Dimensional accuracy enhancement of machined-hole through UAECDM-process under the magnetic-field-assistance

ABSTRACT Electrochemical discharge machining (ECDM) is a micro-machining hybrid technique that utilizes electrical discharge and electrochemical machining principles. However, the issue of insufficient electrolyte in the hydrodynamic region hinders the continuation of the machining action. Although ultrasonic tool vibrations have been used to overcome this problem to some extent, the excessive mechanical energy produced by high-amplitude tool vibration may lead to surface crack formations. As a result, the present work employs two flushing improvement methods, namely the ultrasonic vibrations and magnetic filed assistances, in the ECDM process. A comparative study has been performed to identify the effect of the magnetic field on discharge quality. The material removal rate and depth of penetration were increased by 11% and 24%, respectively, and the observed reduction in hole overcut and taper angle was around 35% and 50%, respectively. Optical microscope images quantified improvement in dimensional accuracy and decreased HAZ area.


Introduction
In the contemporary manufacturing era, miniaturized products have significant demand in the market.Glass possesses beneficial ceramic properties, making it one of the most popular materials in micromachining.Using glass-based composites in MEMS and microfluidic devices is very common because they are chemically less reactive, non-conductive, have high thermal shock resistance, and offer physical transparency. [1,2]Also, in medicine, aerospace, biochemical, and electronic communication, there is a need to fabricate miniaturized components. [3,4]herefore, to fulfill the requirements based on the vital glass properties, researchers widely focused on the micro-machining processes that can easily machine the glass composites, which are non-conductive. [5]Recently, the hybridization of different micro-machining methods makes up the most beneficial techniques for machine non-conductive materials. [6]any advancements have been made to control discharge activity, high-temperature etching, and localized heating in different categories, like tool-based enhancements, process-based enhancements, and electrolyte-based enhancements.Tarlochan et al. have reported the control on the working gap between fastened tool and workpiece; a spring mechanism was employed to maintain almost zero constant working gap.Springs were used in the fixture on all four corners, and the cylindrical micro tool was fastened at a fixed place just above the workpiece; as the tool penetrated inside the workpiece, springs expanded, and therefore the workpiece moved upward and maintained a constant zero gap that produces an effective energy channelization. [7]A similar feeding mechanism was used in the present experimental work.Arya et al. has introduced controlled electrolyte replenishment by injecting electrolyte through the tubular electrode.The required electrolyte flow rate and mass of vaporized electrolyte were investigated to provide precise control of the mechanism. [8]Electrolyte flow rate is one of the most responsible parameters for surface smoothness, local heating of electrolyte damages the work surface.Zheng et al. study promised better electrolyte flow with a flat side wall tool; however, it gives sharp microhole edges. [9]Tool shape is also one of the most dominant parameters affecting the machining efficiency; the curve surface of the spherical tool facilitates the larger volume of electrolyte between tool and workpiece, which ensures the gas film formation at a faster rate and improves machining depth and spark frequency over a cylindrical shape, [10,11] and needle shape tool concentrates the discharge toward the tooltip and improves the machining efficiency. [12]arious studies have been performed to enhance electrolyte flow and increase chemical etching, like tool rotation, magnetic assistance, and ultrasonic vibration in the tool employed. [13,14]ibration can be applied by any means, either by the tool, workpiece, or electrolyte.Yuge Luo et al. induced ultrasonic vibration into the electrolyte and claimed an enhancement in the aspect ratio of the drilled hole by controlling gas film stability and reducing thickness. [15]As per the study of Razfar et al., ultrasonic longitudinal oscillation of the tool breaks the larger bubbles into smaller bubbles and enhances the frequency of smaller bubbles, resulting in more contact of electrolyte with the tool surface and enhanced