simulation has become an essential tool for studying cavitation problems. Deshpande et al. [16] built on the Navier-Stokes equation with compressibility and pseudotime-step progression by coupling the energy equation, and developed a thermodynamic model applicable to the cavitation of low-temperature fluids. Franc et al. [17] performed an analysis founded on the Rayleigh-Plesset equation, modified the cavitation model with temperature as one of the influencing factors of cavitation, and validated it accordingly. Hosangadi et al. [18] described a compressible multiphase flow formulation to account for the energy balance and variable thermodynamic properties of the fluid, identified fundamental changes in the physical characteristics of the cavity when thermal effects are significant, and suggested that the heat transfer model assumed by Hord in the B-factor model variant is a poorer approximation. Watanabe et al. [19] simulated the heat transfer process between the bubble and the work mass using a one-dimensional unsteady-state thermal conductivity model. They analyzed the flow using the singularity method. Using an agent model, Goel et al. [20] synthesized the evaporation and condensation coefficients and the degree of influence of the thermophysical parameters on the objective function in the cavitation model. They gave optimal equation coefficients for the cavitation model. Tani et al. [21] applied the B-factor theory to correct the saturated vapor pressure variation brought about by temperature differences in the cavitation process and proposed a cavitation model considering thermodynamic effects. Tseng et al. [22] established an interface-based cavitation model, modified the model according to the low-temperature fluid medium, and investigated the thermodynamic effects by solving the energy equation in the full basin and combining the available physical parameters to verify the validity of the calculation method and the model. To study thermodynamic effects in different fluids at different temperatures, De et al. [23] proposed a stable semi-one-dimensional model based on the Rayleigh-Plesset equation to study the internal cavitation considering thermodynamic effects. Research on cavitation under thermodynamic effects has made some achievements, but it mainly focuses on inducer and airfoil flow cavitation. The research on the internal flow pattern and cavitation characteristics under a thermodynamic effect in small centrifugal pumps such as automobile electronic pumps remains to be further studied.

This study is focused on the cavitation flow field characteristics at different operating points of a high-speed automotive electronic water pump at a rated speed (5400 r/min), modifying the Singhal cavitation model considering the influence of thermodynamic effects, and carrying out numerical simulations of the cavitation full flow field at different temperatures (25 ◦C, 50 ◦C and 70 ◦C) based on the modified cavitation model to investigate the cavitation performance, bubble distribution law and pressure pulsation characteristics of an automotive electronic water pump at different temperatures, providing a theoretical basis for preventing and reducing the cavitation phenomenon of an automotive electronic pump.

#### **2. Three-Dimensional Model and Grid Division**

#### *2.1. Model Pump Parameters*

In this study, an automotive electronic water pump with a specific speed of 81 is used as the object. The working environment temperature of the pump is −40 ◦C to 80 ◦C, which is a micro high-speed pump driven by a DC brushless motor and controlled by an electronic unit. Table 1 shows the main parameters of the automotive electronic pump.

**Table 1.** Automotive electronic water pump parameters.


The automotive electronic water pump structure uses a closed centrifugal impeller and spiral pressurized volute as the main hydraulic components and an integral molding of the rotor and motor rotor. The whole pump body is divided into a pump barrel, impeller, and motor base, as shown in Figure 1.

**Figure 1.** Structure diagram of automotive electronic water pump: (**a**) pump barrel, (**b**) impeller, and (**c**) motor base.

#### *2.2. Division of Computational Grid*

Due to the complex structure, ICEM CFD software was used for unstructured meshing of the computational domain of the main overcurrent components of the automotive electronic water pump, as shown in Figure 2. To consider the calculation cycle and its reliability of numerical calculation, grid-independent analysis was carried out, as shown in Figure 3. Since the previous literature [24,25] showed that if the absolute error of the predicted value of the two heads before and after is within 2%, then the influence of the mesh elements can be ignored. From Figure 3, when the grid number is less than 1.72 million, the grid number has a large influence on the head. When the grid number is larger than 1.72 million, the numerical calculation of the head varies by 1% with the increase of the grid number, and the final determination of the numerical calculation grid number is around 1.72 million. Grid information for parts of automotive electronic pumps is shown in Table 2.

**Figure 2.** Grid of automotive electronic water pump: (**a**) inlet section, (**b**) impeller, and (**c**) volute and outlet.

**Figure 3.** Grid independence analysis.

**Table 2.** Grid information of domains.


#### **3. Numerical Method**

#### *3.1. Turbulence Model*

The corresponding Reynolds numbers at different temperatures in this study are 1.97 <sup>×</sup> <sup>10</sup><sup>5</sup> (25 ◦C), 1.95 <sup>×</sup> <sup>10</sup><sup>5</sup> (50 ◦C) and 1.93 <sup>×</sup> 1 0<sup>5</sup> (70 ◦C), which are high Reynolds number cases. Based on the research experience and the literature analysis [26], the RNG *k-ε* turbulence model is chosen to calculate the cavitation. Its control equation is:

$$\frac{\partial(\rho k)}{\partial t} + \nabla \cdot (\rho k u\_i) = \nabla \cdot \left[ \left( \mu + \frac{\mu\_t}{\sigma\_k} \right) \nabla k \right] + P\_l - \rho \varepsilon \tag{1}$$

$$\frac{\partial(\rho\varepsilon)}{\partial t} + \nabla \cdot (\rho\varepsilon u\_i) = \mathbb{C}\_{\varepsilon1}\frac{\varepsilon}{k}P\_t - \mathbb{C}\_{\varepsilon2}\rho\frac{\varepsilon^2}{k} + \nabla \cdot [(\mu + \frac{\mu\_t}{\sigma\_\varepsilon})\nabla\varepsilon] \tag{2}$$

$$
\mu\_t = \frac{\mathcal{C}\_\mu \rho k^2}{\varepsilon} \tag{3}
$$

where *k* is turbulent kinetic energy; *ε* is turbulent dissipation term; *P*<sup>t</sup> is turbulent kinetic energy generation term; *Cε*<sup>1</sup> = 1.42, *Cε*<sup>2</sup> = 1.68, *C<sup>µ</sup>* = 0.085, *σ<sup>k</sup>* = 0.7179, *σ<sup>ε</sup>* = 0.7179.

#### *3.2. Modification of Cavitation Model Considering Thermodynamic Effects*

The commonly used cavitation simulation is based on the cavitation dynamics equation, namely the Rayleigh-Plesset equation [27]. The specific form is as follows:

$$\frac{p\_B(t) - p\_\infty(t)}{\rho\_l} = R\_B \frac{d^2 R\_B}{dt^2} + \frac{3}{2} \left(\frac{dR\_B}{dt}\right)^2 + \frac{4\nu\_l}{R} \frac{dR\_B}{dt} + \frac{2S}{\rho\_l R} \tag{4}$$

The left side of the equation is the pressure-driven term, determined by the vacuum's boundary conditions. The right side of the equation shows the second-order motion term of the vacuole, the first-order motion term of the vacuole, the viscosity term, and the surface tension term, in that order, where *R*<sup>B</sup> is the radius of the vacuole; *pB*(*t*) is the pressure inside the vacuole; *p*∞(*t*) is the pressure at infinity; *ρ<sup>l</sup>* is the density of the liquid; is the kinematic viscosity of the liquid phase; *S* is the surface tension coefficient.

Based on this equation, the Singhal cavitation model [28] is derived by neglecting the second-order term, the viscous term, and the effect of surface tension of the equation:

When *p* < *pv*, liquid vaporizes into bubbles

$$m^{+} = \mathcal{C}\_{vap} \frac{3\alpha\_{\rm nuc}(1 - \alpha\_{\nu})\rho\_{\nu}}{R\_B} \sqrt{\frac{2}{3} \frac{p\_B(t) - p\_{\infty}(t)}{\rho\_{\rm l}}} \tag{5}$$

When *p* > *pv*, the cavity condenses into liquid

$$m^{-} = \mathcal{C}\_{\rm con} \frac{3a\_{\nu}\rho\_{\nu}}{R\_{B}} \sqrt{\frac{2}{3} \frac{p\_{\infty}(t) - p\_{B}(t)}{\rho\_{I}}} \tag{6}$$

where *Cvap* and *Ccon* are the correction factors for the vaporization and condensation source terms, respectively, *αnuc* is the volume fraction of the cavitation nucleus, and their values are *<sup>C</sup>vap* <sup>=</sup> 50, *<sup>C</sup>con* <sup>=</sup> 0.01, *<sup>α</sup>nuc* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>4</sup> .

Singhal cavitation model is derived based on the isothermal assumption, ignoring the effect of thermodynamic effects in cavitation. When cavitation occurs, the liquid vaporization absorbs the latent heat of vaporization, resulting in a decrease in temperature near the vacuole, and a certain temperature difference is formed inside and outside the vacuole. The temperature difference affects the growth of the vacuole. Moreover, the Singhal cavitation model is modified in this paper to consider the thermodynamic effect of cavitation under different temperature conditions. The second-order term, viscous term, and surface tension of the Rayleigh-Plesset equation is neglected, and the Taylor series expansion of cavitation pressure is carried out to retain the first-order term. The secondorder term and other terms after they are neglected [29], we can obtain the following:

$$\frac{dR\_B}{dt} = \sqrt{\frac{2}{3} \left[ \frac{p\_B(t) - p\_\infty(t)}{\rho\_l} + \frac{dp\_B}{dT} \frac{T\_B - T\_\infty}{\rho\_l} \right]} \tag{7}$$

From the Clapeyron-Clausius equation, we can obtain:

$$\frac{dp\_B}{dT} = \frac{\rho\_l \rho\_B}{T(\rho\_l - \rho\_B)} L \tag{8}$$

where *L* is the latent heat of vaporization.

