This paper presents the design of a novel testbed that effectively combines pulsed electric field waveforms, ultrasonic velocity, and magnetic field waveforms in an anodic dissolution electrochemical machining (ECM) cell. The testbed consists of a custom three-dimensional (3D)-printed flow cell that is integrated with (i) a bipolar-pulsed ECM circuit, (ii) an ultrasonic transducer, and (iii) a custom-built high-frequency electromagnet. The driving voltages of the ultrasonic transducer and electromagnet are calibrated to achieve a timed workpiece velocity and magnetic field, respectively, in the machining area. The ECM studies conducted using this testbed reveal that phase-controlled waveform interactions between the three assistances affect both the material removal rate (MRR) and surface roughness (Ra) performance metrics. The triad-assisted ECM case involving phase-specific combinations of all three high-frequency (15.625 kHz) assistance waveforms is found to be capable of achieving a 52% increase in MRR while also simultaneously yielding a 78% improvement in the Ra value over the baseline pulsed-ECM case. This result is encouraging because assisted ECM processes reported in the literature typically improve only one of these performance metrics at the expense of the other. In general, the findings reported in this paper are expected to enable the realization of multifield assisted ECM testbeds using phase-specific input waveforms that change on-the-fly to yield preferential combinations of MRR and surface finish.

## Introduction

Pulsed electric fields [13], ultrasonic velocity [4,5], and magnetic fields [6] are three common assistances used in an anodic dissolution electrochemical cell [7]. In anodic dissolution-based manufacturing processes such as electrochemical machining (ECM) and electrochemical finishing/polishing (ECF/P), these assistances have been reported to result in higher material removal rate (MRR), improved surface finish, increased accuracy, and higher electrical efficiency [7]. With an increased push toward the manufacture of complex microscale parts such as turbines and reactors, it has become critical to design electrochemical platforms that can exploit synergistic interactions between these different assistances [8].

The literature related to ECM and ECF/P highlights the benefits of using the three assistances [8]. Pulsed electric fields aid the dissolution of highly passivated metals and increase machining accuracy, by focusing current using the electrical double layer (EDL) pseudo-capacitance [9,10]. Ultrasonic velocity adds agitation to an anodic dissolution cell, which facilitates the removal of metal hydroxide byproduct out of the interelectrode gap (IEG). This increases both the MRR and electrical efficiency of the process. Additionally, cavitation from ultrasonic velocity can inhibit the formation of a passivation layer, which also increases the MRR [4]. Magnetic field assistance is typically generated using permanent magnets [1113]. In these permanent magnet implementations, the field variations are created using a rotary motion of either the magnets [11], the workpiece [12], or both [13]. When electromagnets are employed, they typically function using either direct current [14] or a low frequency alternating current [15]. The use of a constant magnetic field assistance has been shown to increase machining accuracy in ECM [6,16] and improve surface finish in ECM and ECF/P [14].

The literature has also shown the benefits of dual-assisted anodic-dissolution processes that combine two different assistances [1113,1720]. Pa [17,18] studied the effect of combining pulsed electric fields with ultrasonic vibrations, each at a different frequency, to improve surface roughness (Ra). Low-frequency (50 Hz) pulsed electric fields have been combined with in-phase electrode gap oscillations that clear the reaction byproducts during the pulse-off time (coinciding with the maximum electrode gap condition), thereby increasing the MRR [19]. Ultrasonic vibrations have been combined with oscillating magnetic fields to improve ECF/P, though the waveform frequencies of the two assistances were vastly different [20]. Pa [11,12] also combined an oscillating magnetic field with pulsed electric fields to improve surface quality. However, the phasing between the two waveforms was not considered in those studies.

In order to control the coupled effects between multiple assistances, the influence of the phase difference, relative frequency, and relative orientation between the assistances must be carefully investigated. While the studies in the literature have considered the direction of the input waveforms [12,13,17,18,20], the effects of the relative frequency and phase difference have been ignored. This is largely because the frequencies of the assistances used in those studies differed significantly. Furthermore, study of the interaction effects has been limited to only dual-assisted anodic dissolution processes. There has been no work done to explore the triad-assisted case involving the simultaneous influence of pulsed electric fields, ultrasonic velocity, and magnetic fields. This gap in knowledge is mainly because of the complexity of designing such an experimental setup.

In light of the above state-of-the-literature, this paper introduces a method for effectively combining pulsed electric field waveforms, ultrasonic velocity, and magnetic field waveforms in an anodic dissolution electrochemical cell. A novel electrochemical cell has been designed to apply all possible dual-assistance and triad-assistance combinations for ECM. The experimental results show that for both dual-assisted and triad-assisted ECM cases, the machining performance is impacted by the phase difference between the waveforms. The experimental findings also point toward the possibility of complex interactions between the three assistances that will require future modeling efforts in the area of multifield-assisted ECM.

The remainder of the paper is structured as follows: Section 2 outlines the theory related to multifield-assisted ECM. Section 3 presents the details regarding the design of the novel experimental testbed. Section 4 outlines the experimental conditions pertinent to this paper, and Sec. 5 discusses the findings. Finally, Sec. 6 outlines the specific conclusions that can be drawn from this study.

## Theory of Multifield-Assisted Electrochemical Cells

Figure 1 shows a diagram of an anodic dissolution cell where the cathode (i.e., tool) is labeled with “−” symbols and the anode (i.e., workpiece) with “+” symbols. For illustration purposes, the ions labeled as “M++” represent generic metal ions with a plus two charge that form part of the anode EDL. Charged particles labeled with an “e” symbol are electrons. Finally, the small, unlabeled arrows (gray colored) illustrate the most significant portions of a typical anodic dissolution electrochemical reaction.