electrolysis phenomenon, which results in higher MRR and reduces machining time. [16,17]However, if the vibration amplitude is beyond 10 µm, the hole's outer surface is damaged because direct contact between tool and workpiece at high amplitude creates a high impact load, [18] and still, the issue (high DOP) remains challenging to achieve at lower voltages.As per the study of Tarlochan et al., tool rotation causes an additional centrifugal force on hydrogen bubbles that reduce gas-film thickness formed around the tool surface; further study also proves that tool rotation ranges from 400 to 700 rpm increases aspect ratio of the drilled hole with higher DOP; however, beyond 700 rpm, tool rotation weakens the gas film and decreases the process efficiency. [19]Cheng et al. applied the magnetohydrodynamic effect produced by a permanent magnet and enhanced electrolyte circulation and chemical etching.The study brought forward stable discharge quality and a high depth of penetration as compared to the usual ECDM method. [20]In the ECDM mechanism, when an electric current starts flowing, H 2 and O 2 gas bubbles start generating near the cathode surface (tool) and anode surface (secondary electrode), respectively; as the setup voltages increase beyond the critical voltage, a greater number of bubbles are generated, and a hydrogen bubble layer is generated around the tool surface periphery called gas film.The gas layer thickness is reduced due to the magnetic field's ability to reduce the size of the hydrogen gas bubble growing around the tool's periphery.Gas film quality is responsible for discharge frequency and consistency, and it is one of the most responsible factors for MRR and machined surface quality in the ECDM.The presence of a magnetic field with electric current induces Lorentz force onto hydrogen ions that rotate the gas bubble around the tool periphery, which helps in electrolyte circulation and improves the surface coverage of the tool.Many hybridization methods have been examined to improvise the ECDM process capability.Mukund et al. examined the rotary tool ECDM process and found an increase in MRR in the presence of a magnetic assistant; however, there was no significant reduction in tool wear. [14]As per the investigation done till now, it is clear that gas film plays an influential function in the material removal mechanism concerning dimensional accuracy and the surface quality of the hole produced by the ECDM process. [19,21]In the magnetic field presence, moving ions experience a Lorentz force at an angle of 90° to the direction of motion.Due to this phenomenon under a magnetic field, bubbles about to leave in an upward direction move around the tool periphery, improving wettability and gas film stability. [22]Ultrasonic vibration in the tool electrode helps to provide sufficient space and time for moving out the machined material and enhancing electrolyte circulation underneath the tooltip.It helps to concentrate the electric discharge to the bottom of the tool and reduces hole overcut.
Hence, this research attempts to employ the magnetohydrodynamic effect with the sonication of tool electrodes to improve the machining accuracy together with a high depth of penetration.Trial experiments were conducted to discover the suitable vibration magnitude, required magnetic field intensity, and required energy input.The magnetic field induces a Lorentz force on moving bubbles that rotate the electrolyte around the tool surface, enhances the wettability, and helps to generate the stable gas film around the tool.Force analysis on a single bubble attached to the tool electrode is also elaborated to understand the Lorentz force effect on the gas film thickness.In terms of stability and thinness, the gas film quality is an important phenomenon that produces consistent electrical discharge.The combined influence of ultrasonic tool vibration and magnetic field assistance in the ECDM process provides good electrolyte recirculation.It helps to remove machined material and the extra heat from the vicinity of the machining area.Experimental results highlight that UAECDM under a magnetic field provides a crack-free hole surface with high dimensional accuracy.MFA in UAECDM enhances the process capability by improving both phenomena that cause material removal -the chemical etching and the discharge mechanism.It also enhances DOP with a measurable reduction in taper angle, surface damage, and HOC at a constant voltage input.The mechanism and process parameters used in this process are described in the next section.