Substituting Equation (8) into Equation (7) yields:

$$\frac{d\mathcal{R}\_B}{dt} = \sqrt{\frac{2}{3} \left[ \frac{p\_B(t) - p\_\infty(t)}{\rho\_l} + \left( \frac{\rho\_l \rho\_B}{T(\rho\_l - \rho\_B)} L \right) \frac{T\_\mathcal{B} - T\_\infty}{\rho\_l} \right]} \tag{9}$$

From Equations (5), (6) and (9), the condensation source term and the vaporization source term of the cavitation model considering thermodynamic effects are:

$$m^{+} = \mathcal{C}\_{\text{cap}} \frac{3a\_{\text{nuc}}(1 - a\_{\text{v}})\rho\_{\text{v}}}{R\_{\text{B}}} \sqrt{\frac{2}{3} \left[ \frac{p\_{\text{B}}(t) - p\_{\infty}(t)}{\rho\_{l}} + \left( \frac{\rho\_{l}\rho\_{\text{B}}}{T(\rho\_{l} - \rho\_{\text{B}})}L \right) \frac{T\_{\text{B}} - T\_{\infty}}{\rho\_{l}} \right]} \tag{10}$$

$$m^{-} = \mathcal{C}\_{\rm con} \frac{3a\_{\nu}\rho\_{\nu}}{R\_{B}} \sqrt{\frac{2}{3} \left[ \frac{p\_{\infty}(t) - p\_{B}(t)}{\rho\_{l}} + \left( \frac{\rho\_{l}\rho\_{B}}{T(\rho\_{l} - \rho\_{B})}L \right) \frac{T\_{B} - T\_{\infty}}{\rho\_{l}} \right]} \tag{11}$$

#### *3.3. Boundary Condition Setting*

CFX software was used to simulate the flow field of the automotive electronic water pump at different temperatures with pure water as the medium for single-phase steady simulation and two-phase flow simulation with the addition of cavitation model. The RNG k-ε turbulence model was used for each phase of the simulation, the simulation speed was 5400 r/min, the inlet and outlet boundary conditions were set for the total pressure inlet and mass flow outlet, the cross-interface connection of GGI was used, and the convergence accuracy of all simulations was set to 1 <sup>×</sup> <sup>10</sup>−<sup>4</sup> .

For the single-phase stability simulation, the dynamic-static interface is set as the frozen rotor and the number of iterations is 1000. For steady cavitation simulation, the modified cavitation model is written into the CFX using the CEL language, pure water at the corresponding temperature is added as the working medium, and water vapor is added as the bubble generated during cavitation. The calculation sets the volume fraction of the liquid phase at the inlet boundary to 1 and the volume fraction of the vapor phase to 0. The inlet pressure is adjusted downwards by 0.2 atm for each simulation, and the change in the head is compared to determine the inlet pressure at which cavitation occurs. The physical parameters of pure water and water vapor at different temperatures are shown in Table 3. It can be seen that the temperature has a large effect on the physical parameters of water density, dynamic viscosity, and vaporization pressure, and the value of each physical parameter is smaller for water vapor compared with water.


**Table 3.** Physical parameters of water and water vapor at different temperatures.

To obtain a stable and reliable solution, the unsteady simulation of the cavitation flow field takes its steady simulation results at the corresponding temperature as the initial conditions. The dynamic-static intersection is modified to a transient rotor stator in the calculation; the impeller rotation of 360◦ is taken as a calculation cycle, the time step is set to 6.17 <sup>×</sup> <sup>10</sup>−<sup>5</sup> s (calculated for every 2◦ rotation of the impeller), the number of inner loops at each time step is 20, and the total calculation time is set to 0.2 s (18 rotation periods). The Courant number is used as a criterion to determine whether the time step satisfies the periodic numerical simulation, and is defined as:

$$\mathbf{C}\_0 = v \frac{\Delta t}{L} < 100 \tag{12}$$

where *L* is the smallest size of the grid cell, *v* is the biggest velocity of the main flow, and ∆*t* is the time step. The maximum *C*<sup>0</sup> obtained by the calculation is 5.23, which satisfies the independence of the time step.

#### *3.4. Monitoring Point Setting*

To study the pressure variation inside the impeller of an automotive electronic water pump during cavitation under thermal effects, 12 monitoring points are set up at the impeller position of the pump, as shown in Figure 4.

**Figure 4.** Monitoring points position in an automotive electronic water pump.

## **4. Analysis of Internal Flow of Automotive Electronic Water Pump under Non-Cavitation Condition**

#### *4.1. Verification of External Characteristics by Numerical Calculation*

The external characteristic curve is the external expression of the internal flow characteristics of the automotive electronic water pump. Numerical calculations are performed for the automotive electronic water pump at different flow rates, and tests verify the reliability of the numerical calculation results. The performance test of an automotive electronic water pump is carried out concerning GB/T 3216–2016, and the test bench is shown in Figure 5.

Using the head coefficient *ψ* to calculate the external characteristics, the head coefficient can be calculated as the following equation:

$$
\psi = \frac{gH}{u\_2^2/2} \tag{13}
$$

where *u*<sup>2</sup> is the circumferential exit speed of the impeller.

Figure 6 shows a comparison of the external characteristics results. As can be seen from the figure, the experimental head coefficient and efficiency are slightly lower than the numerical calculation due to the simplification of the model during the numerical calculation for the same flow conditions. At a small flow rate (0.2*Q*d), the difference between the simulated and experimental values of the head coefficient is 0.06; at 0.8*Q*d~1.6*Q*d, the two curves are in good agreement, and it can be considered that the numerical calculation method can accurately predict the external characteristics of the pump and ensure the accuracy of the subsequent analysis.

**Figure 5.** Test bench for an automotive electronic water pump: (**a**) experimental schematic, (**b**) experimental loop.

**Figure 6.** Comparison of pump performance between numerical and experimental results.

## *4.2. Pressure Field Distribution in the Pump at Different Temperatures*

Figure 7 shows the static pressure distribution clouds of the impeller of the automotive electronic water pump under four different flow conditions at 25 ◦C, 50 ◦C, and 70 ◦C (speed of 5400 r/min). The static pressure distribution at different temperatures is similar; from the blade inlet to the blade outlet, the pressure in the impeller is of a gradient-type growth, and the pressure distribution is more uniform. As the flow rate increases, the blade suction surface pressure gradually decreases, and the low-pressure area gradually increases. Under the large flow condition (1.2*Q*d), the area of the low-pressure area at the inlet gradually decreases as the temperature increases.

**Figure 7.** Pressure distribution of impeller under at different temperatures. (**a**) 0.6Q<sup>d</sup> at 25 ◦C; (**b**) 0.8*Q*<sup>d</sup> at 25 ◦C; (**c**) 1.0*Q*<sup>d</sup> at 25 ◦C; (**d**) 1.2*Q*<sup>d</sup> at 25 ◦C; (**e**) 0.6*Q*<sup>d</sup> at 50 ◦C; (**f**) 0.8*Q*<sup>d</sup> at 50 ◦C; (**g**) 1.0*Q*<sup>d</sup> at 50 ◦C; (**h**) 1.2*Q*<sup>d</sup> at 50 ◦C; (**i**) 0.6*Q*<sup>d</sup> at 70 ◦C; (**j**) 0.8*Q*<sup>d</sup> at 70 ◦C; (**k**) 1.0*Q*<sup>d</sup> at 70 ◦C; (**l**) 1.2*Q*<sup>d</sup> at 70 ◦C.

#### **5. Automotive Electronic Water Pump Cavitation Performance Analysis**

*5.1. Computational Analysis of Cavitation Performance Considering Thermodynamic Effects*

The net positive suction head is the surplus energy per unit weight of water at the pump suction inlet that exceeds the vaporization pressure and is expressed as follows:

$$\text{NPSHa} = \frac{p\_1 - p\_v}{\rho \text{g}} \tag{14}$$

where *p*<sup>1</sup> is the automotive electronic water pump inlet pressure; *p<sup>v</sup>* is the saturation vapor pressure of water at that temperature; *ρ* is the fluid density.

Figure 8 shows the cavitation performance curves of the simulated and tested automotive electronic water pump at a temperature of 25 ◦C (flow rate of 1.25 m3/h and speed of 5400 r/min). As can be seen from the figure, the head coefficient of the test value is smaller than the simulated value under the same inlet conditions, which are related to the existence of friction between the fluid and the pipe wall and energy loss between the motor and the impeller. Overall, the simulated and experimental cavitation performance curves have the same stagnation point position and trend. It can be considered that the numerical calculation method can accurately predict the cavitation performance of the pump and ensure the accuracy of subsequent cavitation calculations.

**Figure 8.** Comparison of cavitation performance curves between numerical and experimental results.

Figure 9 shows the cavitation performance curves of the simulated automotive electronic water pump at three different temperatures (flow rate of 1.25 m3/h and speed of 5400 r/min). We define the automotive electronic water pump head drop of 1% as incipient cavitation, a head drop of 3% as cavitation, and the NPSH corresponding to the head drop of 3% as the required net positive suction head of the pump (NPSHr). The NPSHrs at three temperatures were 1.15 m at 25 ◦C, 1.01 m at 50 ◦C, and 0.91 m at 70 ◦C. As can be seen from the figure, with the decrease of NPSHa, the head coefficient maintains a level for a period of time and then rapidly decreases, which is because the flow pattern inside the automotive electronic water pump is turbulent and sensitive to cavitation, and the hydraulic performance deteriorates sharply once cavitation occurs; with the increase of temperature, NPSHr gradually decreases, and the anti-cavitation performance of the automotive electronic water pump gradually increases.