In Fig. 1, the assistance field directions and the resulting Lorentz force, F, are indicated on only one nitrate ion ($NO3−$) for illustrative purposes. The magnetic field vector is represented by the arrow labeled B, with the ultrasonic electrode velocity vector represented by the arrow labeled V. As seen in Fig. 1, the magnetic field and ultrasonic velocity vectors are orthogonal to each other. The bipolar, pulsed electric field is represented by the arrow labeled E, resulting from the electric potential difference between the two electrodes (represented as rectangular plates in Fig. 1). The electric field, E, is applied parallel to the direction of the ultrasonic velocity, V.

The three assistance fields have coupled effects that are related through the Lorentz force, F, defined by the following equation:
$F=q(E+v×B)$
(1)
where q is the ion charge, E is the electric field, v is the ion velocity, and B is the magnetic field. The time-dependent matrix formulation of Eq. (1) is given by
$F(r,r˙,t,q)=q[E(r,t)+r˙×B(r,t)]$
(2)

where r is the ion position vector, $r˙$ is the ion velocity, and t the is time (Fig. 1). All charged bodies in the assisted electrochemical cell uniquely experience this force. Equation (2) shows that ion motion under the influence of F can be much more complex when using time-dependent inputs for the assistance fields. This is expected to alter ion motion in the electrochemical cell, which, in turn, will change their interaction with the electrode surfaces and the overall rate of reaction.

Pulsing the electric field in a unipolar or bipolar manner not only alters the flow of current in the electrochemical cell, but also alters the motion of ions in the field according to Eq. (2). This paper considers bipolar, pulsed electric fields whenever pulsed ECM (PECM) is discussed. Furthermore, the ultrasonic velocity in this paper operates as a linear actuation method for the workpiece, thereby allowing for a direct addition to the velocity term in Eq. (2) for ions at or near the workpiece surface. It should be noted that the magnetic force on the ions in solution is a function of the cross product of ion velocity and the magnetic field. Therefore, the ions that are accelerated straight toward an electrode by the electric field or ultrasonic velocity will instead have a curvilinear trajectory according to Eq. (2) [14]. This modified trajectory potentially allows for consistent oblique angles of incidence for the negatively charged anions that are directed toward the anode. This, in turn, increases the probability of anions making contact with surface “peaks” rather than “valleys,” thereby removing the peaks and decreasing surface roughness [14]. Additionally, any ancillary increase in ion agitation in the IEG increases the likelihood of ion reactions. This, in turn, is expected to lower the effective resistance in the IEG machining area and also increase the electrical efficiency of the reactions.

In addition to the primary effects of the Lorentz force, a secondary mechanism comes into play for ECM cases involving PECM or time-varying magnetic fields [22]. This secondary mechanism is captured by the Maxwell-Faraday equation
$∇×E(r,t)=−∂∂tB(r,t).$
(3)

As seen in Eq. (3), a nonzero time derivative of the magnetic field results in an induced electric field (and its associated electrical current) in conductive materials including the electrolyte. Therefore, anytime there is a changing electromagnetic field, an induced current will be generated that is capable of participating in the electrochemical cell reaction. This effect is compounded by a workpiece moving within an electromagnetic field. While it is difficult to experimentally isolate the effects of this induced current, it is expected to affect the material removal rates and surface roughness encountered in dual-assisted and triad-assisted ECM.

Electrochemical machining is an ideal process for investigating the effect of assistance waveform interactions because two of its key measurable metrics, viz., surface finish and MRR, can be expected to be sensitive to these interactions. Therefore, an experimental platform that allows for the application of all three assistance waveforms, with phase control in an ECM cell, will allow for the study of the aforementioned effects. Such a platform will allow for all assistance combination scenarios in Fig. 2, where the circles represent an assistance used to augment the traditional direct current (DC) ECM, and the square represents nonassisted DC ECM. The dashed circles are assistance waveforms that cannot be used in isolation for machining, viz., the magnetic field and ultrasonic velocity. Since this paper deals with the combination of waveforms in assisting ECM, experimental treatments are represented in the diagram by regions encompassed by two or more circles. As can be seen, the three individual assistance treatments can be combined to give three distinct dual-assisted ECM processes (i.e., Pulse–Ultra, Mag–Pulse, and Ultra–Mag treatments in Fig. 2). All three fields can be used simultaneously for a triad-assisted ECM cell (Pulse–Ultra–Mag treatment in Fig. 2). The two primary baselines involve the pulsed current case (PECM) and the direct current case (DC ECM). It should be noted here that the DC ECM process is necessary as an additional baseline because neither the ultrasonic velocity nor the magnetic field can meaningfully drive the electrochemical reaction for the Ultra–Mag case in Fig. 2. The two secondary baseline cases are ultrasonically assisted DC ECM and magnetic field-assisted DC ECM denoted, respectively, as Mag and Ultra in Fig. 2.

## Design of Experimental Testbed

Figure 3 presents the system schematic of the experimental platform. While most of the components of this system are comparable to the ECM cells found in the literature, the core of the experimental platform is the “flow cell assembly” (described ahead in Fig. 4), where the electrochemical machining takes place. As seen in Fig. 3, all three assistance waveforms are monitored and conditioned in the control enclosure before being routed to the flow cell assembly. The “control computer” regulates the operation of three power supplies, viz.:

• the anodic and cathodic power supplies: used to create the PECM machining voltage responsible for the electric field (E in Fig. 1);

• the ultrasonic power supply: used to drive the ultrasonic transducer that results in the desired velocity profile (V in Fig. 1);

• the magnet power supply: used to drive the electro-magnet that generates the desired magnetic field, (B in Fig. 1).

