Observation and simulation investigation for the crater formation under discharge plasma movement in RT-WEDM

Observations of the discharge gap were conducted to investigate the discharge plasma motion in reciprocated traveling wire electrical discharge machining (RT-WEDM). It was found that a discharge plasma continuously slides on the surface of a workpiece. An oscillating moving heat source is proposed to better describe the characteristics of discharge plasma motions. Based on an oscillating moving heat source, a novel thermal-fluid coupling model by adopting a level-set method is proposed to investigate the formation of a crater and the effects of machining parameters on craters. Discharge plasma sliding, latent heat, and molten pool forces are comprehensively considered in the proposed model. Simulation and experimental results show that a sliding discharge plasma has a significant effect on a crater. At the end of a discharge, a considerable proportion of molten materials remains in the molten pool. A high sliding speed of discharge plasma can lead to a low aspect ratio in a crater and a thin recast layer. Due to discharge plasma sliding, an increase in pulse duration can significantly increase the length of a crater and decrease the aspect ratio, while an increase in peak current can significantly increase the depth and volume of the crater. Simulation and experimental results also show that morphologies of the simulated crater and experimental craters are consistent, verifying the feasibility and accuracy of the proposed simulation model in explaining the mechanism of crater formation in RT-WEDM.


Introduction
Wire electrical discharge machining (WEDM), with its capability of machining parts with complex shapes, is widely used in mold and die industries [1]. WEDM can be divided into reciprocated traveling WEDM (RT-WEDM), whose wire electrode speed is generally between 8 and 10 m/s, and uni-directional traveling low-speed WEDM (LS-WEDM), whose wire speed is generally lower than 0.25 m/s [2]. Due to a high wire electrode traveling speed, RT-WEDM has distinguished advantages, so that debris can easily be evacuated from a discharge gap. Therefore, RT-WEDM can be used to machine large height and large taper workpieces, which are difficult to be machined by LS-WEDM [3]. Due to its distinctive advantages, RT-WEDM has become one of the widely used non-conventional material removal processes [4].
In EDM, the discharge plasma motion inevitably affects the formation of a discharge crater. Since a crater is a basic unit of a machining process, a model of crater formation is crucial for understanding the material removal mechanism. Besides, the study of the effects of parameters on craters under the condition of plasma sliding can provide a guidance for the selection of electrical parameters in machining. However, it is difficult to model the crater formation due to an extremely short discharge time and the complexity of discharge plasma. Therefore, the EDM mechanism is not yet fully revealed. Unlike traditional EDM process, as shown in Fig. 1, the relative speed between a wire electrode and a workpiece cannot be ignored in RT-WEDM. However, basic theoretical researches are relatively insufficient for RT-WEDM as compared with traditional EDM and LS-WEDM. Therefore, the machining mechanism in RT-WEDM needs to be reevaluated.
Many studies have discussed the formation of the discharge plasma and craters in traditional EDM by observation and simulation. Kojima et al. [5] adopted a high-speed video camera to observe the arc plasma motion and measure the diameter of the arc plasma using spectroscopy. The paper indicated that the arc plasma expands significantly within 2 μs, and thereafter the diameter remains unchanged. Yue and Yang [6][7][8] observed a molten pool and its motion behavior in a discharge by using a high-speed video camera, an invisible laser light source illumination device, and a band-pass filter for eliminating the influence of a plasma arc in a discharge process. Kunieda et al. [9] found that the discharge plasma moves quickly on an electrode surface during a single-pulse discharge by adopting a high-speed video camera. Although the abovementioned observations are mainly focused on EDM processes, the methods can be used as a reference for observations of RT-WEDM in this paper.
Meanwhile, there are several simulations and experiments dedicated to elucidate crater formations in EDM and WEDM. Tang and Yang et al. [10] used a level-set method, which comprehensively considered the force and mass transfer of a molten pool, to simulate the formation of a discharge crater. However, the simulation model only considered a steady heat source, while the heat source was moving in RT-WEDM. Esteves et al. [11] pointed out the asymmetry of a WEDM crater and the paper suggested that the development of a crater is restricted by the wire geometry, and the crater mainly develops along the axial direction of the wire. Zhang et al. [12] investigated motion characteristics of the discharge plasma in RT-WEDM and fitted crater dimensions by experiments. Kai et al. [13] studied the effect of a relative speed between electrodes in RT-WEDM and found that a high wire electrode speed significantly affects crater dimensions. Hou et al. [14] studied the effects of peak current, pulse duration, and wire speed on craters in RT-WEDM through simulating a temperature field and a stress field. However, limited number of studies so far explain in detail the formation of a crater comprehensively, by considering discharge plasma sliding, force, and phase transition in RT-WEDM.
This paper proposes an observation method and a thermal-fluid coupling model to study the formation of the discharge plasma and craters under discharge plasma movement in RT-WEDM. Effects of electrical parameters and wire speed on the machining performance are discussed to guide the selection of machining parameters. However, this paper mainly focuses on the formation of craters during pulse duration, while evacuations of molten metal materials and debris are not discussed in this paper.
Microscopic observations of a discharge process by adopting a high-speed video camera are conducted. Then, a thermal-fluid coupling model is built up to simulate the formation of a crater. The relative motion between electrodes and molten pool forces is considered in this model. Meanwhile, the influences of wire electrode speed and machining parameters on the crater are evaluated through simulations and experiments.