**Figure 9.** Cavitation performance curves with different temperatures.

## *5.2. Cavitation Steady Analysis Considering Thermodynamic Effects* 5.2.1. Bubble Shape during Cavitation Formation

The bubble is the most visual product when cavitation occurs, and the volume fraction of the bubble can judge the degree of cavitation. Figure 10 shows the distribution of bubbles in the impeller at different NPSHa for a bubble volume concentration of 10% at a temperature of 25 ◦C (flow rate of 1.25 m3/h and speed of 5400 r/min) for an automotive electronic water pump. It can be seen from the figure that when the NPSHa is larger, no bubble is generated in the impeller; when the NPSHa is reduced to 1.68 m, a small number of bubbles appears at the inlet side of the impeller near the suction surface of the blade, which is the cavitation inception stage. As the NPSHa gradually decreases, the distribution area of the bubble starts to spread from the suction surface to the pressure surface, and cavitation further develops; when the NPSHa decreases to NPSHr, the bubbles gradually increase and develop to the pressure surface and start to block the impeller flow channel, and the high-speed jet caused by the rupture of the bubbles will damage the impeller and produce cavitation, resulting in a serious drop in the head.

**Figure 10.** Bubble distribution during the cavitation formation process.

5.2.2. Analysis of the Pressure Field during Cavitation Formation

The occurrence of cavitation is pressure-dependent, and its distribution is influenced by the law of hydrostatic pressure distribution. Figure 11 shows cloud plots of static pressure distributions at different NPSHas of an automotive electronic water pump at a temperature of 25 ◦C (flow rate 1.25 m3/h, speed 5400 r/min). As can be seen from the figure, from the blade inlet to the blade outlet, the pressure gradually increased; five blades on the static pressure distribution show a similar pattern in which the static pressure of the fluid along with the fluid flow direction increased. In the blade outlet pressure, it reached the maximum. The range of local low-pressure areas gradually expands with the decrease of NPSHa. In the no cavitation and incipient cavitation stage, the influence of NPSHa on the size of the low-pressure area range is small; from the cavitation development stage to the cavitation stage, the influence of NPSHa size on the size of the low-pressure area range at the impeller inlet of the automotive electronic water pump is large. Because of the low pressure at the impeller inlet, cavitation generally occurs first from the suction surface of the impeller inlet blade.

**Figure 11.** Pressure distribution of bubble formation process.

## 5.2.3. Cavitation Flow Field Analysis

Figure 12 shows the bubble distribution inside the impeller at three temperatures when the NPSHa is 1.15 m (flow rate 1.25 m3/h, speed 5400 r/min). At 70 ◦C, when the inlet pressure is 0.407 atm, some bubbles are produced near the suction surface of some of the impeller's blades, and the pump head does not drop significantly at this time. At 50 ◦C, when the inlet pressure is 0.221 atm, the bubble area becomes larger, and all impeller blades produce bubbles and development to the middle of the radial direction of the impeller; at this time, the pump head drops by 1.5%. It can be seen that the bubbles generated at this time are enough to impact the performance of the pump. At 25 ◦C, when the inlet pressure is 0.131 atm, the bubbles cluster continues to increase and begins to block the flow channel, at which time the pump head decreases by 3%, and cavitation occurs. At 25 ◦C, the low-pressure area at the impeller inlet suction surface is larger, and as the temperature rises, the area of the low-pressure area becomes smaller and smaller, and the area of the corresponding bubbles also gradually decreases. In addition, both the low-pressure area and the bubble cluster are axially distributed.

**Figure 12.** Bubble distribution with different temperatures based on the same. (**a**) T = 25 °C; (**b**) T = 50 °C; (**c**) T = 70 °C.

Combining Figures 8 and 9, it is found that the number of bubbles is higher during the stage of a sharp decline in the head, and the bubbles have a certain influence on the head; the bubbles are all generated from near the low-pressure area at the blade inlet and develop along with the impeller outlet, and the temperature has a certain influence on the distribution of bubble in the automotive electronic water pump. The bubble distribution inside the impeller is consistent with the cavitation performance curve: the more bubbles are generated, the more obvious the drop of its head.

## *5.3. Cavitation Transient Analysis Considering Thermodynamic Effects* 5.3.1. Transient Bubble in the Impeller

Figure 13 shows the distribution of bubbles at a temperature of 25 ◦C and an inlet pressure of 0.131 atm for an impeller with a vapor volume concentration of 10% at six different moments in a cycle. It can be seen from the figure that at the moment t = 0, the suction surface in each flow channel adheres to a continuous bubble, and the shape of the bubble is of an irregular rugby ball with a wide middle and narrow front and back; as the blades are periodically arranged, with the impeller rotation, the bubble change in each flow channel has a similar pattern. Take runner No. 1 as an example: at *t* = 2/6 T, the bubble in the middle of the flow channel will be detached; at *t* = 3/6 T, the volume of the bubble in runner No. 1 is smaller than at *t* = 2/6 T. At this time, the bubble has detached and collapsed in the high-pressure area; with the development of time, at *t* = 3/6 T to *t* = 5/6 T, the bubble in runner No. 1 slowly develops toward the end and detaches. On the whole, the detachment and collapse of the bubble occurred in the middle and tail of the bubble cluster, where the middle bubble detached less and the tail detached more; the changes in the position and shape of the bubble were relatively small, indicating that the whole process of cavitation was relatively stable at this time.

**Figure 13.** Bubble distribution in the impeller domain. (**a**) *t* = 0; (**b**) *t* = 1/6 T; (**c**) *t* = 2/6 T; (**d**) *t* = 3/6 T; (**e**) *t* = 4/6 T; (**f**) *t* = 5/6 T.

5.3.2. Comparative Analysis of Pressure Pulsation in the Frequency Domain

To analyze the relative pressure variation at each monitoring point within the impeller, we use a pressure coefficient expressed as:

$$C\_{\mathbb{P}}^{\*} = \frac{p - \overline{p}}{0.5\rho u\_{2}^{2}} \tag{15}$$

where *p* is the instantaneous pressure, *p* is the average pressure, *ρ* is the fluid density, and *u*<sup>2</sup> is the circumferential velocity at the impeller outlet. *p* is the average pressure of the last eight cycles simulated at the monitoring points in this study.

Figure 14 shows the frequency domain of the pressure pulsation at the monitoring point inside the impeller at 25 ◦C (flow rate 1.25 m3/h, speed 5400 r/min) during a no cavitation operating condition of the automotive electronic water pump. As can be seen from the figure, along with the impeller runner from the blade inlet to the blade outlet, the pressure pulsation amplitude at each monitoring point gradually increases, the amplitude frequency is the axial frequency and its multiplier frequency, and the pressure pulsation amplitude reaches the maximum at the axial frequency. At the axial frequency, the pressure pulsation amplitude from the blade suction surface to the blade pressure surface pressure pulsation amplitude gradually increases; at the impeller runner inlet, the blade suction surface (BS1) and pressure surface (BP1) pressure pulsation amplitude is higher than the middle of the impeller runner (BM1), which is because at the impeller inlet, the threejaw ring disturbs the incoming flow field and intensifies the pressure fluctuation at the impeller inlet.

**Figure 14.** Frequency characteristic in the impeller. (**a**) Blade suction surface; (**b**) Middle of the flow channel; (**c**) Blade pressure surface.

Figure 15 shows the maximum values of pressure pulsations at the monitoring points inside the impeller during no cavitation, incipient cavitation, and cavitation of the automotive electronic water pump. The maximum amplitude value increases gradually along the fluid flow direction, except for individual monitoring points, and reaches the maximum value at the exit of each working surface. Overall, the maximum value of pressure pulsation during cavitation is higher on the blade working surface than no cavitation, which may be related to the generation and collapse of bubbles.

**Figure 15.** The maximum amplitude of pressure fluctuations in the impeller. (**a**) Blade suction surface; (**b**) Middle of the flow channel; (**c**) Blade pressure surface.

#### **6. Conclusions**

In this study, we have considered the influence of thermodynamic effect on the cavitation performance of hydromechanics, corrected the Singhal cavitation model considering a thermodynamic effect, written the corrected model into CFX software for numerical simulation of cavitation of automotive electronic water pump, explored the cavitation performance and the distribution pattern of cavitation bubble of automotive electronic water pump under different temperature (25 ◦C, 50 ◦C, 70 ◦C), and drawn the following conclusions:


the same trend. The pressure is closely related to the generation and development of cavitation.


**Author Contributions:** Data curation, K.W.; Validation, A.A. and C.S.; Formal analysis, Q.C.; Resources, Q.S.; Funding acquisition, Q.S.; Investigation, C.S and K.W.; Supervision, C.F.; Writing original draft, K.W.; Writing—review and editing, A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (51976079, 12002136), the financial support of the National Key R&D Program of China (2020YFC1512403), and the Research Project of State Key Laboratory of Mechanical System and Vibration (MSV202201).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data supporting this study's findings are available within the article. The data pressented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors gratefully acknowledge the National Natural Science Foundation of China (51976079, 12002136), the financial support of the National Key R&D Program of China (2020YFC1512403), and the Research Project of State Key Laboratory of Mechanical System and Vibration (MSV202201).

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**


**Zhisen Ye <sup>1</sup> , Guilin Qiu <sup>1</sup> and Xiaolei Chen 1,2,\***


**Abstract:** Deep-narrow grooves (DNGs) of nickel-based alloy GH4169 are extensively used in aerospace industry. Electrochemical milling (EC-milling) can manufacture special structures including DNGs by controlling the moving path of simple tool, showing a flexible process with the advantages of high machining efficiency, regardless of material hardness, no residual stresses, burrs, and tool wear. However, due to the inefficient removal of electrolytic by-products in the interelectrode gap (IEG), the machining accuracy and surface quality are always unsatisfactory. In this paper, a novel tube tool with wedged end face is designed to generate pulsating flow field in IEG, which can enhance the removal of electrolytic by-products as well as improve the machining quality of DNG. The flow field simulation results show that the electrolyte velocity in the IEG is changed periodically along with the rotation of the tube tool. The pulsating amplitude of electrolyte is changed by adjusting the wedged angle in the end face of the tube tool, which could affect the EC-milling process. Experimental results suggest that the machining quality of DNG, including the average width, taper of sidewall, and surface roughness, is significantly improved by using the tube tool with wedged end face. Compared with other wedged angles, the end face with the wedged angle of 40◦ is more suitable for the EC-milling process. DNG with the width of 1.49 mm ± 0.04 mm, taper of 1.53◦ ± 0.46◦ , and surface roughness (Ra) of 1.04 µm is well manufactured with the milling rate of 0.42 mm/min. Moreover, increasing the spindle speed and feed rate can further improve the machining quality of DNG. Finally, a complex DNG structure with the depth of 5 mm is well manufactured with the spindle speed of 4000 rpm and feed rate of 0.48 mm/min.