Experimental set-up
The self-developed Machining setup, as shown in Fig. 1, has been used to perform experiments.An electrochemical cell is formed between the tool and a workpiece with a circular counter electrode made of stainless steel.Self-prepared stainless steel cylindrical tool is fixed to the ultrasonic horn by the tool head (as shown in Fig. 1) [23,24] and connected to a constant DC voltage negative terminal."50 × 25 * 1.3" mm 3 borosilicate glass slides mounted on fixture used as workpiece submerged in electrolyte 20%wt.NaOH and placed underneath the tool.The tool electrode is dipped in the electrolyte at a 2 mm depth.With the arrangement of a pressurized feeding mechanism, the tool tip and the workpiece remain in continuous contact.To complete the electrochemical cell, a circular counter electrode (anode) with a negligible thickness was placed in the electrolyte, surrounding the tool at 50 mm.DC pulsed power supply "Delta electronic SM330-AR-22" was used to provide and regulate voltage and current.Table 1 shows all constant and variable parameters used for experimentation.A neodymium magnet was placed inside the nonconductive and nonmagnetic casing underneath the workpiece.A digital Gauss meter was used to directly calibrate the magnetic field strength at the machining zone by placing the sensor probe at the workpiece.The change in the magnetic field was regulated by adjusting the number of magnets and the gap between the workpiece and the magnet.After machining, magnified images of the microhole from the top view were taken from an optical microscope to determine the hole diameter and identify the heat-affected zone (HAZ).Three-point method has been used to identify the average hole diameter for irregular shape.Response parameters HOC and MRR were calculated using Equations 1 and 2. [25] Digital oscilloscope was used to record voltage signal and identify the intensity and consistency of discharge during machining.A weighing machine of least counts 0.01 mg (Made by Shimadzu, Model: AUW220D) was used to weigh the material removal.
Experiments of UAECDM without a magnetic field were performed in the same setup by removing the magnets.
Each experiment was performed three times.The result was quantified using the arithmetic mean.The machined hole workpiece was split vertically into two parts, and FESEM images were captured to spot the magnetic field effect on the surface.Ranges for experimental parameters were decided after pilot experimentation using the OFAT approach. [26,27]

Working mechanism
Electrochemical discharge machining uses thermal and chemical energies to remove the workpiece material.Ultrasonic vibrations incorporate mechanical energy with the above two.Magnetic field assisted with these three energies to improve dimensional accuracy; furthermore, it also enhances the surface of the machined hole.In electrochemical discharge machining, as electrodes are coupled to a DC source, current starts flowing within the electrochemical cell, O 2 molecules, present near the anode, form oxygen bubbles, and H + ions attract toward the cathode, merge with free electrons and form H 2 bubbles near the cathode.Any change in voltage directly affects the formation of bubbles; if the voltage increases nucleation of bubbles also increases.These hydrogen bubbles around the tool periphery form a gas layer that creates a resistance called IR (voltage) drop.(The current flow through the electrolyte encounters some resistance, known as internal resistance or IR drop.)Hence, a potential difference between the cathode (tool) and the anode (counter electrode) leads to an electrical discharge from the tool.Electrical discharges also form because of thermionic emission, depending on various parameters like the tool's surface, temperature, and so on.Many previous studies have also claimed that because of joule heating, electrons are liberated from the tool and that creates a spark. [28,29]The continuous discharge causes an increase in the workpiece surface temperature and removes the workpiece material through melting.Chemical etching enhances at higher temperatures and machines the glass workpiece.The architecture of gas film affects the discharge mechanism and directly contributes to the machining efficiency, accuracy, and surface quality.Any change in gas layer thickness directly affects the IR drop.A thick gas layer required higher voltages to generate a spark.More dense and consistent sparks lead to more MRR and a good surface finish.The stable gas film leads to a smooth machining surface, as shown in FESEM images under a magnetic field.For microholes, electrolyte availability in the machining zone is the most significant issue during ECDM.The literature states that the drilling speed in glass workpieces during the ECDM process decreases with the depth of penetration. [30]Based on drilling speed, machining hole depth is divided into two regimes; one is the discharge regime, where the machining rate is dependent on setup voltage.Second, beyond a limiting machining speed, drilling is no longer dependent on discharge activity; now, the electrolyte flow controls the drilling speed, called the hydrodynamic regime. [31]In the feed mechanism, like gravity flow and pressurized feeding approach, the tool-workpiece contact is maintained and helps reduce side discharging.Still, the drawback, incomplete flushing of the machined glass substrate that hinders the electrolyte flow, must be tackled.To overcome this drawback, many researchers have incorporated ultrasonic vibrations by any means, either by tool, workpiece, or electrolyte itself.It enhances the discharge consistency and improves the machining efficiency and geometrical accuracy.Ultrasonic vibration in the tool can amplify the output parameters, depth, and drilling speed by reducing overcut because of better electrolyte recirculation and slug removal.This ultrasonication reduces gas layer thickness; however, vibration amplitude can lead to crack formation. [15,32]Ranjeet et al. produced 850µm-deep holes with the sonicated tool at 66 V with 10 µm amplitude of vibration with 510 µm overcut; however, due to high discharge energy at this voltage, electrolyte evaporates, and due to low availability of electrolyte, inconsistent discharges occur that reduce the smoothness of the machined surface.Drag force reduces the departing bubble radius; therefore, tiny bubbles coalesced to form a fine gas film compared to conventional ECDM. [13]Introducing a magnetic field with an ultrasonic-assisted ECDM process is efficient in deep-hole drilling without deteriorating the surface integrity and dimensional accuracy; the qualitative investigation on the hole surface is carried out through an optical microscopic image technique.