Experimental setup
As illustrated in Fig. 2, to observe a discharge gap, a novel observation pose is proposed. The center of a wire electrode is aligned with the edge of a workpiece. Therefore, a molten pool, i.e., a crater during formation, can be observed clearly. The viewing direction is perpendicular to the workpiece so that the molten pool will not be blocked by the wire electrode. A high-speed video camera with model Phantom V2012 was adopted to observe discharges. A laser light source with a band frequency of 810 nm is adopted to  illuminate the discharge gap. Meanwhile, a band-pass filter was mounted on the camera lens. The wavelength band-pass range is between 800 and 820 nm. Therefore, the visible light whose wavelengths are between 380 and 780 nm [7] produced by arcs and high-temperature melting materials can be filtered out, and the discharge gap phenomena can be observed clearly.
Experiments were carried out on a BKD2 RT-WEDM machine by Suzhou Puguang Cooperation, China. Molybdenum wire electrode was used as the cathode, while tool steel Cr12 workpieces with a height of 1 mm were used as the anode in machining tests. A discharge pulse power supply is adopted to provide a single-pulse discharge energy. A smart CNC system is developed to control a discharge gap and axial motions. The experimental setup of observation is shown in Fig. 3.
During a single discharge, the wire electrode remains stationary in horizon, while the workpiece table moves 1 μm at each step in the XY directions to the wire electrode until a discharge occurs. The pulse duration is set to 40 μs, while the peak current is set to 25 A. The wire speed is set to 10 m/s. Parameters of the high-speed video camera the laser light source are listed in Table 1.

Observation experiments
Limited by the camera performance and shooting requirements, the depth of a field is only within 200 μm. Therefore, obtained images are deblurred for a clearer view of the evolution of a molten pool. Images of the evolution of a molten pool are shown in Fig. 4. D w is the moving direction of the wire electrode.
During a discharge, the area with a weak bright light in the image is the center of a discharge plasma. With the movement of a wire electrode, the center of the discharge plasma also continuously slides along the surface of a workpiece, and the molten pool evolves in response to the sliding discharge plasma. At the instant of t = 40 μs, the molten pool evolves to a length of 320 μm along the sliding direction of the discharge plasma, while the molten pool evolves to a depth of 5-20 μm. The length of the molten pool evolves significantly, while the depth evolution is relatively shallow, resulting in a low aspect ratio crater in the case of discharge plasma sliding.
Meanwhile, it can be seen that the dimension of a discharge plasma and the length of a molten pool are not equal. The discharge plasma action area is relatively small, while the length evolution of the molten pool is mainly caused by the continuous sliding discharge plasma.  The wire electrode travels reciprocally in RT-WEDM. To study the effects of a wire electrode traveling direction and gravity on the evolution of a molten pool, the evolution of a molten pool when the wire electrode travels upward is observed. The evolution of the molten pool is illustrated in Fig. 5. It can be found that as the wire electrode moves, the molten pool evolves upward. The observation results show that the evolution of the molten pool is mainly affected by the discharge plasma sliding, without a noticeable impact from gravity.