**Keywords:** deep-narrow groove; GH4169 alloy; electrochemical milling; wedged end face

## **1. Introduction**

Due to their excellent fatigue resistance, corrosion resistance, radiation resistance, and high-temperature strength, Ni-based superalloys are used widely in die-casting molds, medical devices, and the aerospace sector as demand in the manufacturing field grows [1,2]. However, due to their material property of high-strength and poor heat conductivity, conventional machining often suffers from high tool wear, poor machining stability, and low process efficiency [3]. Nowadays, nontraditional processes with a low cost and high efficiency for manufacturing difficult-to-cut material are attracting more attention, including electrical discharge machining and laser machining. However, both cause heat affected layer and microcrack in machining surfaces, leading to lower machining quality [4,5].

Compared to other machining methods, electrochemical machining (ECM) has significant advantages for machining difficult-to-cut material, such as titanium alloys and Ni-based superalloys, due to the absence of tool wear, thermal and residual stresses, and cracks and burrs [6,7]. Electrochemical milling (EC-milling) combines the capabilities of ECM with the flexibility of numerical control (NC) technology, which can machine special

**Citation:** Ye, Z.; Qiu, G.; Chen, X. Electrochemical Milling of Deep-Narrow Grooves on GH4169 Alloy Using Tube Electrode with Wedged End Face. *Micromachines* **2022**, *13*, 1051. https://doi.org/ 10.3390/mi13071051

Academic Editor: Stelios K. Georgantzinos

Received: 5 June 2022 Accepted: 29 June 2022 Published: 30 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

structures, including deep-narrow grooves (DNGs), by controlling the moving path of the simple tool [8]. Natsu et al. fabricated three-dimensional complicated structures in SUS304 stainless using a tube electrode with an inner diameter of 0.26 mm by superimposing simple patterns [9]. Mitchell-Smith et al. produced different groove geometries by optimizing the bottom structure of a metallic nozzle to change current density distribution [10]. Liu et al. proposed a method of ultrasonic vibration-assisted electrochemical milling, which was helpful to improve the machined surface quality, and a three-dimensional structure with the total depth of 300 µm was machined [11]. Liu and Qu analyzed the anodic polarization curves of TB6 in NaNO<sup>3</sup> solution and the effect of current density on the morphology, and grooves and flat surfaces were machined successfully by electrochemical milling [12]. Zhu et al. established the electrochemical milling with nanosecond pulse model and machined 2D and 3D complex structures with good shape precision and surface quality [13]. Rathod et al. used sidewall insulation electrode to prevent the dissolution of the material along the sidewall of microgroove and reduced the taper angle from 58.39◦ to 25.20◦ for microgroove [14].

In the above studies, the electrochemical milling process is started from an initial gap between the bottom of the electrode and the surface of the workpiece, in which the electric field is mainly provided by the bottom of the electrode. With a motion along the feed direction, a very thin layer of material is removed from the surface of the workpiece. As a result, when a high-aspect-ratio structure is machined with this method, the tube tool is needed to multipass feed along the depth and length directions. Due to the stray corrosion, electric fields are repeatedly formed at the machined zone during the multipass feed, the machining accuracy and surface quality are always unsatisfactory. In an attempt to achieve better machining profile, Ghoshal and Bhattacharyya proved that the taper angle of grooves generated by sinking and milling method was far less than layer-by-layer method and then proposed a reversed taper tube tool for electrochemical milling to reduce the taper angle of groove [15]. This clearly showed that one-pass milling with the tube tool is more suitable for machining DNG structure.

However, the electric field for electrochemical anodic dissolution is provided by the sidewall of tool electrode in this method, in which large amounts of electrolytic by-products (sludge, gas bubbles, and heat) are generated in the inter-electrode gap (IEG). When the machining gap becomes small, it is difficult to remove them from the IEG. To maintain the stability of electrolyte flow during the whole machining process, a rapid removal of the electrolytic by-products is needed in the deep and narrow IEG. If the removal capacity is insufficient, the machining accuracy and surface quality will become poor. To obtain high machining accuracy and machining stability, Wang et al. suggested electrochemical machining with vibration superimposed to improve the removal of sludge and hydrogen bubbles [16]. Bilgi et al. proposed an ECM process with rotating electrode movement to enhance the uniformity of electrolyte flow and reduce or eliminate the flow field disrupting processes [17]. Moreover, Niu et al. proposed a flow channel structure with six slits in sidewall for improving the uniformity of flow field, and a thin-wall structure with the depth of 3 mm was machined [18]. However, the machining accuracy and surface quality in high-aspect ratio structures by EC-milling still need to be improved.

Pulsating flow is one of the unsteady flows that can change the characteristics of hydrodynamics and enhance mass transport [19,20]. This paper proposes a method for using a tube tool with wedged end face to generate pulsating flow field in the IEG to enhance the removal of electrolytic by-products, as well as improve the machining accuracy and surface quality in EC-milling. The parameters of pulsating flow field could be changed by adjusting the wedged angle in the end face of the tube tool, which would affect the EC-milling process. The flow field distributions of different wedged angles in the end face of the tube tool are simulated numerically. Experiments also are conducted to investigate the effects of different wedged angles in the end face of the tube tool on the machining quality of DNG.

#### **2. Description of the Method and Numerical Simulation** *2.1. Description of the Method*

**2. Description of the Method and Numerical Simulation**

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 3 of 17

#### *2.1. Description of the Method* Figure 1 shows a schematic diagram of EC-milling of DNG with a wedged end face

the machining quality of DNG.

Figure 1 shows a schematic diagram of EC-milling of DNG with a wedged end face tube electrode. The milling procedure is divided into two processes. First, the tube electrode with wedged end face is fed along the *Z*-axis to the required machining depth through electrochemical drilling (Figure 1a). Second, the workpiece then is controlled to move along the specified rail in the *X-Y* plane (Figure 1b). The electrolyte flows from the bottom of the tube electrode into the IEG, thereby dissolving the workpiece material while simultaneously flushing out the electrolytic by-products. tube electrode. The milling procedure is divided into two processes. First, the tube electrode with wedged end face is fed along the *Z*-axis to the required machining depth through electrochemical drilling (Figure 1a). Second, the workpiece then is controlled to move along the specified rail in the *X-Y* plane (Figure 1b). The electrolyte flows from the bottom of the tube electrode into the IEG, thereby dissolving the workpiece material while simultaneously flushing out the electrolytic by-products. As shown in Figure 1b, the front sidewall of the tube electrode provides an electric

to investigate the effects of different wedged angles in the end face of the tube tool on

As shown in Figure 1b, the front sidewall of the tube electrode provides an electric field for electrochemical anodic dissolution, and the amounts of electrolytic by-products are generated in the IEG. By using the wedged end face of the tube tool in the experiment, the quantity and flow rate of electrolyte flowing into IEG will be changed periodically with the rotation of the tube tool, and the pulsating flow field is generated, which could enhance the removal of electrolytic by-products. In addition, the pulsating parameters of electrolyte, including pulsating amplitude and pulsating frequency, can be changed by adjusting the wedged angle (α) and rotating speed of the tube tool, which will affect the EC-milling process. field for electrochemical anodic dissolution, and the amounts of electrolytic by-products are generated in the IEG. By using the wedged end face of the tube tool in the experiment, the quantity and flow rate of electrolyte flowing into IEG will be changed periodically with the rotation of the tube tool, and the pulsating flow field is generated, which could enhance the removal of electrolytic by-products. In addition, the pulsating parameters of electrolyte, including pulsating amplitude and pulsating frequency, can be changed by adjusting the wedged angle (α) and rotating speed of the tube tool, which will affect the EC-milling process.

**Figure 1.** The schematic diagram of EC-milling of DNG with a wedged end face tube electrode. (**a**) Electrochemical drilling hole, (**b**) Electrochemical milling. **Figure 1.** The schematic diagram of EC-milling of DNG with a wedged end face tube electrode. (**a**) Electrochemical drilling hole, (**b**) Electrochemical milling.

In the EC-milling process, the evolution process of DNG is illustrated in Figure 2. When the machining process is in a stable state, the front gap *Δx* in X direction can be described as [21]: In the EC-milling process, the evolution process of DNG is illustrated in Figure 2. When the machining process is in a stable state, the front gap ∆*x* in X direction can be described as [21]:

$$
\Delta \mathfrak{x} = \frac{\eta \omega \kappa \mathcal{U}\_R}{v\_{\mathfrak{x}}} \tag{1}
$$

 = (1) where *η* is the current efficiency, *ω* is the volumetric electrochemical equivalent of the where *η* is the current efficiency, *ω* is the volumetric electrochemical equivalent of the metallic material, *κ* is the electric conductivity of electrolyte, *U<sup>R</sup>* is the supply voltage, and *v<sup>x</sup>* is the feed rate of the tube tool.

metallic material, *κ* is the electric conductivity of electrolyte, *UR* is the supply voltage, and *v<sup>x</sup>* is the feed rate of the tube tool. As shown in Figure 2a, when the tube tool is fed along the milling path in the plan *X-Y*, the relationship between the side gap and the *Y*-axis can be expressed as

$$\frac{dy}{dt} = \frac{\eta \omega \kappa \mathbf{U}\_R}{y} \tag{2}$$

 At the initial time, *t* = 0 and *y* = *y*0. Equation (2) can be integrated as follow:

$$\frac{y^2}{2} = \eta \omega \kappa l I\_R t + \frac{y\_0^2}{2} \tag{3}$$

 2 = + 0 2 (3) As the initial side gap, *y*<sup>0</sup> can be assumed to be the same with the front gap ∆*x*, the machining side gap ∆*y* in the *Y* direction can be expressed as:

$$
\Delta y = \sqrt{\eta \omega \kappa l I\_R t + \Delta x^2} = \sqrt{\eta \omega \kappa l I\_R \frac{D}{v\_\chi} + \Delta x^2} \tag{4}
$$

where *D* is the outer diameter of the tube tool. Thus, the groove width *W* can be described as:

where *D* is the outer diameter of the tube tool.