During real-time operation, experimentally calibrated time-delays are used within the control computer to synchronize the phase differences between the three assistance waveforms.

A gear pump is used to force the electrolyte through the machining area. Pressure and flow are controlled using a combination of pulse width modulation pump control and a needle valve on the discharge side of the flow cell. This configuration allows the use of a higher pressure across the entire machining surface as well as reduces the relative pressure differential through the IEG. This added pressure helps to reduce the size of bubbles caused by gas evolution from over-potential in the IEG [23]. The remainder of this section will describe the details of the flow cell design and the generation/synchronization of the electric field, ultrasonic velocity, and magnetic fields.

### Novel Flow Cell Design.

Figures 4(a)4(c) show the details of the flow cell assembly that is capable of performing ECM while also allowing for the simultaneous use of all dual-assisted and triad-assisted waveform combinations in Fig. 2. As see in Fig. 4(a), the cylindrical cathode tool is mounted to the flow cell, whereas the anode workpiece is attached to the ultrasonic transducer. A C-core electromagnet is designed such that the magnetic field can be focused in the IEG region of the electrochemical cell.

The flow cell where the reaction occurs was made using an Objet350 multimaterial three-dimensional (3D) printer. This 3D printer allowed for the integrated manufacture of several elastomeric rod seals within the flow cell (refer Fig. 4(b)). These seals were critical in ensuring that ultrasonic motion could be imparted to the workpiece without an ensuing leakage of the electrolyte. Furthermore, the capabilities of the Objet system allowed for the printing of the flow channel with thin watertight walls, thereby reducing the distance between the magnetic poles and the IEG (Fig. 4(c)). This design feature of the flow cell aided the realization of higher magnetic flux densities in the IEG. The flow cell structure shown in Fig. 4 allows ultrasonic velocity to be orthogonal to the magnetic field vector directed from one magnet pole to the other.

The electrolyte flow path in the cell, illustrated by the “flow in” and “flow out” arrows in Fig. 4(b), is orthogonal to both the magnetic field (indicated by the red-arrow in Fig. 4(c)) and the ultrasonic velocity (indicated by the blue-arrow in Fig. 4(c)). The electric field, directed from the workpiece (anode) to the tool (cathode), is parallel to ultrasonic velocity and is shown using a yellow-arrow in the detail of Fig. 4(b). The flow cell is designed to discharge the electrolyte after a single use to limit the possibility of metal hydroxides being redeposited in the machining area.

### Electric Field Generation.

Bipolar pulsed ECM is common when machining highly passivated metals like tungsten carbide or niobium [9]. In such an implementation, while the anodic pulse does the machining, the cathodic pulse is typically used to remove the oxide layer from passivated metals and expose the metal surface for ECM or electropolishing. Since the oxide layer forms periodically during machining, the electric field must be pulsed repeatedly to allow continuous workpiece machining.

For the PECM cases in this study, the electric field was generated using an asymmetric bipolar pulsed voltage. This was accomplished using an H-bridge, shown in Fig. 5, composed of P-channel and N-channel metal-oxide-semiconductor field-effect transistors combined with two precision power supplies. This circuit resides in the block labeled “control enclosure” in Fig. 3, utilizing power from the anodic and cathodic power supplies. Unlike typical H-bridge configurations, this design separates the forward and reverse inputs, which correspond to the anodic and cathodic electric field pulses, respectively. This circuit allows for an economical high-frequency implementation versus that offered by a dedicated pulse power supply. Each bench top power supply can be set to a different voltage or current value thereby allowing for asymmetrical anodic and cathodic pulses. In addition to PECM, the system is also capable of imparting DC voltage for specific baselines (DC ECM, Ultra, and, Mag in Fig. 2) and for the Ultra–Mag dual-assisted case in Fig. 2.

### Ultrasonic Velocity Generation.

As velocity is a prominent component in the Lorentz force expression (Eq. (1)), it was chosen as the experimental treatment for this study, as opposed to the position of the workpiece attached to the ultrasonic actuator. The ultrasonic waveform is defined where a positive workpiece velocity reduces the IEG, i.e., along the positive Y-direction in Fig. 4(b). The size of the IEG at time t, dtot(t) (refer Fig. 4(b)), and the corresponding rate of change of the IEG, V(t), are given by Eqs. (4) and (5), respectively,
$dtot(t)=d−A( sin (2πft+ϕ+π2)2+12)$
(4)
and
$V(t)=Aπf sin (2πft+ϕ)$
(5)

where A is the ultrasonic displacement, which lags the velocity by 90 deg, and d is the maximum interelectrode gap. Furthermore, ϕ and f are the phase and frequency, respectively, of the driving voltage for the ultrasonic actuator.

The ultrasonic velocity was generated using an Etrema CU18A magnetostrictive transducer, which has a widely variable frequency response. The transducer was powered by one channel of a Crown XLS 2000 amplifier at 50 V. In order to accurately set the phase difference between the ultrasonic velocity and the two other assisting waveforms (viz., PECM voltage and magnetic field), it is critical to estimate the time-delay between the peaks of the ultrasonic driving voltage (i.e., amplifier input) and that of the oscillating workpiece velocity. The remainder of this section describes the characterization of this critical time delay.