Magnetic field intensifies the tool surface wettability, brings down the width of the gas layer, and strengthens the gas layer's stability.The previous study on wettability also found a similar hypothesis on the contact angle of the gas bubble with the tool side wall and its effect on gas film stability. [33,34]Lorentz force acts on moving charges on the bubble periphery, creating a magnetohydrodynamic effect on bubbles.
The MHD effect recirculates the electrolyte in a limited space around the tool surface, as shown in Fig. 2(a), which can improve the wettability of the tool surface. [35]It can be observed in Figs.2(b,c) under a magnetic field; the bubble shape modifies from spherical to ovoid.At the same time, it covers the tool surface and increases the wettability, thus helping to build a thin and more stable gas layer and enhancing discharge quality.
In the present study, small neodymium disc magnets were placed below the workpiece in a fixture.Magnetic strength at the machining zone can be increased by any means, either by decreasing the distance between the magnet and the workpiece or by increasing the number of small magnets.The magnitude and orientation of magnetic flux during machining are visible in the electric field simulation in Fig. 3(b).It shows the magnetic flux in the first legend and the surface electric field in the second legend.During ECDM, as the power source connected current starts flowing, gas bubbles nucleation begins around the tool electrode.The magnetic fields influence ions on the periphery of these bubbles and start rotating around the tool electrode.Ultrasonic tool vibration pushes the electrolyte toward the tool bottom, and the magnetic field rotates it and increases the flow of electrolyte so that machined material can flush easily from the bottom of the tool electrolyte and the same place availability of electrolyte is also maintained because of better electrolyte rotational flow.More bubbles start nucleating as the magnetic field enhances the electrolysis process and helps to improve the void fraction. [35]Due to the magnetic field and ultrasonic vibration, gas bubbles alter their shapes.Furthermore, these smaller bubbles occupy the smallest space on the tool surface area and form a thin monolayer of hydrogen gas that blocks the flow of current passing through the tool electrode, which escalates the potential difference and leads to electrochemical sparks.The magnetohydrodynamic effect increases the electric field in the dielectric, further imposes the high-intensity discharge, and increases MRR.This phenomenon is validated hereinafter with experimental results.

Study of forces applicable on the gas bubble during UAECDM under the influence of magnetic field
Fig. 4 represents a tiny hydrogen gas bubble attached to the sidewall of the tool (cathode) at two different contact angles (α) and (β).These contact angles of the attached bubble with the cathode surface are the product of the net surface tension produced and the degree of the tool's surface wettability.The longitudinal oscillation of the tool's vertical surface imposes continuous lift and drag on attached bubbles.In UAECDM without MFA, as represented in Fig. 4(a), the bubble tends to depart in the vertical direction.In addition, when the MFA is applied, as shown in Fig. 4(b), Lorentz forces start working on the moving electric charges on the bubble periphery in the perpendicular direction of motion. [36]As shown in Fig. 4(c), this tries to rotate the electrolyte.Therefore, attached bubbles sense an extra force that tends to change the bubble's shape and create more wettability. [33,37]An increase in wettability may increase current density.d w1 and d w2 are the contact diameters assumed during UAECDM and UAECDM under magnetic field machining.
where θ 0 represents the mean of contact angles, and R 1 and R 2 represent bubble radius in cases 1 and 2, respectively.
Forces acting on the bubble can be deduced as-Where the surface tension in the y and x directions is F sy and F sx , respectively, the drag force (F d ) and the lift force (F li ) are the forces that depend upon the circulation and position of the bubble.