Δ

machining side gap

Thus, the groove width *W* can be described as:

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 4 of 17

$$W = D + 2\Delta y = D + 2\sqrt{\eta \omega \kappa \mathcal{U}\_R \frac{D}{\upsilon\_\chi} + \Delta x^2} \tag{5}$$

 

+ <sup>2</sup> (4)

As shown in Equation (5), it can be obtained that the width of DNG is affected by numerous parameters, including the outer diameter of the tube tool, feed rate, supply voltage, and electrolyte conductivity. During machining, the workpiece is dissolved. Meanwhile, hydrogen and oxygen are generated on the cathode and anode surfaces, respectively. The electrolyte in the IEG will be warmed by Joule heat. All these factors interactively influence the distribution of electrolyte conductivity along the flow path, resulting in a taper sidewall, as illustrated in Figure 2b. The relationship among the electrolyte conductivity *κ*, electrolyte temperature *T*, and gas void fraction *βgas* can be described as follows: numerous parameters, including the outer diameter of the tube tool, feed rate, supply voltage, and electrolyte conductivity. During machining, the workpiece is dissolved. Meanwhile, hydrogen and oxygen are generated on the cathode and anode surfaces, respectively. The electrolyte in the IEG will be warmed by Joule heat. All these factors interactively influence the distribution of electrolyte conductivity along the flow path, resulting in a taper sidewall, as illustrated in Figure 2b. The relationship among the electrolyte conductivity κ, electrolyte temperature *T*, and gas void fraction *βgas* can be described as follows:

As the initial side gap, *y0* can be assumed to be the same with the front gap *Δx*, the

*y* in the *Y* direction can be expressed as:

= √ + <sup>2</sup> = √

$$\kappa = \kappa\_0 \left( 1 - \beta\_{\mathcal{g}as} \right)^{bp} \left( 1 + \kappa (T - T\_0) \right) \tag{6}$$

where *κ*<sup>0</sup> is the initial electrolyte conductivity, *T*<sup>0</sup> is the initial electrolyte temperature, *α* is the degree of temperature dependence, and *bp* is Bruggeman's coefficient. where *κ0*is the initial electrolyte conductivity, *T<sup>0</sup>* is the initial electrolyte temperature, *α* is the degree of temperature dependence, and *bp* is Bruggeman's coefficient.

**Figure 2.** Diagram of the electrochemical milling process: (**a**) Sketch of the *X-Y* plane and (**b**) sketch of *Y-Z* plane. **Figure 2.** Diagram of the electrochemical milling process: (**a**) Sketch of the *X-Y* plane and (**b**) sketch of *Y-Z* plane.

Equation (6) shows that the efficient removal of electrolytic by-products (sludge, gas bubbles, and heat) is helpful to reduce the difference of electrolyte conductivity along the depth direction of DNG; thus, the taper of DNG's sidewall can be reduced. Equation (6) shows that the efficient removal of electrolytic by-products (sludge, gas bubbles, and heat) is helpful to reduce the difference of electrolyte conductivity along the depth direction of DNG; thus, the taper of DNG's sidewall can be reduced.

#### *2.2. Numerical Simulation 2.2. Numerical Simulation*

In this research, different wedged angles in the end face of the tube tool were used for generating different pulsating parameters for the electrolyte, and the flow field distribution in IEG was analyzed by computational fluid dynamics (CFD). In this research, different wedged angles in the end face of the tube tool were used for generating different pulsating parameters for the electrolyte, and the flow field distribution in IEG was analyzed by computational fluid dynamics (CFD).

#### 2.2.1. Model Building

2.2.1. Model Building Three-dimensional simulation model based on the flow field is established, as shown in Figure 3. The fluid domain includes the inner region of the tube electrode and DNG. Due to the rotation of the tube electrode, it needs to divide the fluid domain into a stationary zone and a rotation zone. The pink area represents the stationary zone, and the green area represents the rotation zone, which are transmitted data through the interface. In addition, the walls of the tube electrode are set as moving walls. Since the designed 3D model is relatively complex, tetrahedral meshes are used for the simulation model, and the mesh refinement is performed on the rotation zone and the around zone to ensure the accuracy of simulation results. In order to simplify the above model, this paper makes the following assumptions:


For incompressible viscous fluids, the fluid flow in the turbulent state is restricted by the Navier–Stokes equation:

$$
\nabla \cdot \overline{v} = 0 \tag{7}
$$

$$(\frac{\partial \overline{v}}{\partial t} + (\overline{v} \cdot \nabla)\overline{v} = -\frac{1}{\rho} \nabla p + \mu \nabla^2 \overline{v} \tag{8}$$

where *ρ* is the electrolyte density, *v* is the flow velocity, *p* is the pressure, and *µ* is the dynamic viscosity of the electrolyte.

Based on the change of the flow field, the *k-ε* turbulence model in the standard equation is used to solve the turbulent energy *k* and the turbulent dissipation rate *ε* in the electrolyte flow process:

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \left[ \left( \mu + \frac{\mu\_l}{\sigma\_k} \right) \frac{\partial k}{\partial \mathbf{x}\_j} \right] + \mathbf{G}\_k - \rho \varepsilon \tag{9}$$

**Parameter Value**

Wedged angles, *α* 0°, 40°, 50°, 60° Groove length, *L* 5 mm Groove depth, *H* 5 mm

Figure 4 shows the contour of flow velocity on the cross section with different wedged angles under different rotational degrees. In the standard flat end face model (see Figure 4a), the velocity of electrolyte in the IEG is constant. In contrast, it can be found that the velocity of electrolyte in both front IEG and side IEG is changed in the wedged end face models under different rotation degrees (Figure 4b–d). The simulation results indicate that the pulsating flow field can be well generated with the wedged end face in tube electrode. Meanwhile, with the increase in the wedged angle, the velocity change of electrolyte in the IEG is more obvious. In the wedged angle of 40° model, the maximum and minimum velocities of electrolyte in the IEG are about 30 m/s and 8 m/s. In the wedged angle of 60° model, the maximum and minimum velocities of electrolyte

Outlet pressure, *pout* 0 MPa Rotational speed, *ω* 3000 rpm Inter-electrode gap, *Δ* 0.25 mm Dynamic viscosity of electrolyte, *μ* 1.003 × 10−<sup>3</sup> Pa·s Density of electrolyte, *ρ* 1100 kg/m<sup>3</sup>

External diameter of tube electrode, *D* 1 mm Internal diameter of tube electrode, *d* 0.8 mm

$$\frac{\partial(\rho\varepsilon)}{\partial t} + \frac{\partial(\rho\varepsilon u\_{\text{i}})}{\partial \mathbf{x}\_{\text{i}}} = \frac{\partial}{\partial \mathbf{x}\_{\text{j}}} \left[ \left( \mu + \frac{\mu\_{\text{I}}}{\sigma\_{\varepsilon}} \right) \frac{\partial k}{\partial \mathbf{x}\_{\text{j}}} \right] + \frac{\mathbf{C}\_{1\varepsilon}}{k} \mathbf{G}\_{\text{k}} - \mathbf{C}\_{2\varepsilon} \rho \frac{\varepsilon^{2}}{k} \tag{10}$$

where *P<sup>k</sup>* is the generating term of turbulent energy, *σ<sup>k</sup>* and *σ<sup>ε</sup>* are Prandtl numbers corresponding to *k* and *ε* with values of 1.0 and 1.3, and *C1<sup>ε</sup>* and *C2<sup>ε</sup>* are model constants with values of 1.44 and 1.92. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 6 of 17

> All the models are solved by ANSYS FLUENT 19.2, and the simulation parameters are listed in Table 1.

**Figure 3.** Building of three-dimensional model for the flow field simulation. **Figure 3.** Building of three-dimensional model for the flow field simulation.

**Table 1.** The parameters for the simulation.

2.2.2. Simulation Results

in the IEG are about 32m/s and 0 m/s.


**Table 1.** The parameters for the simulation.

#### 2.2.2. Simulation Results

Figure 4 shows the contour of flow velocity on the cross section with different wedged angles under different rotational degrees. In the standard flat end face model (see Figure 4a), the velocity of electrolyte in the IEG is constant. In contrast, it can be found that the velocity of electrolyte in both front IEG and side IEG is changed in the wedged end face models under different rotation degrees (Figure 4b–d). The simulation results indicate that the pulsating flow field can be well generated with the wedged end face in tube electrode. Meanwhile, with the increase in the wedged angle, the velocity change of electrolyte in the IEG is more obvious. In the wedged angle of 40◦ model, the maximum and minimum velocities of electrolyte in the IEG are about 30 m/s and 8 m/s. In the wedged angle of 60◦ model, the maximum and minimum velocities of electrolyte in the IEG are about 32 m/s and 0 m/s. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 7 of 17

**Figure 4.** The contour of flow velocity on the cross section with different wedged angles in the end face of the tube tool. (**a**) 0°; (**b**) 40°; (**c**) 50°; (**d**) 60°. **Figure 4.** The contour of flow velocity on the cross section with different wedged angles in the end face of the tube tool. (**a**) 0◦ ; (**b**) 40◦ ; (**c**) 50◦ ; (**d**) 60◦ .