Using a Yokogawa DL716 oscilloscope, the voltage and current inputs were trigger-synced with a Phantom V7.3 high-speed camera focused to observe the corner of the workpiece mounted on the ultrasonic actuator. This allows timing of the motion data extracted from the raw footage to be synced with the oscilloscope data, thereby connecting the voltage input timing to the transducer motion output. The ultrasonic transducer is driven at its load-dependent resonant frequency of 15.625 kHz with the oscilloscope recording at 10 MHz and the camera recording at 142, 857 frames per second. Video frames were recorded with a field-of-view of a ∼52 μm square window for over 3000 cycles, after the transients had settled, and at over 4.5 times the Nyquist frequency. Each tracked frame displacement was measured from the first frame (i.e., base frame) to avoid measurement drift while maintaining accuracy.

Corner detection using the features from accelerated segment test method [24] was then used to extract matching features based on video frame local intensity, relative to the base frame. The features from accelerated segment test method correlates a set of tracking points in the base frame (Fig. 6(a)) to the corresponding points in a tracked frame (Fig. 6(b)). The mean position of the tracking points then gives the coordinates for the central tendency of position for each frame (Fig. 6(c)). The difference in these means is the displacement shown in Fig. 6(c). The ultrasonic velocity of the workpiece is then estimated as the derivative of this time-varying displacement. Based on the analysis conducted through this characterization effort, the time delay between the driving input voltage peak to the workpiece velocity peak was found to be 46.6 μs.

### Magnetic Field Generation.

There are two aspects to the generation of the magnetic field, viz., (1) design of the high frequency magnet and (2) characterization of the spatial-temporal characteristics of the oscillating magnetic field. In addition to measuring the strength of the varying magnetic field within the ECM area, the second aspect of this work is critical for establishing the time-delay between the peaks of the driving voltage (for the electromagnet) and the resulting magnetic field. Similar to the efforts presented in Sec. 3.3, this time-delay is a critical piece of information needed to establish the phase difference between the three assistances.

It should be noted here that the dual-assisted ECM studies found in the literature that included magnetic-field assistance [7,1113,20] have never ensured high frequency magnetic fields that are of the same frequency as that of the pulsed electric fields or ultrasonic motion. Furthermore, because those studies did not investigate the effect of phase difference, no attempt was made to characterize the spatial-temporal characteristics of the oscillating magnetic field [7,1113,15,20]. The remainder of this section focuses on both these novel aspects of the magnetic field generation applied to the flow cell outlined in Sec. 3.1.

#### Design of High Frequency Magnet.

Given the goal of achieving phase control between the multiple assistance fields, the electromagnet designed for this ECM application should enable high frequency operations involving high magnetic flux densities achieved using relatively low power consumption. Standard grain-oriented electric steel and powdered metal used in electromagnets or transformers have a high magnetic field saturation, but neither of the materials have the high magnetic permeability required for low power, high frequency operation [25]. Therefore, the Hiperco 50 alloy with a high magnetic permeability was used to fabricate the electromagnet for this application.

Annealed Hiperco 50 was used to manufacture the final electromagnet used on the testbed (Fig. 4). The electromagnet was made of 38 layers of 157 μm thick annealed Hiperco 50, with epoxy binding the laminations. Furthermore, after curing the epoxy, cuts were made to the structure to create a C-core shape that accommodated the flow cell machining area while also tapering the poles to increase the magnetic flux density (Fig. 4). The current was supplied to this electromagnet by copper wire coils (19 AWG).

#### Characterizing the Magnetic Field.

The magnetic field generated by the C-core electromagnet was mapped using a F.W. Bell 5080 Gauss meter with a transverse probe. During this mapping process, the probe was held steady, while the electromagnet was translated to discrete measurement locations spanning a total area of 8 mm × 4 mm, centered around the electrochemical machining region. Since the magnetic field is sinusoidal, several cycles of field measurements were recorded at each position, synced to a clock pulse, and then averaged.

The plot in Fig. 7 shows the maximum and minimum field for the composite field map created using the spatial–temporal measurements. It should be noted that, in Fig. 7, the electrochemical machining area is comprised of a 1.5 mm diameter cylinder with an instantaneous IEG of dtot(t) (Eq. (4)), centered on the magnetic field map surface (refer machining area markers in Fig. 7(d)). Furthermore, the time difference of 32 μs between Figs. 7(a) and 7(d) corresponds to half the time-period of the 15.625 kHz driving voltage for the electromagnet. As seen in Fig. 7, the peak flux density average within the machining area is 142±6 mT. Furthermore, based on the analysis conducted through this characterization effort, the time delay between the driving input voltage peak to the peak magnetic field was found to be 20.7 μs.

According to the Maxwell-Faraday equation (Eq. (3)), the time-varying nature of the magnetic field shown in Fig. 7 will induce an electric current in conductive materials within the field, including the electrolyte, workpiece, and tool. In addition, the cross product in the Lorentz force (Eq. (2)) also generates a voltage and induced current in the form of ion motion. These induced currents are expected to participate in the electrochemical reaction.

### Defining Phase Difference Between Assistances.

Figure 8 presents an illustrative sketch of the three assistance waveforms, for the purposes of defining the phase difference terminology used in this paper. The following two things should be noted with regards to Fig. 8: (i) the PECM voltage and current data are from an actual baseline PECM test, whereas the sinusoidal profiles for the ultrasonic velocity and magnetic field are simulated only for illustrative purposes; and (ii) all input voltage waveforms in this study have a frequency (f) of 15.625 kHz, which is the resonant frequency of the Etrema CU18A ultrasonic transducer (refer Sec. 3.3).