Thermal-fluid coupling model in RT-WEDM
It can be seen from the observation that a discharge plasma continuously slides on a workpiece surface during a discharge. Unlike an axisymmetric crater in traditional EDM, which can be described and simulated with a 2D profile, a crater generated by RT-WEDM is asymmetric. Therefore, simulations for crater formation of RT-WEDM need to be conducted in 3D configurations due to discharge plasma sliding.
To simulate the formation of a crater, a thermalfluid coupling model used comprehensively incorporates heat transfer, phase change, fluid flow, and forces. A simulated domain includes a metal solid phase and a gas phase, representing a molten pool and a discharge gap, respectively.
The essence of crater simulation is to find an interface between gas and liquid. A level-set method is usually used in finding an interface between different phases. Therefore, a level-set method is adopted to track an interface of solid phase and gas phase. In the level-set method, a variable, φ, ranging from 0 to 1, is defined. The variable φ is taken as 0 in gap phase, while φ is taken as 1 in the liquid (and solid) phase. The interface of the gas phase and liquid (and solid) phase can be tracked by locating φ = 0.5. The model takes into account the latent heat by using an equivalent heat capacity. Finally, the results are obtained by iteratively solving a set of conservation equations.
There are a solid phase, a liquid phase, and a solid-liquid mixed region during the transition between the solid and liquid phases. To study the conversion between solid and liquid phases, a binary mixed model is adopted. Besides, by analyzing this region, the evolution of a recast layer can be obtained.

Model settings and governing equations
In RT-WEDM, with the formation of a discharge plasma, a workpiece is continuously heated by a heat source acting on a discharge spot, resulting in a rapid temperature rise.
Descoeudres et al. [15] and Kojima [5] indicated that the equivalent heat source of a discharge plasma can be described as a Gaussian heat source, which can be written as where q(r,t) is the heat flux distribution at time t and position (x, y), u and i represent the gap voltage and current, respectively, and F a is the distribution ratio. In this paper, F a is set to 42% [16]. r f ocus is the position of a discharge plasma center, while r is the spatial position. R is the heat source radius. However, due to discharge plasma sliding, the heat source needs to be revised in RT-WEDM, which is introduced in the next section. During a discharge, phase transition and liquid flow occur continuously. Therefore, in the thermal-fluid coupling model, the conservation equations of energy, mass, and momentum need to be solved. However, with a comprehensive consideration for the effects of gravity, surface tension, and vapor force, the momentum conservation equation needs to be revised. While surface tension is taken into account, the Marangoni effect is ignored in this paper. Gas and liquid materials are assumed to be incompressible, and fluids are assumed to be Newtonian. The conservation equations can be described as where C p is specific heat capacity, T is temperature, μ is dynamic viscosity, ρ is density, k is thermal conductivity, β is the volume expansion coefficient of liquid, u is velocity vector, P is pressure, I is unit matrix, F g is gravity, F s is surface tension, and F v is vapor force. The conservation equations comprehensively consider solid, liquid, and gas phases. During a crater formation, the interface of a molten pool and a discharge gap is tracked by the level-set method [10], which is described by Physical properties of solid-liquid materials on both sides of a free interface are significantly different, which can easily result in a convergence failure in solving the equations. To avoid a calculation failure due to a sudden change in material properties, the physical properties of the materials near the interface are functions of the level set as described by where ρ v and ρ m are gas and liquid material density, respectively, k v and k m are thermal conductivity of gas and liquid materials, respectively, and μ v and μ m are viscosity coefficients of gas and liquid materials, respectively. Besides, the vaporization phase transition during a discharge needs to be computed as where T v and T m are the temperature range in which gasification and liquefaction occur. T v and T m are the vaporing point and melting point, respectively, and L v and L m are the latent heat of vaporization and melting, respectively. Due to the mass transition, the mass conservation equation near the gas-liquid interface and the revised levelset equation can be expressed as whereṁ is the evaporation rate, m is the atomic mass of a workpiece material, k b is the Boltzmann constant, and β r is the condensation coefficient.
In the solid-liquid phase, there are some issues such as the continuity of mass, momentum, and energy conservation due to phase transitions. To cope with these issues appropriately, a classical binary hybrid model is adopted. Physical properties within a solid-liquid region can be calculated according to the mass percentage and volume percentage of each item in the material as ρ = g s ρ s + g l ρ l k = g s k s + g l k l c = g s c s + g l c l (7) where f s and f l are mass ratios of solid and liquid materials in a mushy region, respectively, and g s and g l are volume ratios of solid and liquid materials, respectively.