In order to further analyze the change of electrolyte flow rate in the IEG, points A to

The trends of the velocity of pulsating field with different wedged angles are the same. There are two peaks of electrolyte velocity in one cycle in the front machining gap, while the velocity of electrolyte changes like a sine wave in the side machining gap. With the increase in the wedged angle, the pulsating amplitude of electrolyte increases. When the end face with the wedged angle is 40°, the velocity of electrolyte at point A ranges from 6.7 to 30.6 m/s. When the wedged angle increases to 60°, the velocity of

tools. In the standard flat end face model, the value of flow velocity at points A to C is constant. The velocity of electrolyte in the front gap and side gap is 23.8 m/s and 15.3

m/s, respectively.

electrolyte ranges from 0.3 to 32.8 m/s.

In order to further analyze the change of electrolyte flow rate in the IEG, points A to C marked in Figure 4a are referenced to describe the specific electrolyte velocity in the IEG. Figure 5 shows the change of flow velocity at points A to C under different tube tools. In the standard flat end face model, the value of flow velocity at points A to C is constant. The velocity of electrolyte in the front gap and side gap is 23.8 m/s and 15.3 m/s, respectively.

The trends of the velocity of pulsating field with different wedged angles are the same. There are two peaks of electrolyte velocity in one cycle in the front machining gap, while the velocity of electrolyte changes like a sine wave in the side machining gap. With the increase in the wedged angle, the pulsating amplitude of electrolyte increases. When the end face with the wedged angle is 40◦ , the velocity of electrolyte at point A ranges from 6.7 to 30.6 m/s. When the wedged angle increases to 60◦ , the velocity of electrolyte ranges from 0.3 to 32.8 m/s. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 8 of 17

**Figure 5.** The variation of electrolyte velocity on points A to C in the IEG under kinds of tube tools. **Figure 5.** The variation of electrolyte velocity on points A to C in the IEG under kinds of tube tools.

## **3. Experimental Section**

**3. Experimental Section** Figure 6 shows a schematic of EC-milling system with a tube electrode. The experimental setup included the pulse power supply, electrolyte supply unit, and electrolysis devices. The workpiece was installed on an *X-Y* stage. The electrode tool was carefully attached at the terminal of the spindle, and then the spindle was installed on a *Z*-axis and driven by an inverter. The speed of the spindle was adjusted by controlling the output frequency of the inverter. In addition, the function of internal flushing was achieved by Figure 6 shows a schematic of EC-milling system with a tube electrode. The experimental setup included the pulse power supply, electrolyte supply unit, and electrolysis devices. The workpiece was installed on an *X-Y* stage. The electrode tool was carefully attached at the terminal of the spindle, and then the spindle was installed on a *Z*-axis and driven by an inverter. The speed of the spindle was adjusted by controlling the output frequency of the inverter. In addition, the function of internal flushing was achieved by using a rotating joint, which could transfer electrolyte from a pipeline into a rotating spindle. Figure 7 shows a photograph of the tube electrodes with different end faces, which were made from stainless steel 304, and the outer diameter and inner diameter were 1.0 mm and 0.8 mm, respectively.

using a rotating joint, which could transfer electrolyte from a pipeline into a rotating spindle. Figure 7 shows a photograph of the tube electrodes with different end faces, which were made from stainless steel 304, and the outer diameter and inner diameter

**Figure 6.** Schematic diagram of the experimental system.

were 1.0 mm and 0.8 mm, respectively.

**Figure 5.** The variation of electrolyte velocity on points A to C in the IEG under kinds of tube tools.

Figure 6 shows a schematic of EC-milling system with a tube electrode. The experimental setup included the pulse power supply, electrolyte supply unit, and electrolysis devices. The workpiece was installed on an *X-Y* stage. The electrode tool was carefully attached at the terminal of the spindle, and then the spindle was installed on a *Z*-axis and driven by an inverter. The speed of the spindle was adjusted by controlling the output frequency of the inverter. In addition, the function of internal flushing was achieved by using a rotating joint, which could transfer electrolyte from a pipeline into a rotating spindle. Figure 7 shows a photograph of the tube electrodes with different end faces, which were made from stainless steel 304, and the outer diameter and inner diameter

**Figure 6. Figure 6.** Schematic diagram of the Schematic diagram of the experimental system. experimental system.

**3. Experimental Section**

were 1.0 mm and 0.8 mm, respectively.

**Figure 7.** The photo of tube electrodes with different end faces. **Figure 7.** The photo of tube electrodes with different end faces.

In this work, the workpiece material was GH4169, and the machining depth and length of the electrode were 5 mm and 10 mm, respectively. The machining accuracy of DNG was investigated by detecting the width and taper. The size measurement of DNG is shown in Figure 8, where five points along the length of a DNG were measured, the width was the sectional width on the top, and the taper was the angle between the vertical line and the sectional sidewall. The average values of the width and taper were obtained, and the SD (standard deviation) was used to evaluate the dimensional uniformity. The morphologies of DNGs were examined using a scanning electron microscope. In this work, the workpiece material was GH4169, and the machining depth and length of the electrode were 5 mm and 10 mm, respectively. The machining accuracy of DNG was investigated by detecting the width and taper. The size measurement of DNG is shown in Figure 8, where five points along the length of a DNG were measured, the width was the sectional width on the top, and the taper was the angle between the vertical line and the sectional sidewall. The average values of the width and taper were obtained, and the SD (standard deviation) was used to evaluate the dimensional uniformity. The morphologies of DNGs were examined using a scanning electron microscope. The profiles and surface roughness (Ra) of DNGs were measured using a confocal laser-scanning microscope (CLSM, Olympus LEXT OLS4100, Tokyo, Japan) and a Step profiler (Kosaka, ET-150, Tokyo, Japan).

The profiles and surface roughness (Ra) of DNGs were measured using a confocal laser-scanning microscope (CLSM, Olympus LEXT OLS4100, Tokyo, Japan) and a Step profiler (Kosaka, ET-150, Tokyo, Japan). Experiments were performed on each proposed tool to analyze its effect for ma-Experiments were performed on each proposed tool to analyze its effect for machining accuracy and surface quality in the electrochemical milling process. Moreover, the influence of other parameters on machining quality was explored by single-factor experiment. The machining parameters are listed in Table 2.

chining accuracy and surface quality in the electrochemical milling process. Moreover, the influence of other parameters on machining quality was explored by single-factor

> **Parameters Value** Electrolyte concentration 12% (wt.%), NaNO<sup>3</sup>

Electrolyte temperature 25 °C Electrolyte pressure 1.2 MPa

experiment. The machining parameters are listed in Table 2.

**Figure 8.** Schematic diagram of deep-narrow groove measurement.

**Table 2.** Machining parameters.

In this work, the workpiece material was GH4169, and the machining depth and length of the electrode were 5 mm and 10 mm, respectively. The machining accuracy of DNG was investigated by detecting the width and taper. The size measurement of DNG is shown in Figure 8, where five points along the length of a DNG were measured, the width was the sectional width on the top, and the taper was the angle between the vertical line and the sectional sidewall. The average values of the width and taper were obtained, and the SD (standard deviation) was used to evaluate the dimensional uniformity. The morphologies of DNGs were examined using a scanning electron microscope. The profiles and surface roughness (Ra) of DNGs were measured using a confocal laser-scanning microscope (CLSM, Olympus LEXT OLS4100, Tokyo, Japan) and a Step

Experiments were performed on each proposed tool to analyze its effect for machining accuracy and surface quality in the electrochemical milling process. Moreover,

**Figure 8.** Schematic diagram of deep-narrow groove measurement. **Figure 8.** Schematic diagram of deep-narrow groove measurement.


**Figure 7.** The photo of tube electrodes with different end faces.

profiler (Kosaka, ET-150, Tokyo, Japan).


#### **4. Results and Discussion**

*4.1. The Comparison of DNGs Generated with Different Wedged Angles*

In order to compare the difference of DNGs generated with different wedged angles in the end face of the tube tool, comparative experiments were designed with the following machining parameters: the applied voltage of 25 V, pulse duty cycle of 50%, pulse frequency of 1 kHz, feed rate of 0.42 mm/min, and spindle speed of 3000 rpm.

Figures 9 and 10 show the SEM images, dimensions, and 3D profiles of DNGs generated with different wedged angles in the end face of the tube tool. Using standard flat end face with the wedged angle of 0◦ , the average width and taper of the grooves are 1.57 mm ± 0.06 mm (mean ± SD) and 2.2◦ ± 0.43◦ , respectively. When using the end face with wedged angle of 40◦ , the average width and taper of DNG decrease to 1.49 mm ± 0.04 mm and 1.53◦ ± 0.46◦ . However, with the increase in the wedged angle, the average width and taper of DNG gradually increase, reaching to 1.60 mm ± 0.04 mm and 2.3◦ ± 0.45◦ , respectively, when the wedged angle reaches to 60◦ .

External diameter of tube electrode 1 mm Internal diameter of tube electrode 0.8 mm

*4.1. The Comparison of DNGs Generated with Different Wedged Angles*

0.45°, respectively, when the wedged angle reaches to 60°.

frequency of 1 kHz, feed rate of 0.42 mm/min, and spindle speed of 3000 rpm.