As shown in Fig. 8, the anodic and cathodic duty cycles for the PECM tests are 50% and 2%, respectively, with a delay of 20% from the anodic pulse. The cathodic pulse is shorter than the anodic pulse, thereby creating an asymmetric bipolar pulsed waveform. It can also be seen that the current in PECM decays over the course of the anodic pulse, which usually indicates EDL charging [10]. In this study, the PECM waveform has the rising edge of the anodic current pulse at t(0), when phase is equal to 0 deg (Fig. 8). Therefore, for the PECM waveform, every additional phase difference of 90 deg can be realized by an additional delay of 16 μs (i.e., 1/4th the period of a 15.625 kHz signal). Once the PECM waveform is defined, the time-delays characterized in Secs. 3.3 and 3.4 can be used to program specific phase differences between the three assistances acting on the ECM cell. This is done using the appropriate time-delays of the driving voltages to sync the PECM voltage with the actual ultrasonic velocity and magnetic field, offset in time by the desired phase difference.

For the illustrative signals in Fig. 8:

• The phase difference between the pulsed electric field and the ultrasonic velocity is +45 deg, and it is labeled as Pulse ϕ–Ultra ϕ. (Note: for the electric field, the phase is defined with respect to the driving voltage of PECM.)

• The phase difference between the ultrasonic velocity and the magnetic field is +45 deg (labeled as Ultra ϕ–Mag ϕ).

• The phase difference between the magnetic field and pulsed electric field is −90 deg (labeled as Mag ϕ–Pulse ϕ).

Each phase difference in Fig. 8 defines a unique dual-assisted ECM cell and corresponds to an area enclosed by two circles in Fig. 2. Furthermore, it can also be seen that the three assistance waveforms only have two degrees-of-freedom with respect to phase difference. This is demonstrated in the example in Fig. 8 where any phase difference shown can be calculated using the remaining two phase differences. This implies that for the triad-assisted cases, while all three waveforms act on the ECM cell, independent control of the phase differences will only be possible between any two of those waveforms.

## Experimental Conditions

This experimental study was focused on an ECM system comprising of a 316-stainless steel tool (cathode) and a flat 7075 aluminum alloy workpiece (anode). Table 1 lists the composition of this aluminum alloy used widely by the aerospace industry [26]. The 7075 aluminum alloy was specifically chosen as the workpiece because it is nonferromagnetic with a relatively high ion valence and low atomic weight. This allows the ECM assistance fields to induce maximum ion motion, without introducing ferromagnetic effects that would otherwise confound the interpretation of the assisted ECM results (refer Sec. 2).

In order to focus this study on the coupling of the three assistances, the more traditional ECM process parameters were held constant throughout the experiments. The initial IEG (d) was maintained at 200 μm. All experimental runs were performed with NaNO3 electrolyte at 20% concentration and a flow rate of $125±20 ml/min$, with a back pressure of 6 psi and temperature of 21±1 °C. The electrolyte was chosen to avoid additional corrosion of aluminum associated with the Cl ions from NaCl [27]. The machining diameter of the 316-stainless steel tool was constant at 1.5 mm, and the tool was insulated with an acetal resin cylindrical annulus. In order to prepare the tool and workpiece surfaces for ECM, they were successively polished from 180 grit down to 2000 grit. The electrochemical machining time was kept to 15 s to minimize the changes in electrolyte turbulence from start to finish of an experimental run. MRR and Ra were chosen as the performance metrics of interest.

The nature of the PECM waveform was as outlined earlier in Sec. 3.5. The oscilloscope data were sampled at 2 MHz, which is 64 times the Nyquist frequency of f. For each combination of the assistance waveforms, the phase difference was varied at four levels from –90 deg to 180 deg in 90 deg increments. Table 1 summarizes the overall experimental conditions.

## Results and Discussion

The MRR and average Ra are the two performance metrics used to quantify the effect of the three assistance fields. In order to calculate the MRR, workpieces were weighed before and after machining using a Sartorius microbalance ME36S with an ISO calibrated accuracy of 1 μg. MRR was then calculated as the weight loss (i.e., weight of machined material) divided by machining time measured by the oscilloscope, which was held constant at 15 s for all experimental runs. According to Faraday's law, the material removed is proportional to the total charge passing through an electrochemical cell. Therefore, as an additional validity of the MRR measurement, the total anodic charge for each experiment was calculated by integrating the electrical current signal.

Surface roughness was measured with an Alicona G5 InfiniteFocus™ focus variation optical profiler with a vertical resolution of 0.01 μm. For each of the samples, an average Ra value was calculated from ten profile scans (160 μm long) taken at the center of the workpiece. The remainder of this section presents a discussion of the MRR and Ra trends seen for the dual-assisted and the triad-assisted cases encountered in this study.

### Dual-Assisted Cases.

Figures 9(a)9(c) and 9(d)9(f) depict the trends seen in the MRR and Ra values, respectively, for each of the three dual-assisted cases outlined in Fig. 2. These dual-assisted cases include: (1) Pulse–Ultra: the pulsed electric field and ultrasonic velocity interaction; (2) Ultra–Mag: the ultrasonic velocity and the sinusoidal magnetic field interaction, under DC ECM conditions; and (3) Mag–Pulse: the sinusoidal magnetic field and pulsed electric field interaction. It should be noted that in Figs. 9(a)9(c), the MRR (mg/min) and the total anodic charge (daC) are both displayed along the vertical axis. For all three dual-assistance cases, it can be seen that there is a general agreement in the proportionality between the two quantities, which suggests that the MRR measurements are reliable. In Figs. 9(d)9(f), Ra (μm) and anodic peak current (A) share an axis. For comparative purposes, the data from the baseline cases specific to each of the dual-assistances cases are also indicated in Figs. 9(a)9(f). The baseline value is indicated with a yellow-plane.