The forces used in Equations 5 & 6 can be calculated using the following equations: Where σ indicates the tension coefficient of the surface, and α, β denotes the contact angles. [13]C D, C L , ρ L, V, and A ɑ are the drag and lift force proportionality coefficient, the density of the liquid, flow velocity, and the area of the gas bubble attached to the cathode surface consecutively. [38]f ρ l and ρ g represent densities of electrolyte and gas bubbles, then V b represents the volume of the bubble.The buoyancy force on the bubble (F b ) from Archimedes' principle is-Lorentz force (F L ) acts in the normal direction of charge motion in the x-z plane, and its value in the y direction is zero because of the magnetic field induced in the y direction.B and J represent the magnetic field and current density induced in the process.The Lorentz force on the bubble imposes helicity along the electrode periphery, and an increase in the Lorentz force leads to a rise in the flow rate of the electrolyte, which can be calculated from the Navier-Stokes equations-Where Ñ. V represents the divergence of velocity, and its zero value denotes the incompressibility of flow.P and R denote the flow pressure and the resultant forces acting on the bubble, respectively.The net force on the bubble will increase or decrease the velocity of the electrolyte, and therefore increasing the magnetic force will increase the electrolyte velocity.Thus, enhanced electrolyte flow positively influences material removal from the machining zone and aids smoother machining.However, beyond a limit, an increment in magnetic field strength can decrease the machining rate as the gas film becomes unstable because of very high electrolyte flow. [8]he departing radius of the bubble in UAECDM under a magnetic field will be smaller than the departing radius in UAECDM without a magnetic field, [39] and it can be calculated as- The result quantifies that both tool's vibration and availability of magnetic field affect the volume and shape of the bubble and aid in reducing the thickness of the gas layer around the tool (cathode) surface, thus, enhancing the dimensional accuracy.

Results and discussion
Hole overcut, depth of penetration, and hole integrity are the essential measures that can indicate the machining efficiency of electrochemical discharge machining under any machining arrangement.Increasing DOP without increasing HOC and surface damage area indicates high dimensional accuracy that is highly desirable for Lab-on-a-chip device applications of borosilicate glass.High depth of penetration with high dimensional accuracy infers the capability of machining to utilize the discharge energy into machining the workpiece without affecting tool quality.In this article, the performance of UAECDM under the magnetic field and without a magnetic field has been evaluated through experimental results.Evidence of discharge energy variation due to the magnetic field has been verified through oscilloscope observations.This effect is also visible in electric field surface simulations done through COMSOL Multiphysics software (Fig. 3).The I-V characteristics in the machining zone vary with the local heat, which causes the melting of glass workpiece, and are, therefore, related to the output performance parameter MRR. [40]The arithmetic means of every set of conducted experiments were taken to identify the effect of setup parameters on Overcut, DOP, and MRR.Input parameters like the voltage, the amplitude of vibration, the intensity of the magnetic field and pulse on/off ratio, their working range, and fixed value are selected by one factor at a time approach.Electrolyte and electrolyte concentration 20 wt.% NaOH has been fixed as it was found to be the optimal value from the literature survey for surface finish and machining depth. [41]As per the study of Kumar et al., surface finish diminishes with a rise in electrolyte concentration, although this effect is lesser in the presence of a magnetic field. [42]Further, 20% wt./vol is the most efficient electrolyte concentration as it provides the maximum chemical etching; therefore, more MRR and minimum hole overcut that improves dimensional machining accuracy. [8]Increasing the electrolyte concentration above the mentioned level increases the MRR, HOC, and tool wear. [43]It counterintuitively increases the risk associated with health hazards (skin irritation and breathing trouble).The following sections present the outcomes of experiments in the form of DOP, HOC, and MRR.The magnetic field's effect on discharge frequency and consistency is shown in the oscilloscope's observations, inferring the evidence of gas film stability with the magnetic field.

Effect of the set-up voltage and amplitude of vibration on performance characteristics during UAECDM without magnetic field
In the UAECDM, the vibration amplitude is essential in gas film thickness, bubble departure, and adhesion, affecting the output parameters like HOC, DOP, MRR, and tool wear.Multiple researchers have evaluated the vibration effect on MRR, DOP, HOC, and tool wear. [44,45]Gas film thickness is the main parameter responsible for discharge intensity, and when the input voltage rises, the intensity of discharge and gas layer thickness also elevates. [46]Fig. 5 shows the relation between MRR, HOC, and DOP with applied voltage on three different amplitudes of vibration.