Heat source in RT-WEDM
It can be seen from observations that a discharge plasma slides on a workpiece. Therefore, a heat source needs to be revised. As shown in Fig. 6, a crater formed by a stationary discharge plasma is non-axisymmetric, while a crater formed by a sliding discharge plasma is elongated. For craters as shown in Fig. 6, the length (L) and width (W ) are defined, while the depth (D) refers to the distance from the bottom of a crater to the workpiece surface. According to the crater morphology, two types of equivalent heat sources are attempted to establish a simulation model. (1) A discharge plasma is equivalent to an axis-symmetric circular moving Gaussian heat source. However, a simulated crater using this equivalent heat source is different from an actual crater when the moving speed of the heat source is set to 0. (2) A discharge plasma is equivalent to a two-dimensional Gaussian heat source with different variances in two dimensions. However, due to the sliding of a heat source with a large diameter, the discharge energy is dispersed, resulting in an ineffective material removal.
According to the morphology of craters formed by a stationary discharge plasma and a sliding discharge plasma, a discharge plasma is equivalent to a periodic oscillating moving heat source with a certain diameter. For relative movements between a wire electrode and a workpiece, an oscillating moving heat source is supposed to continuously slide on the surface of a workpiece with a certain speed. In this equivalent heat resource, the diameter of a heat source and the oscillation amplitude are related to the width and length of craters formed by a stationary heat source, while the sliding speed of a heat source is related to the speed of a wire electrode. The schematic diagram of an oscillating moving heat source is shown in Fig. 7.
Many researchers proposed that the moving speed of a heat source is linearly proportional to the moving speed of Fig. 6 Craters formed by discharge plasma: a formed by stationary discharge plasma, b formed by sliding discharge plasma a wire electrode [14,17]. The relationship can be described as v p = f p v w (10) where v p is the sliding speed of a discharge plasma, v w is the moving speed of a wire electrode, and f p is the proportional coefficient. By trial and error, f p is chosen to be 0.4 in this paper. The effect of wire electrode movements on a crater is essentially affected by the discharge plasma sliding. To emphasize this essential Fig. 7 Schematic diagram of the oscillating moving heat source impact, in the subsequent study, this relationship is used to obtain an approximate sliding speed of the discharge plasma relative to the wire electrode speed. The dimension of a crater is closely related to pulse duration and peak current. The empirical formula proposed by Ikai et al. [18] is widely used in the fitting of crater dimensions. Therefore, the length and width of a crater formed by a stationary discharge plasma in RT-WEDM can be approximately described as where K l , K w , a, b, c, and d are fitting coefficients, T on is the pulse duration, and I p is the peak current.
To determine coefficients in an approximate fitting formula of crater dimensions, the length and width of craters formed by a stationary discharge plasma under different pulse durations and peak currents are obtained through experiments. Each group of experiments was repeated for 10 times, while the average dimensions are used for fitting. Experimental results are shown in Table 2.
The required coefficients are solved by a least error squares method, and the approximate fitting formula is written as By trial and error, the equivalent heat source diameter R w of the heat source is set to 1.35 times the radius of a crater, while the amplitude of oscillating motions is equal to the length of a crater formed by a stationary discharge plasma. The frequency of an oscillating motion is set to 500 kHz [19].
According to the above analysis, the revised equivalent heat source of a sliding discharge plasma is described as (13) where r l and r w are the spatial positions in the length and width dimensions, respectively. r f ocus is the moving distance of the heat source due to the discharge plasma sliding. r osc is the offset position from the center of a heat source due to oscillating motions.