#### Pulsed Electric Field and Ultrasonic Velocity Interaction.

This dual-assisted case is abbreviated as Pulse–Ultra in Figs. 9(a) and 9(d). The results in these figures suggest that the phasing between ultrasonic velocity and PECM voltage is critical to both the MRR and Ra outcomes. The best MRR obtained at a phase lead of 0 deg is found to be 14% higher than the baseline PECM value. This phase lead of 0 deg also gave the most improvement in surface roughness, with an Ra value that is 68% better than that of the baseline PECM (Fig. 9(d)).

At the 0 deg phasing, the average anodic current was observed to be higher than any other phase difference values. This loss in the combined electrochemical cell resistance may be caused by better clearing of byproducts from the IEG or increased kinetics at the electrode surface caused by cavitation, both of which could explain the benefits seen in MRR and Ra [28,29]. The debris removal mechanism is particularly plausible because, at the 0 deg phase difference, the IEG starts at its largest value and compresses for the entire duration of the anodic pulse, with the ultrasonic velocity defined in Eq. (5). This positive pressure generated by the pumping motion profile is likely to result in better clearing of the byproducts from the IEG while also discouraging bubble formation.

At each of the other phase-lead values, the surface roughness is greater than that seen for the 0 deg phase difference. The worst surface roughness is seen at a phase-lead of 180 deg, where it becomes worse than the baseline PECM. At this phase difference, the ultrasonic motion would result in a negative pressure in the IEG during the entire anodic pulse, thereby encouraging bubble formation. The 180 deg phase difference case also highlight the fact that the increase in MRR comes at the expense of an increased surface roughness.

#### Ultrasonic Velocity and Sinusoidal Magnetic Field Interaction.

This dual-assisted case is abbreviated as Ultra–Mag in Figs. 9(b) and 9(e). For the Ultra–Mag case, the DC ECM process is taken as the baseline since neither of the two assisting fields, by themselves, can cause a significant ECM reaction to occur. It should be noted that the DC ECM baseline is more aggressive, in terms of MRR, when compared to the pulsed ECM baseline. As seen in Fig. 9(b), combining the ultrasonic and magnetic waveform assistances at the same frequency, regardless of phase, results in an MRR that is greater than the DC ECM baseline. The highest MRR for this dual-assisted case occurs at 180 deg phase difference (54% increase over the DC ECM baseline), and it is also the highest MRR of any assisted-ECM case tested in this study (refer Sec. 5.3 ahead). A possible explanation for this behavior at 180 deg phase difference can be given by looking at the Lorentz force equation plots, as a function of its constituent components and the phase angle.

For the Ultra–Mag case, the $r˙×B(r,t)$ component of the Lorentz force (refer Eq. (2)) is its only phase-dependent component. The E component remains constant in the Y-direction under the DC ECM conditions and, as such, can be ignored for the analysis of the phase effects. Figures 10(a)10(d) show a series of plots that illustrate the four phase differences used in the Ultra–Mag interaction and an estimate of the resulting $r˙×B(r,t)$ component of the Lorentz force. For illustrative purposes, this component is plotted only for a positively charged particle located close to the ultrasonically vibrating workpiece surface, so that the particle can be assumed to have the same Y-directional velocity (refer Fig. 4(b)) as that of the vibrating workpiece. Furthermore, these plots ignore the impact of secondary electric fields on the charged particles, so E is zero along the X and Z directions. Under these assumptions, the $r˙×B(r,t)$ is the only nonzero component of the Lorentz force directed along the Z-direction of the flow cell (Fig. 4(b)). Therefore, a positive value for this component in Figs. 10(a)10(d) indicates that its direction coincides with the direction of the electrolyte flow (Fig. 4(b)), thereby accelerating the positively charged particles across the IEG. In a similar vein, a negative value for this Lorentz force component in Figs. 10(a)10(d) implies a deceleration of the positively charged particles across the IEG. In addition, since Figs. 10(a)10(d) are for a positively charged particle, the direction of the $r˙×B(r,t)$ component acting on a negatively charged particle will be opposite to that plotted in Figs. 10(a)10(d). With this interpretation framework in place, the phase implications of Figs. 10(a)10(d) can now be discussed.

As seen in Fig. 10(d), the 180 deg phase difference represents a Lorentz force component with minimum peaks for a positively charged cation. Given that the direction of this force is predominantly opposite to the electrolyte flow direction, it will slow down the motion of the cations across the IEG. However, for negatively charged anions, like nitrate, the opposite is true, i.e., this force would coincide with the direction of the electrolyte flow, thereby accelerating their flow across the IEG. The higher MRR seen at the 180 deg phase difference may result from this directed Lorentz force, because the added nitrate anion velocity is likely to increase the electrode reaction rate by increasing the number of anions coming in contact with the workpiece electrode. The increase in reactions would effectively increase both the current flow and MRR, according to Faraday's laws of electrolysis.

To consider surface roughness changes from a Lorentz force perspective, as was done for MRR, we consider the worst surface finish case that occurs at a phase lead of 0 deg. The Lorentz force at this phase lead has maximum peaks for a cation (Fig. 10(b)). At this phase lead of 0 deg, the Lorentz force in the Z-direction tends to slow the negatively charged anions flowing across the IEG. This potentially results in the anion trajectories being more direct on the anode (i.e., less oblique) so that the anions contact both the surface peaks and valleys at the same rate. Without the preferential removal of the surface peaks, this would result in a poor surface roughness value. This suggested mechanism is a contraposition of the rationale used by Fang et al. [14] to explain the improvement of the surface roughness using oblique ion trajectories that selectively remove the peaks on the surface.