**4. Results and Discussion**

Wedge angle 0°, 40°, 50°, 60° Spindle speed 2500, 3000, 3500, 4000 rpm Feed rate 0.30, 0.36, 0.42, 0.48 mm/min

Applied voltage 25 V Pulse frequency 1 kHz Pulse duty cycle 50% Machining depth 5 mm Machining length 10 mm Material of workpiece GH4169

In order to compare the difference of DNGs generated with different wedged angles in the end face of the tube tool, comparative experiments were designed with the following machining parameters: the applied voltage of 25 V, pulse duty cycle of 50%, pulse

Figures 9 and 10 show the SEM images, dimensions, and 3D profiles of DNGs generated with different wedged angles in the end face of the tube tool. Using standard flat end face with the wedged angle of 0°, the average width and taper of the grooves are 1.57 mm ± 0.06 mm (mean ± SD) and 2.2° ± 0.43°, respectively. When using the end face with wedged angle of 40°, the average width and taper of DNG decrease to 1.49 mm ± 0.04 mm and 1.53° ± 0.46°. However, with the increase in the wedged angle, the average width and taper of DNG gradually increase, reaching to 1.60 mm ± 0.04 mm and 2.3° ±

**Figure 9.** The SEM images of DNGs machined with different wedged angles in the end face of tube electrode. (**a**) Wedged angle = 0°; (**b**) wedged angle = 40°; (**c**) wedged angle = 50°; (**d**) wedged angle = 60°. **Figure 9.** The SEM images of DNGs machined with different wedged angles in the end face of tube electrode. (**a**) Wedged angle = 0◦ ; (**b**) wedged angle = 40◦ ; (**c**) wedged angle = 50◦ ; (**d**) wedged angle = 60◦ . *Micromachines* **2022**, *13*, x FOR PEER REVIEW 11 of 17

**Figure 10.** The dimension and 3D profile of DNGs milled with different wedged angles in the end face of the tube tool: (**a**) wedged angle = 0°; (**b**) wedged angle = 40°; (**c**) wedged angle = 50°; and (**d**) wedged angle = 60°. **Figure 10.** The dimension and 3D profile of DNGs milled with different wedged angles in the end face of the tube tool: (**a**) wedged angle = 0◦ ; (**b**) wedged angle = 40◦ ; (**c**) wedged angle = 50◦ ; and (**d**) wedged angle = 60◦ .

Figure 11 shows the comparison of the SEM images and surface roughness (Ra) of DNGs milled with different wedged angles. The surface roughness (Ra) of sidewall is 1.387 μm under the standard flat end face. When the wedged angle is 40°, the surface roughness (Ra) suddenly drops to 1.09 μm. When the wedged angle varies from 50° to 60°, the surface roughness (Ra) increases to 1.65 μm. The reason is that a pulsating electrolyte is generated in the IEG by using the wedged end face of the tube tool, which occurs as flow separation resulting in a large number of vortices at the wall surface and increasing the turbulence and mixing of fluid. The boundaries of this flow are characterized by the creation and destruction of eddies of large turbulence energy and vortex shedding, which helps the removal of electrolytic by-products and reduces the difference of electrolyte conductivity in the IEG along the depth direction of DNG [19]. Hence, the material dissolution rate becomes uniform, reducing the taper of DNG and improv-Figure 11 shows the comparison of the SEM images and surface roughness (Ra) of DNGs milled with different wedged angles. The surface roughness (Ra) of sidewall is 1.387 µm under the standard flat end face. When the wedged angle is 40◦ , the surface roughness (Ra) suddenly drops to 1.09 µm. When the wedged angle varies from 50◦ to 60◦ , the surface roughness (Ra) increases to 1.65 µm. The reason is that a pulsating electrolyte is generated in the IEG by using the wedged end face of the tube tool, which occurs as flow separation resulting in a large number of vortices at the wall surface and increasing the turbulence and mixing of fluid. The boundaries of this flow are characterized by the creation and destruction of eddies of large turbulence energy and vortex shedding, which helps the removal of electrolytic by-products and reduces the difference of electrolyte conductivity in the IEG along the depth direction of DNG [19]. Hence, the material dissolution rate becomes uniform, reducing the taper of DNG and improving the surface quality. In addition, due to the reduction in the accumulation of electrolytic by-products in the IEG, the flow resistance decreases, avoiding the accumulation of electrolyte at the edge of DNG and reducing the stray corrosion at the upper edge of DNG. Thus, the upper

ing the surface quality. In addition, due to the reduction in the accumulation of electrolytic by-products in the IEG, the flow resistance decreases, avoiding the accumulation of

DNG. Thus, the upper width of DNG decreases. With the increase in the wedged angle, the machining quality becomes poor. As the wedged angle increases, the electric field distribution on the sidewall becomes nonuniform, which will lead to the nonuniform electrochemical dissolution. Thus, the taper of DNG increases. Meanwhile, combined with flow field simulation results, the pulsating amplitude of electrolyte increases but the minimum velocity of electrolyte decreases to about 0 m/s with the increase in the wedged angle. There is a low velocity zone of electrolyte in the IEG. Thus, anodic dissolution occurs in an instant static flow, the electrolytic by-products cannot be removed from IEG, which is not beneficial to the machining process. In fact, many studies have reported that a pulsating flow with proper pulsating parameters is helpful to the transfer

process [22].

width of DNG decreases. With the increase in the wedged angle, the machining quality becomes poor. As the wedged angle increases, the electric field distribution on the sidewall becomes nonuniform, which will lead to the nonuniform electrochemical dissolution. Thus, the taper of DNG increases. Meanwhile, combined with flow field simulation results, the pulsating amplitude of electrolyte increases but the minimum velocity of electrolyte decreases to about 0 m/s with the increase in the wedged angle. There is a low velocity zone of electrolyte in the IEG. Thus, anodic dissolution occurs in an instant static flow, the electrolytic by-products cannot be removed from IEG, which is not beneficial to the machining process. In fact, many studies have reported that a pulsating flow with proper pulsating parameters is helpful to the transfer process [22]. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 12 of 17

**Figure 11.** The SEM and surface roughness of sidewall of DNGs generated with different wedge angles in the end face of the tube tool: (**a**) wedged angle = 0°; (**b**) wedged angle = 40°; (**c**) wedged angle = 50°; and (**d**) wedged angle = 60°. **Figure 11.** The SEM and surface roughness of sidewall of DNGs generated with different wedge angles in the end face of the tube tool: (**a**) wedged angle = 0◦ ; (**b**) wedged angle = 40◦ ; (**c**) wedged angle = 50◦ ; and (**d**) wedged angle = 60◦ .

#### *4.2. The Effect of Spindle Speed on the Generation of DNGs 4.2. The Effect of Spindle Speed on the Generation of DNGs*

In this subsection, single-factor experiments were performed to investigate the effect of spindle speed of 2500, 3000, 3500, and 4000 rpm on the dimension by using tube electrode with wedged angle of 40°. Additionally, other machining parameters were set as the applied voltage of 25 V, feed rate of 0.42 mm/min, pulse frequency of 1 kHz, and pulse duty cycle of 50%. In this subsection, single-factor experiments were performed to investigate the effect of spindle speed of 2500, 3000, 3500, and 4000 rpm on the dimension by using tube electrode with wedged angle of 40◦ . Additionally, other machining parameters were set as the applied voltage of 25 V, feed rate of 0.42 mm/min, pulse frequency of 1 kHz, and pulse duty cycle of 50%.

Figures 12 and 13 show the SEM images, dimensional change, and 3D profiles of DNGs generated with different spindle speeds. It can be observed that the average width of DNG decreases from 1.54 ± 0.04 mm to 1.49 ± 0.04 mm, and the average taper decreases Figures 12 and 13 show the SEM images, dimensional change, and 3D profiles of DNGs generated with different spindle speeds. It can be observed that the average width of DNG decreases from 1.54 ± 0.04 mm to 1.49 ± 0.04 mm, and the average taper decreases

from 1.62° ± 0.44° to 1.53° ± 0.46° when the spindle speed increases from 2500 rpm to 3000 rpm. As the spindle speed increases from 3000 to 4000 rpm, the average width maintains

0.32°. This result indicates that the spindle speed has no obvious influence on the width of DNG, while increasing spindle speed can improve the verticality of sidewall. High rotation is effective for the removal of electrolytic by-products from the IEG [23,24]. Meanwhile, the high pulsating frequency of electrolyte further improves the transfer of heat and electrolytic by-products, reducing the differences of electrolyte conductivity and material dissolution rate along the depth direction of DNG. Thus, the taper angle of DNG decreases. In addition, the spindle speed also affects the surface quality of DNGs.

from 1.62◦ ± 0.44◦ to 1.53◦ ± 0.46◦ when the spindle speed increases from 2500 rpm to 3000 rpm. As the spindle speed increases from 3000 to 4000 rpm, the average width maintains at about 1.5 mm, and the average taper gradually decreases from 1.53◦ ± 0.46◦ to 1.32◦ ± 0.32◦ . This result indicates that the spindle speed has no obvious influence on the width of DNG, while increasing spindle speed can improve the verticality of sidewall. High rotation is effective for the removal of electrolytic by-products from the IEG [23,24]. Meanwhile, the high pulsating frequency of electrolyte further improves the transfer of heat and electrolytic by-products, reducing the differences of electrolyte conductivity and material dissolution rate along the depth direction of DNG. Thus, the taper angle of DNG decreases. In addition, the spindle speed also affects the surface quality of DNGs. With the spindle speed increased, the pulsating frequency of electrolyte is increased, which could further enhance the removal of electrolytic by-products in IEG; thus, the electrochemical dissolution of material becomes more uniform, and the milled surface quality is improved. As shown in Figure 14, when the spindle speed increases from 2500 rpm to 4000 rpm, the surface roughness (Ra) of sidewall decreases from 1.14 µm to 0.92 µm. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 13 of 17 With the spindle speed increased, the pulsating frequency of electrolyte is increased, which could further enhance the removal of electrolytic by-products in IEG; thus, the electrochemical dissolution of material becomes more uniform, and the milled surface quality is improved. As shown in Figure 14, when the spindle speed increases from 2500 rpm to 4000 rpm, the surface roughness (Ra) of sidewall decreases from 1.14 μm to 0.92 μm. *Micromachines* **2022**, *13*, x FOR PEER REVIEW 13 of 17 With the spindle speed increased, the pulsating frequency of electrolyte is increased, which could further enhance the removal of electrolytic by-products in IEG; thus, the electrochemical dissolution of material becomes more uniform, and the milled surface quality is improved. As shown in Figure 14, when the spindle speed increases from 2500 rpm to 4000 rpm, the surface roughness (Ra) of sidewall decreases from 1.14 μm to 0.92 μm.