Boundary conditions and simulation setup
To reduce the simulation time, a surface-symmetrical threedimensional model is used to simulate a crater in this paper, as illustrated in Fig. 8. The boundary conditions are also shown in Fig. 8. IGKL is the thermal insulation surface. ABGI, CDLK, and ADLI are the boundary convection surfaces. ABCD is the outflow surface. BCKG is set as the symmetry plane. EFGH is the initial action surface of the Gaussian heat source and the initial interface of the level set. In this paper, COMSOL Multiphysics 5.5 is used to iteratively solve the differential equations to study the formation of a discharge crater. The gap voltage is set to 25V. The pulse duration is set to 30 μs, while the peak current is set to 25 A. The main properties of air and steel are set according to Table 3. When investigating the effects of a certain machining parameter on simulation, other parameters are kept unchanged to ensure the effect of the machining parameter on simulation results.

Simulation results and analysis
The phase-field distribution of the level set φ>0.5 in the workpiece domain can not only describe the evolution of a molten pool and morphological changes of the gas-liquid (solid) interface, but also obtain a transformation between the solid and liquid metal. Results of the metal liquid phase ratio which is between 0 and 1 are used to show the process

Effects of discharge plasma sliding and gravity on crater
Figures 9 and 10 show two craters formed by a stationary discharge plasma and a sliding discharge plasma, respectively. The morphology of a traditional crater (formed by a stationary discharge plasma) is axisymmetric, while the morphology of the crater in RT-WEDM is asymmetrical due to discharge plasma sliding. The length of a crater formed by a stationary discharge plasma is greater than that formed by a sliding discharge plasma. The depth of the crater is shallower than a traditional crater formed by a stationary discharge plasma.
As shown in Fig. 10, differences in the length, width, and depth of craters formed under different gravity directions are within 5%. Therefore, it can be considered that in the formation of a single-pulse discharge crater, the effect of gravity is insignificant. Instead, the formation is mainly affected by the sliding direction of a discharge plasma, which is also the movement direction of a wire electrode. Next, craters formed when gravity and discharge plasma