Surface roughness changes can also be considered from a peak current density perspective. ECM is typically conducted in the transpassive dissolution region where the dissolution rate is mass transport limited [28]. Under these conditions, the thickness of the diffusion layer above the workpiece is directly proportional to the current density [28]. If the diffusion layer is thicker than the surface roughness features, then the peaks of those features will be preferentially removed, thereby creating a “leveling-effect” that improves the surface finish [30]. The mechanism is also plausible for all four Ultra–Mag phase differences since the Ra trends are seen to be more or less inversely proportional to the peak current values (Fig. 9(e)). It should be noted here that the peak current in this case results from the combination of both the DC ECM current and the magnetically induced current (Fig. 9(e)), which is a function of the cross product between the ultrasonic workpiece velocity and the magnetic field and is therefore phase dependent.

The DC ECM baseline is seen to outperform all the assistances in the Ultra–Mag case. This is confirmed by even the single-assistance cases presented ahead in (Fig. 12(b)). This implies that for the DC machining conditions in this study, the use of ultrasonic assistance degrades surface finish, possibly by a reduction in the diffusion layer thickness resulting from locally increased electrolyte flow [29].

It should be noted here, that according to the Maxwell-Faraday equation (Eq. (3)), the sinusoidal magnetic field induces a voltage and resulting current in the conductive work piece. The same Eq. (3) also shows that the ultrasonic velocity affects the induced current because it moves the workpiece relative to the magnetic field. This complex induced-current relationship plays a role in the ECM process, because it is active regardless of phase, but its direction and magnitude are phase-dependent, requiring additional modeling to predict.

#### Sinusoidal Magnetic Field and Pulsed Electric Field Interaction.

This dual-assisted case is abbreviated as Mag–Pulse in Figs. 9(c) and 9(f). As seen in Fig. 9(c), dual assistance using a sinusoidal magnetic field combined with PECM has a significant increase in MRR only at a 0 deg phase lead of the magnetic field from the PECM waveform. At the 0 deg phase lead, the MRR was seen to increase by 17% over the baseline PECM. All other phase differences were seen to result in MRRs lower than the baseline PECM. Figure 9(f) shows that the best Ra for this dual-assisted case also occurs at the 0 deg phase difference with a 47% reduction in surface roughness over the baseline PECM case.

In this dual-assisted case, the pulsed electric field accelerates the ions and affects their velocity. Therefore, the approximation made for the Ultra–Mag case in Fig. 10 is not valid for this case, and similar magnitude estimates cannot be made a priori. For this Mag–Pulse case, the ion velocity resulting from the velocity field crossed with the magnetic field will have a complex resultant force because the ion velocity evolves over time as a differential equation. As such, a multiphysics model is needed to fully explain the effects of this interaction. In this case, the PECM current is combined with the magnetically induced current. The Ra values of all four phases and the PECM baseline are more or less inversely proportional to the peak current seen in Fig. 9(f). This trend makes the diffusion layer thickness rationale described for the Ultra–Mag case plausible even for this dual-assisted case [2830].

The triad-assisted ECM cases involve the use of phase-specific combinations of all three assistances, viz., pulsed electric field, ultrasonic velocity, and magnetic field. As highlighted in Sec. 3.5, the phase differences between the three waveforms have two degrees-of-freedom. This coupled with the fact that there are four levels of phase differences explored in this study, implies 16 unique experimental runs for the triad-assisted case.

Figures 11(a) and 11(b) depict the MRR and Ra response contour plots for the 16 experimental runs. In Fig. 11, the horizontal axes represent the phase difference between the pulsed electric field and the ultrasonic velocity, whereas the vertical axis denotes the phase difference between the ultrasonic velocity and the magnetic field. An additional set of diagonal lines are also overlaid on these two axes to indicate the corresponding phase difference between the magnetic field and the pulsed electric field. Furthermore, the baseline PECM performance is indicated using a horizontal marker on the color scale bars for both the MRR and Ra plots. The data points in Fig. 11 are denoted using a ○ or a ▽ marker, with the ○ marker indicating a superior performance compared to the baseline PECM case and the ▽ marker indicating a correspondingly inferior performance. The response contour is interpolated between the 16 data points in Figs. 11(a) and 11(b) to better illustrate the interrelations. End constraints of the interpolated contour are cyclic, so the response contours tessellate with themselves.

Figure 11(a) shows the MRR contour plot for triad-assisted ECM. The phasing combination for the highest MRR involves a phase difference of (i) 180 deg between the PECM and ultrasonic velocity (Pulse–Ultra); (ii) 180 deg between the ultrasonic velocity and magnetic field (Ultra–Mag); and (iii) 0 deg between the magnetic field and the PECM (Mag–Pulse). This phasing combination (indicated by a ★ in Fig. 11(a)) results in a MRR increase of 55% over the baseline PECM case. The contour plot in Fig. 11(b) indicates that those same phasing conditions also result in a 52% improvement in Ra. For the dual-assisted case, the 180 deg Ultra–Mag phase difference results in the highest MRR (Fig. 9(b)), whereas the 0 deg Mag–Pulse phase difference results in the second highest MRR (Fig. 9(c)). Interestingly, this means the phase combination resulting in the highest MRR for triad-assisted ECM lies at the intersection of the top two dual-assisted phase combinations.

The surface roughness performance is shown in Fig. 11(b). The phasing combination for the lowest Ra value involves a phase difference of (i) 0 deg between the PECM and ultrasonic velocity (Pulse–Ultra); (ii) –90 deg between the ultrasonic velocity and magnetic field (Ultra–Mag); and (iii) 90 deg between the magnetic field and PECM (Mag–Pulse). This phasing combination (indicated by a ★ in Fig. 11(b)) is different from the combination discussed earlier for the highest MRR, and it results in a 78% improvement over the baseline PECM Ra value. An added benefit of this phasing combination is that, with a corresponding MRR increase of 52%, it is nearly as good as the triad phasing for the highest MRR. For the dual-assisted case, the 0 deg Pulse–Ultra phase difference results in the lowest Ra (Fig. 9(d)), whereas the 90 deg Ultra–Mag phase difference corresponds to the second best Ra (Fig. 9(e)). Interestingly, this again puts the best triad-assisted Ra phase combination at the intersection of the top two dual-assisted phase combinations.