Fig. 5(a) shows that MRR escalates with an elevated applied voltage and vibration amplitude.It is known that tool vibration reduces the gas layer thickness by reducing the departing bubble radius. [45,47]An increase in the tool's vibration amplitude lowers the potency of electrical discharge.Because of unstable gas film, inconsistent discharge is produced at lower voltages in UAECDM; this mechanism gives better results at higher voltages.Fig. 5(b) shows an increasing trend for HOC on increasing voltage and decreasing vibration amplitude.As the voltage rises, electrochemical discharge energy increases because the energy channelization beneath the tool edges increases the hole diameter.Fig. 5(c) indicates the relationship between DOP and applied voltage at different amplitudes.As explained earlier, the growing setup voltage escalates the formation of bubbles and enhances the MRR and DOP.Further, longitudinal tool vibration increases the drag force and improves electrolyte recirculation, enhancing the material removal from the workpiece.Fig. 5(c) shows that DOP increases with applied voltage and vibration amplitude.At higher vibration amplitude, high drag force is produced; therefore, smaller bubbles are generated beneath the tool electrode; energy channelized beneath the tool results in a higher DOP and lower HOC. [48]As per the previous study by Ranjeet et al., DOP increases up to 70 V at 7 µm amplitude of vibration; above 70 V, it starts decreasing because of gas film instability as the electrolyte evaporates at a very high rate on higher applied voltages. [13,15]However, as shown in Fig. 6, an excessive increase in vibration has a negative effect on output responses, like it diminishes the machined surface integrity and produces cracks at the hole periphery.
Therefore, the vibration amplitude provides good electrolyte circulation only to an extent.So, it can be inferred that there is an upper limit of vibration amplitude for specific voltage input; as this limit exceeds, the quality of the gas film starts degrading, causing hole surface damage, and reversing any positive effect on performance. [17]It has been observed from the literature available on ECDM that higher input voltage increases the tool wear rate, HOC, and crack formation, which makes it challenging to get precise micromachining.Therefore, parametric ranges for setup voltage have been consciously kept lower for higher dimensional accuracy than the earlier studies on ultrasonic vibration assisted ECDM. [15,49,50]It can be confirmed with the experimental results depicted in Figs. 5 and 6 that there is a refinement in the grade of the hole with an increase in vibration amplitude up to 7 µm.However, as shown in Fig. 6, at 60 V, there is a crack formation beyond 11 µm amplitude vibration.It indicates that a high amplitude of vibration (beyond 11 µm) creates unfavorable turbulence in electrolyte flow, creating adverse conditions for gas film stability. [51]Therefore, the discharge consistency is disturbed because the high amplitude ultrasonic tool's vibration damages the workpiece's surface and initiates crack formation.

UAECDM under the magnetic field
It is well known that gas film quality has an impact on the performance of electrochemical discharge machining.Initially, ultrasonic vibration was also employed to boost MRR and reduce the dimensional inaccuracy in micromachining.The implementation of ultrasonic vibration alters the gas film geometry.Further, it provides a more stable, thin gas film that enhances spark discharge quality.Experimental results and other researchers have also concluded that ultrasonic vibration enhances the performance of ECDM.However, it necessitates a comparatively high input voltage as opposed to conventional ECDM to maintain the stability of gas film. [13,15,52]The number of bubble formations increases with increasing applied voltage and produces high-potency discharges. [45]An increase in the potency of electrical discharge increases the machining zone temperature and, therefore, boosts the melting of the workpiece, i.e., the machining rate.However, excessive heat becomes counterproductive, diminishes the surface quality, and increases the tool wear rate. [16]Therefore, this excess heat needs to be evacuated immediately from the vicinity of the workpiece to improve the machined geometry's dimensional accuracy and surface quality. [21,30]In the present experimental arrangement, the incorporation of a magnetic force into the UAECDM mechanism to overcome this issue and improve dimensional accuracy is undertaken.