Evolution of a molten pool
To investigate the mechanism of an RT-WEDM process, the evolution of a molten pool is simulated. Variations in length, width, and depth of a molten pool with respect to time are shown in Fig. 11. The three-dimensional morphology and longitudinal section of the molten pool under discharge plasma sliding are shown in Fig. 12.
As shown in Fig. 11, it can be seen that the length continues to evolve until the end of a discharge. The width and depth evolve at first and then remain unchanged. Besides, the length, width, vaporization depth, and melting Fig. 10 Simulated crater formed by sliding discharge plasma: a The direction of gravity is the same as the sliding direction of discharge plasma; b the direction of gravity is opposite to the sliding direction of discharge plasma Fig. 11 Simulation of crater length, width, and depth as functions of time depth evolve nonlinearly with time, which shows that there is a nonlinear relationship between material removal rate and discharge energy.
From the morphology of the molten pool at the instant of t = 5 μs, it can be seen that the solid material continuously heated by the heat source gradually produces a phase transition, resulting in a molten pool. At the instant of t = 10 μs, it can be seen that the material near the center of the heat source is vaporized. Correspondingly, the contact surface of the heat source on the molten pool changes with the change in the gas-liquid interface. During the process, the heat source contact surface and the heat and mass transfer process are constantly iterated, eventually forming a molten pool.
Between 5 and 30 μs, with the heat source moving, the discharge energy center continues to shift. It can be found that the morphology of the molten pool is asymmetrical but plane-symmetric. With the moving and heating of the heat source, the length, width, and depth of the molten pool continue to evolve. The length of the molten pool evolves faster than the depth of the molten pool. The rate of change of the depth and width of the molten pool becomes smaller when the depth and width evolve to a certain extent, and then remain unchanged.
At the instant of t = 30 μs, it can be seen from the final crater morphology that the crater has a low aspect ratio. The interface between the gap and the molten material is formed after the workpiece material is vaporized. The molten region where the solid-liquid phase transition occurs finally forms a recast layer.
Meanwhile, the distribution of the velocity field of molten materials, as shown in Fig. 12, reveals the movements of molten materials during the evolution of a molten pool. In the beginning, the velocity of molten materials is small and mainly perpendicular to the surface of the workpiece. The phase transition of the material is relatively slow due to the short action time of the heat source. Then, due to the effects of vaporization force, gravity, and surface tension, the movement directions of Fig. 12 Simulation of the evolution of a molten pool: a t = 5 μs, b t = 10 μs, c t = 20 μs, d t = 30 μs the vaporized molten material begin to diverge. The phase change is mainly concentrated at the center of the heat source, where a vaporization force is the largest. The vaporization force generated by metal evaporation has a significant impact upon the movements of molten materials. The force in the molten region near the center of the heat source is not perpendicular to the sliding direction of the discharge plasma, instead it is along the velocity of molten materials. Vaporization forces cause the molten material to move sideways in the direction of vaporized molten materials. Therefore, the thickness of a recast layer is not uniform. While the thickness of the recast layer is small near the center of the heat source, the thickness on both sides of the crater is large.
It can also be seen from the velocity field that due to the moving heat source, the velocity of molten materials in the depth and width dimension at the same position firstly increases. As the center of the heat source moves away, the velocity gradually decreases. Simulation results can explain the phenomenon that while the length continues to evolve, the depth and width evolve to a certain extent and then remain unchanged.
It is worth noting that the simulation results show that at the end of a discharge, a considerable proportion of molten materials remains in the molten pool, resulting in the formation of a recast layer. The formation of a recast layer is one of the major reasons for a low energy utilization rate in EDM. Figure 13 shows crater dimensions (length, width, depth, and volume) as functions of the sliding speed of a discharge plasma, and Fig. 14 shows the three-dimensional morphology, longitudinal profile, and molten material velocity field of a crater at the end of a discharge.