The mapping between the results from the dual-assisted and triad-assisted cases suggests that the mechanisms responsible for improved MRR and surface roughness in triad-assisted ECM stem from the same Lorentz force (Eq. (2)) and induced currents (Eq. (3)) that influence the outcomes of the dual-assisted cases. However, multiphysics models are needed to fully explain the results seen in the triad-assisted ECM case.

### Comparison Between Cases.

To give a better perspective on the relative performance between the various assisted ECM methods and their baselines, the MRR and Ra values from the best-performing dual and triad-assisted phasing combinations are presented in Figs. 12(a) and 12(b). The colors used in Fig. 12 correspond to those in Figs. 2 and 9 for comparison. Two additional single-assisted DC ECM treatments from Fig. 2, viz., (i) Ultrasonically assisted DC ECM (denoted as Ultra); and (ii) Magnetically assisted DC ECM (denoted as Mag), are also included in Fig. 12 for completeness.

Figure 12(a) compares ECM performance in terms of MRR. As mentioned previously, under the ECM machining conditions chosen, DC ECM is more aggressive than PECM in terms of MRR. Therefore, it is expected that assisted DC ECM treatments will also have generally higher MRRs. The best MRR tested was the dual-assisted DC ECM (Ultra–Mag), which was better than both the ultrasonically assisted DC ECM (Ultra) and the magnetically assisted DC ECM (Mag) cases that comprise it. Of particular interest is that the best triad-assisted ECM phasing has a higher MRR than the DC ECM baseline despite the triad-assisted treatment having only a 50% anodic duty cycle compared to the 100% duty cycle for the DC case.

The surface roughness comparison in Fig. 12(b) shows that triad-assisted ECM results in the best surface finish in this set of experiments. The triad-assisted case shows a 78% improvement in Ra over the most applicable PECM baseline and a 26% improvement over the DC ECM baseline. PECM has the worst surface roughness of all the cases. In this study, PECM generally has a lower average current than DC ECM and therefore a lower current density, which is typically correlated with a poor surface finish when using neutral salts [29]. Since the DC ECM baseline produced a better surface finish than the PECM baseline, it is not surprising that, in general, the DC-assisted ECM cases also have a better surface finish.

The capabilities of the flow cell described in Sec. 3 and the findings reported in Fig. 12, point toward the possibility of realizing multifield assisted ECM testbeds that can use phase-specific input waveforms, programmed to change on-the-fly, yielding preferential combinations of material removal rate and surface roughness. For instance, the system could switch on-the-fly from the best performing MRR waveform input for a roughing operation (using the Ultra–Mag assistance) to the waveform for the best surface finish that relies on the triad-assisted Pulse–Ultra–Mag case. Such a processing flexibility will allow for the development of novel electrochemical machining pathways for complex geometries.

## Conclusions

This paper presents the design of a novel testbed to apply all possible dual-assisted and triad-assisted combinations involving pulsed electric field waveforms, ultrasonic velocity, and magnetic field waveforms to an anodic-dissolution ECM cell. The testbed consists of a custom 3D printed flow cell that is integrated with (i) a bipolar pulsed ECM circuit, (ii) an ultrasonic transducer, and (iii) a custom-built high-frequency electromagnet. The driving voltages of the ultrasonic transducer and electromagnet are calibrated to achieve a timed workpiece velocity and magnetic field, respectively, in the machining area. The input signals to all assistance waveforms are provided by a control computer that allows for precise control of the phase differences between the three assistance energies. The electrochemical machining studies conducted using this testbed reveal the following findings:

1. (1)

Phase-controlled waveform interactions between the three assistances improve both the MRR and surface roughness (Ra) values, over those seen for the baseline cases.

2. (2)

The triad-assisted ECM case involving phase-specific combinations of the three high-frequency assistance waveforms is capable of achieving a 52% increase in MRR, while also simultaneously yielding a 78% improvement in the surface roughness value over the baseline pulsed-ECM case. This result is encouraging because assisted ECM processes reported in the literature typically improve only one of these performance metrics at the expense of the other.

3. (3)

The mapping between the results from the dual-assisted and triad-assisted cases suggests that the mechanisms responsible for improved MRR and surface roughness in triad-assisted ECM stem from the same Lorentz force and induced currents that influence the outcomes of the dual-assisted cases. In general, while the results point to certain phase differences improving the electrochemical machining performance, the specific mechanisms responsible for this are difficult to isolate given that the Lorentz force interactions act alongside complex induced currents. Multiphysics simulations will be needed to study these underlying mechanisms.

The findings reported in this paper are expected to enable the realization of multifield-assisted ECM testbeds that can use phase-specific input waveforms, programmed to change on-the-fly, yielding preferential combinations of material removal rate and surface roughness.

## Acknowledgment

Alicona Imaging GmbH is also acknowledged for their entrustment of the InfiniteFocus G5 3D optical measurement system to the Rensselaer Manufacturing Innovation Learning Lab.

## Funding Data

• U.S. Army—Armament Research, Development and Engineering Center (Internal Lab Independent Research (ILIR) Grant and Science Fellowship Grant).

• Rensselaer Polytechnic Institute (Internal Funds).

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