During machining under a magnetic field, as per the magnetic flux, a magnetic force acts on the moving charge particles that transform the motion of the bubble into the orthogonal direction of velocity. [53]Due to Lorentz's force, the bubbles in motion start rotating on the tool's periphery, giving better electrolyte recirculation under a magnetic field.During conventional ECDM in the microhole (beyond 300 µm), drilling speed is no more dependent on the applied voltage. [54]As indicated in Fig. 7(c,d), trapped machined material starts restricting the electrolyte flow inside the hole; discharges occur from the tool's side wall.Thus, increasing applied voltage contributes toward increasing the hole diameter instead of depth, and drilling speed is governed majorly by electrolyte availability inside the hole.Microhole drilling in ECDM has been classified into discharge and hydrodynamic regimes. [52]he condition up to which drilling speed is governed by applied voltage comes under the discharge regime, and beyond which the hydrodynamic regime starts.Fig. 7(a,b) indicates the discharge regime where the tool penetrates at a shallow depth up to which electrolyte circulation is accessible inside the hole.Therefore, discharge starts occurring from the tip of the tool.As discussed earlier, in this regime, DOP can increase with an increase in voltage.Based on the literature, the conventional ECDM discharge regime is around 200-300 µm. [30,54,55]n the hydrodynamic zone, low potency inconsistent discharge reduces the machining rate with an increase in the heataffected zone due to inefficient electrolyte recirculation.Therefore, there needs to be more efficient residue removal near the machining area.Fig. 7(c,d) indicates that the machined glass ceased the space between the tool's tip and the work material, forming the gas film solely around the tool's side wall.The electrolyte unavailability around the tool bottom face and workpiece causes discharges from side walls to become more prominent at the hole entrance.This results in major HOC and taper in the machined hole; therefore, a major issue is a dimensional accuracy in conventional ECDM.Thus, it can be inferred that the lack of electrolyte recirculation is the major limitation in the machining of deeper holes, as is the cause of dimensional inaccuracy.To bypass this limitation, magnetic field, along with ultrasonic vibration, seems promising to get high DOP and better dimensional accuracy in borosilicate glass workpiece.

Effect of magnetic field
Pilot experimentation to determine the magnetic field's working range has been done with the OFAT approach.As the potency of the magnetic field rises, the rate of electrolyte flow increases, which helps in electrolyte replenishment, providing more MRR with a good surface finish.However, as shown in Fig. 8, increasing the magnetic field beyond 45 Gauss reverses the effect, and the performance starts declining.The magnetic field induces Lorentz force, pushes the moving gas bubbles, and initiates the rotational flow of electrolyte, increasing bubble coverage and positively affecting the tool surface wettability.The magnetic field intensity on the gas bubble depends on the current density, and it is known that the bubble radius grows as the current density grows. [56]A large bubble experiences more buoyant force and gets pushed out through rotation, whereas smaller bubbles with less buoyant force stick to the tool surface.These tiny bubbles attached to the tool surface experience a rotation effect and increase the tool surface coverage area.Therefore, a stable and finer gas film forms close to the tool's surface resulting in a consistent highfrequency discharge (Fig. 9 at 45Gauss).If the Lorentz force on the bubble increases so much that the surface tension force is incapable of keeping the bubbles attached around the tool surface, then stable gas film cannot form.It can be seen from Fig. 9 that low-frequency inconsistent discharges occur at 70 Gauss.A similar effect of increasing magnetic field has been found in the study of S. Zhan et al.. [57] Figs. 8 and 9 show the impact of the magnetic field at 20 wt.% electrolyte concentration and 3:1 pulse on/off on different process outcomes.Experimental results reflect that the optimum range of the magnetic field is 40-45 Gauss.Fig. 8 shows  that an increase in the magnetic field beyond 50 Gauss drastically reduces the MRR and DOP.It is due to the very high electrolyte flow rate, which causes unstable gas film at the tooltip in hydrodynamic regimes. [8]MRR reduces to almost zero, and Fig. 9 depicts that the voltage signal is more consistent at a 45Gauss magnetic field with a drastic reduction in discharge frequency and intensity at a high magnetic field (70Gauss).As observed from Equation 10, the rotational velocity of bubbles increases with a magnetic field.It signifies that the high rate of electrolyte destabilizes the gas film, and a large number of bubbles accumulate at the hole entrance producing localized cooling.