Effects of discharge plasma sliding speed on craters
The sliding speed of a discharge plasma has a significant impact upon the length and depth of a crater. An increase in sliding speed of a discharge plasma leads to a dispersion of energy. An uneven distribution of energy causes some regions being unable to obtain enough energy for phase transition. An increase in sliding speed of a discharge plasma brings an increase in length, a decrease in depth, and a decrease in width of a crater, thus resulting in a lower aspect ratio crater. Besides, due to the plasma sliding, the energy is dispersed and a certain proportion of metal is far away from the heat source before a subsequent phase change. Therefore, it can be seen that the vaporization volume and the melting volume of the crater decrease with an increase in sliding speed of a discharge plasma.
As shown in Fig. 14, when the wire electrode is kept still, the sliding velocity of a discharge plasma is zero. When the wire electrode moves along the X+ direction, the sliding velocity of the discharge plasma is also along the X+ direction. When the sliding velocity is not zero, the velocity of molten materials will not be perpendicular with respect to the sliding velocity of the discharge plasma. With an increase in sliding velocity of the discharge plasma, the magnitude of the X-axial component of the velocity of molten materials increases. As a result, the molten layer in the center region of the heat source is driven to the crater edges. Thus, the molten layer becomes thinner at the center and becomes thicker at the both edges of the crater.
During continuous discharges, the edge of a crater is close to the wire electrode. When a discharge occurs, the edge of the crater is removed at first, but the bottom of the crater remains, resulting in a recast layer on the workpiece surface. Therefore, the molten region at the bottom of the crater can represent the final recast layer on the surface of the workpiece.
Besides, as shown in the velocity field, as the sliding speed of a discharge plasma increases, the material velocity becomes significantly smaller and the phase transition  Figure 15 shows crater dimensions under different pulse durations, and Fig. 16 gives crater dimensions under different peak currents. With an increase in pulse duration and peak current, the length, depth, and volume of a crater increase significantly, while the width of the crater increases slightly. Generally speaking, the length of a crater is greatly affected by pulse duration, while the depth of a crater is greatly affected by peak current. Compared with the increase in peak current, by using the same discharge energy, an increase in pulse duration can lead to a dispersion of energy, resulting in a decrease in material removal rate. Therefore, using the same discharge energy, a long pulse duration can obtain a small aspect ratio crater, while a high peak current can obtain a high material removal rate.

Experimental results and analysis
To verify the feasibility and accuracy of the simulation model, single-pulse discharge experiments were carried out under different wire electrode speeds and machining parameters. Variations in length, width, depth, and volume  Discharge plasma is stochastic. Therefore, each group of experiments is repeated for 10 times and the average value is adopted. Meanwhile, typical craters are used to demonstrate variations of craters. The length, width, depth, and volume of discharge craters and the recast layer of a workpiece surface were measured by the KEYENCE VHX-6000 microscope. To obtain a clear metallographic structure, before observing a recast layer, workpiece surfaces need to be pretreated. A workpiece surface is first ground for a number of times, and then the workpiece surface is corroded for 30 s by a mixture of nitric acid and alcohol with a ratio of 1:25. Therefore, the metallographic structure of the recast layer and the workpiece matrix can be observed clearly.

Effects of relative speed between electrodes on craters
To avoid verbose analysis, a simulated crater and a typical experimental crater under a wire electrode speed of 10 m/s (sliding speed of discharge plasma is approximately 4 m/s) are compared. The pulse duration is set to 30 μs, and the peak current is set to 25 A. As shown in Fig. 17, it can be seen that the length, depth, and width of a crater in simulation and experimental results have good consistency, and the morphology is also relatively consistent. It can be considered that the proposed simulation model in this study is feasible and has a certain accuracy. Figure 18 shows typical craters under different sliding speeds of discharge plasma, while the length, width, depth, and volume of the crater are shown in Fig. 19. It can be found that with an increase in sliding speed of discharge plasma, craters have the following characteristics.
A noticeable feature is that the average length of craters increases significantly under discharge plasma sliding. The average depth of craters decreases significantly, while the average width and volume of craters decrease slightly. Besides, crater depths obtained by experiments are between the vaporization depth and the melting depth obtained by the simulation.
Compared with the simulation results in Fig. 13 and experimental results in Fig. 19, the prediction errors of simulation in length, width, and depth are within 6%, 15%, and 10%, respectively, which verifies the accuracy of the simulation model. In addition, although there is a certain difference between the simulation and experimental results of crater volumes, the changing trend of the crater volume with respect to the sliding speed of a discharge plasma is the same. It can be seen from the simulation that the thickness of a recast layer is not uniform. Besides, the variation in thickness of a recast layer is insignificant when the sliding speed of a discharge plasma changes slightly. Therefore, two-level experiments were conducted to verify the effect of sliding speed of a discharge plasma on a recast layer in roughing and finishing. Machining parameters are shown in Table 4.
The distributions of recast layers in roughing and finishing are shown in Fig. 20. In roughing, as shown in Fig. 20(a), the thickness of the recast layer is about 18-25 μm when v p is 2 m/s, while the thickness of the recast layer is about 13-18 μm when v p is 4 m/s. In finishing, as shown in Fig. 20(b), the thickness of the recast layer is about 12-16 μm when v p is 2 m/s, while the thickness of the recast layer is about 7-13 μm when v p is 4 m/s. It can be found that the thickness of a recast layer decreases with an increase in sliding speed of a discharge plasma. Experimental results verify that the sliding discharge plasma can evacuate a molten pool, thus reducing the thickness of a recast layer.