**Figure 12.** The SEM images of DNGs generated under different spindle speeds. (**a**) Spindle speed = 2500 rpm; (**b**) spindle speed =3000 rpm; (**c**) spindle speed = 3500 rpm; (**d**) spindle speed = 4000 rpm. **Figure 12.** The SEM images of DNGs generated under different spindle speeds. (**a**) Spindle speed = 2500 rpm; (**b**) spindle speed =3000 rpm; (**c**) spindle speed = 3500 rpm; (**d**) spindle speed = 4000 rpm. **Figure 12.** The SEM images of DNGs generated under different spindle speeds. (**a**) Spindle speed = 2500 rpm; (**b**) spindle speed =3000 rpm; (**c**) spindle speed = 3500 rpm; (**d**) spindle speed = 4000 rpm.

Z

Z

speed = 4000 rpm. **Figure 13.** The dimension and 3D profile of DNGs milled with different spindle speeds: (**a**) spindle speed = 2500 rpm; (**b**) spindle speed = 3000 rpm; (**c**) spindle speed = 3500 rpm; and (**d**) spindle speed = 4000 rpm. **Figure 13.** The dimension and 3D profile of DNGs milled with different spindle speeds: (**a**) spindle speed = 2500 rpm; (**b**) spindle speed = 3000 rpm; (**c**) spindle speed = 3500 rpm; and (**d**) spindle speed = 4000 rpm.

**Figure 14.** The surface roughness (Ra) of sidewall with different spindle speeds. **Figure 14.** The surface roughness (Ra) of sidewall with different spindle speeds.

#### *4.3. The Effect of Feed Rate on the Generation of DNGs 4.3. The Effect of Feed Rate on the Generation of DNGs*

In order to investigate the effect of the tube tool feed rate on the machining quality, single-factor experiments with the feed rate at 0.30, 0.36, 0.42, and 0.48 mm/min and the spindle speed at 4000 rpm were conducted. The other machining parameters were set as the applied voltage of 25 V, wedged angle of 40°, rotational speed of spindle of 4000 rpm, In order to investigate the effect of the tube tool feed rate on the machining quality, single-factor experiments with the feed rate at 0.30, 0.36, 0.42, and 0.48 mm/min and the spindle speed at 4000 rpm were conducted. The other machining parameters were set as the applied voltage of 25 V, wedged angle of 40◦ , rotational speed of spindle of 4000 rpm, pulse frequency of 1 kHz, and pulse duty cycle of 50%.

pulse frequency of 1 kHz, and pulse duty cycle of 50%. Figures 15 and 16 show the SEM images, dimensions, and 3D profiles of DNGs generated with different feed rates of tube electrode. As the feed rate increases from 0.30 to 0.48 mm/min, the average width of DNG decreases from 1.63 mm to 1.48 mm, and the average taper decreases from 2.66° to 1.32°. Moreover, the standard deviations of the width and taper of DNG decrease significantly with the increase in the feed rate. Thus, Figures 15 and 16 show the SEM images, dimensions, and 3D profiles of DNGs generated with different feed rates of tube electrode. As the feed rate increases from 0.30 to 0.48 mm/min, the average width of DNG decreases from 1.63 mm to 1.48 mm, and the average taper decreases from 2.66◦ to 1.32◦ . Moreover, the standard deviations of the width and taper of DNG decrease significantly with the increase in the feed rate. Thus, the consistency of the DNG enhances considerably. **Figure 14.** The surface roughness (Ra) of sidewall with different spindle speeds.

the consistency of the DNG enhances considerably. (**a**) (**b**) According to Equation (1), with the increase in feed rate *v<sup>x</sup>* of the tube tool, the front gap ∆*x* decreases. As shown in Equations (4) and (5), with the decrease in the front gap ∆*x*, the width of groove *W* decreases. In addition, when the workpiece is moving toward the electrode, the electric field is provided mostly by the front of the electrode. However, the milled surface of the groove is inevitably exposed to the back of the tube electrode, and a small amount of material is dissolved from the milled surface of the DNG due to corrosion by the stray current. Thus, with the increase in feed rate, the time of secondary stray dissolution to sidewall of DNG reduces, and the taper of sidewall and its standard deviation gradually decreases. At the same time, the reduction in secondary stray dissolution to sidewall improves the surface quality of sidewall. As shown in Figure 17, when the feed rate increases from 0.30 to 0.48 mm/min, the surface roughness (Ra) decreases from 1.41 µm to 0.85 µm. *4.3. The Effect of Feed Rate on the Generation of DNGs* In order to investigate the effect of the tube tool feed rate on the machining quality, single-factor experiments with the feed rate at 0.30, 0.36, 0.42, and 0.48 mm/min and the spindle speed at 4000 rpm were conducted. The other machining parameters were set as the applied voltage of 25 V, wedged angle of 40°, rotational speed of spindle of 4000 rpm, pulse frequency of 1 kHz, and pulse duty cycle of 50%. Figures 15 and 16 show the SEM images, dimensions, and 3D profiles of DNGs generated with different feed rates of tube electrode. As the feed rate increases from 0.30 to 0.48 mm/min, the average width of DNG decreases from 1.63 mm to 1.48 mm, and the average taper decreases from 2.66° to 1.32°. Moreover, the standard deviations of the width and taper of DNG decrease significantly with the increase in the feed rate. Thus, the consistency of the DNG enhances considerably.

**Figure 15.** The SEM images of DNGs generated with varied feed rates. (**a**) Feed rate = 0.30 mm/min; (**b**) Feed rate = 0.36 mm/min; (**c**) Feed rate = 0.42 mm/min; (**d**) Feed rate = 0.48 mm/min. **Figure 15.** The SEM images of DNGs generated with varied feed rates. (**a**) Feed rate = 0.30 mm/min; (**b**) Feed rate = 0.36 mm/min; (**c**) Feed rate = 0.42 mm/min; (**d**) Feed rate = 0.48 mm/min.

1.4

1.6

Width (mm)

1.8

2.0

2.2

 Width Taper

mm/min.

*Micromachines* **2022**, *13*, x FOR PEER REVIEW 15 of 17

**Figure 16.** The dimension and 3D profile of DNGs milled with different feed rates: (**a**) feed rate = 0.30 mm/min; (**b**) feed rate = 0.36 mm/min; (**c**) feed rate = 0.42 mm/min; and (**d**) feed rate = 0.48 **Figure 16.** The dimension and 3D profile of DNGs milled with different feed rates: (**a**) feed rate = 0.30 mm/min; (**b**) feed rate = 0.36 mm/min; (**c**) feed rate = 0.42 mm/min; and (**d**) feed rate = 0.48 mm/min. solution to sidewall improves the surface quality of sidewall. As shown in Figure 17, when the feed rate increases from 0.30 to 0.48 mm/min, the surface roughness (Ra) decreases from 1.41 μm to 0.85 μm.

deviation gradually decreases. At the same time, the reduction in secondary stray dis-

6200 3100 0


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**Figure 17.** The surface roughness (Ra) of sidewall with varied feed rates. **Figure 17.** The surface roughness (Ra) of sidewall with varied feed rates.

#### *4.4. EC-Milling of Complex Narrow Grooves by Using Wedged Tube Electrode*

*4.4. EC-Milling of Complex Narrow Grooves by Using Wedged Tube Electrode* Based on the above research, the complex deep-narrow groove structures with machining depth of 5 mm are machined on GH4169 nickel-based alloy in one-pass feed by using a wedged end face tube electrode with wedged angle of 40°, as shown in Figure Based on the above research, the complex deep-narrow groove structures with machining depth of 5 mm are machined on GH4169 nickel-based alloy in one-pass feed by using a wedged end face tube electrode with wedged angle of 40◦ , as shown in Figure 18. The machining parameters are a feed rate of 0.48 mm/min, applied voltage of 25 V, spindle speed of 4000 rpm, pulse frequency of 1 kHz, and pulse duty of 50%.

Based on the above research, the complex deep-narrow groove structures with machining depth of 5 mm are machined on GH4169 nickel-based alloy in one-pass feed by using a wedged end face tube electrode with wedged angle of 40°, as shown in Figure

*4.4. EC-Milling of Complex Narrow Grooves by Using Wedged Tube Electrode*

18. The machining parameters are a feed rate of 0.48 mm/min, applied voltage of 25 V,

spindle speed of 4000 rpm, pulse frequency of 1 kHz, and pulse duty of 50%.

**Figure 18.** The SEM of complex DNG structures: (**a**) a semi-circular arc DNG structure and (**b**) a linear DNG structure. **Figure 18.** The SEM of complex DNG structures: (**a**) a semi-circular arc DNG structure and (**b**) a linear DNG structure.

#### **5. Conclusions 5. Conclusions**

In this study, a novel tube electrode with wedged end face has been proposed for electrochemical milling, deep-narrow groove on GH4160 alloy and to improve the machining accuracy and surface quality. Based on simulations and experiments, the main conclusions can be obtained as follows: In this study, a novel tube electrode with wedged end face has been proposed for electrochemical milling, deep-narrow groove on GH4160 alloy and to improve the machining accuracy and surface quality. Based on simulations and experiments, the main conclusions can be obtained as follows:


**Author Contributions:** Z.Y. and X.C. conceived and designed the experiments; Z.Y. and G.Q. performed the experiments; Z.Y. and X.C. analyzed the data; Z.Y. wrote the paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work described in this study was supported by National Natural Science Foundation of China (Grant No. 52075105, 51705089).

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