Effects of machining parameters on craters
To verify the effect of machining parameters on a crater, several sets of experiments were conducted under different pulse durations and peak currents. Machining parameters are listed in Table 5. Figure 21 shows crater dimensions under different pulse durations. The length and volume of a crater are affected significantly by pulse duration, while the depth and width are affected slightly by pulse duration. An approximately linear relationship exists between pulse duration and crater length, while a nonlinear relationship exists between pulse duration and crater volume. Compared with the simulation results, the prediction errors of simulation are within 15%. Figure 22 shows crater dimensions under different peak currents. With an increase in peak current, the depth and volume of a crater increase significantly, while the length and width increase slightly. Besides, an approximately linear relationship exists between peak current and crater volume. Compared with the simulation results, the prediction errors of simulation are within 15%. Thus, experimental results are basically consistent with simulation results.

Conclusions
In this paper, the discharge gap phenomenon is observed, and a thermal-fluid coupling model is established to  (1) Through observations of the physical phenomenon in a discharge gap by adopting a high-speed video camera, it is found that a discharge plasma continuously slides on the surface of a workpiece, and a molten pool evolves in response to a sliding discharge plasma, forming a small aspect ratio crater. The proposed oscillating moving equivalent heat source is more suitable for RT-WEDM. Meanwhile, simulation and experimental results show that a thermal-fluid coupling model by adapting a level-set method can accurately predict a microscopic process of material removal by a single-pulse discharge in RT-WEDM. (2) In RT-WEDM, the crater morphology is nonaxisymmetric due to discharge plasma sliding. At the Fig. 22 Experimental results of crater dimensions as functions of peak current: a length, width, and depth; b volume end of a discharge, a small amount of workpiece material is removed by vaporization, while a considerable proportion of molten materials remains in the crater. During a discharge, the force and movement direction of molten materials in a molten pool are significantly affected by discharge plasma sliding, resulting in a thick molten metal layer on the edge of a molten pool and a thin molten metal layer on the bottom of the molten pool at the end of a discharge. (3) The sliding speed of a discharge plasma has a significant impact on the length and depth of a crater. A high sliding speed can result in a small aspect ratio crater and a thin recast layer. Besides, pulse duration has a significant effect on the length and aspect ratio of a crater, while peak current has a significant effect on the depth and volume of the crater. Using the same discharge energy, a long pulse duration can result in a small aspect ratio crater, while a large peak current can result in a high material removal rate. As compared with simulation results, the prediction accuracy error of the simulation model is within 15%. Experimental results are basically consistent with the simulation.
Author contribution Xue-Cheng Xi was responsible for conceptualization, methodology, funding acquisition, and writing and editing. Zi-Lun Li was responsible for software, validation, formal analysis, and writing of draft. Qiang Gao was responsible for formal analysis and validation. Ya-Ou Zhang's contribution was formal analysis and writing of original draft. Wan-Sheng Zhao's contribution was supervision and writing and editing.
Funding This research is financially supported by the National Natural Science Foundation of China (Grant No. 52075333). The authors also gratefully acknowledge the Leading with Wisdom Advanced Manufacturing Research Center, Pinghu, Zhejiang Province, for their kind assistance in this work.

Competing interests
The authors declare no competing interests.