Magnetic field enhances the electrolyte flow and helps to create a stable gas film.Figs. 8 and 9 indicate an adequate magnetic field is required to get a stabilized gas film and proper electrolyte flow at input machining parameters.This effect may vary depending on the wettability of tool electrode for different tool materials and electrolyte. [35]Voltage signals under different magnetic field values show that discharge intensity decreases with an increase in the magnetic field.Reducing the discharge intensity with increased consistency indicates a thin, stable gas film.Magnetic field helps to form the stable gas film, reduces discharge intensity, and improves the consistency of discharge with the enhanced frequency of discharges.The high-intensity magnetic field increases the rotational velocity, as implied by Equation 10.At a constant applied voltage, an increase in electrolyte rotation speed increases the DOP with a reduction in HOC.However, the electrolyte's high rotational speed removes the gas film. [8]It can be seen from Fig. 9 that at 70 Gauss, inconsistent discharge indicates that gas film cannot form completely.However, a stable gas film seems available at 45 Gauss magnetic field strength.
The microscopic images shown in Fig. 10 corroborate that MFA in UAECDM reduces thermal damage.Hole edge deviation from the tool edge and taper angle is also quantified in Fig. 10.C a1 , C b1 , and C c1 are the circles that identify the blind hole bottom surface, C a2 , C b2 , and C c2 identify the inlet surface, and C a3 , C b3 , and C c3 identify the distorted surface around the hole without a magnetic field.Similarly, in UAECDM with magnetic field C a1' , C b1' , and C c1' identify the hole bottom surface and so on.To minimize the experimental error, three experiments were performed in the same parametric settings, and average values are considered for output responses, as presented in Table 2.The measured output response and the average value of all three experiments are presented in Appendix Table A.
The average machined hole inlet diameter with and without magnetic field is denoted by d C2 and d C2', respectively.Taper angle, hole edge deviation from the desired hole, and heataffected zone signify the machining accuracy, which can be derived from the following equations. [7,58,59]or condition (a) with a magnetic field  The output responses obtained from the above equations, along with each measured value, are presented in Table 2. Quantified outputs in Table 2 signify that the surface damage in UAECDM under a magnetic field is lesser than that without a magnetic field.Reduction in taper angle and hole edge deviation also validate the enhancement of dimensional accuracy when a magnetic field is applied.As it is also clear in Fig. 8, HOC reduces with an increase in the magnetic field.Therefore, it can be deduced that MFA enhances the dimension accuracy of the UAECDM process.These results validate that the magnetic field rotates the electrolyte and eliminates the surplus heat from the machining zone, which helps overcome the problem of surface damage due to ultrasonic vibrations and excess heat removal.

Effect of set-up voltage and amplitude of vibration on responses during UAECDM under the magnetic effect
Tool vibration and magnetic field both promote electrolyte circulation.Electrolyte recirculation enhances heat transfer.Hence, it reduces heat damage and provides a smooth machined surface. [30]Better electrolyte circulation promotes electrolyte availability in the hydrodynamic region and generates a uniform, stable, fine gas film on the tool's surface.A uniform gas layer promotes consistent discharge and provides an excellent smooth surface.To explore the effect of ultrasonic vibration, ECDM under magnetic field experiments were performed on selected voltage ranges 50 V, 54 V, 58 V, 62 V, and 66 V on three different amplitudes of vibration 4, 7, and 11 µm.At the same time, other settings were held constant, like UAECDM without a magnetic field.Three experimental runs were performed on each parameter setting, and the arithmetic average of the outcomes was plotted.Fig. 11 shows the plots of MRR, HOC, and DOP trends on selected ranges.The magnetic field's effect with low amplitude ultrasonic vibration shows improved process efficiency, although the trends are similar to those in UAECDM without a magnetic field.MRR and DOP increase with growing setup voltage, although the escalation rate in material removal slows beyond 62 V; further, it starts decreasing.It may be because, at high energy inputs, the tool electrode starts wearing; at high discharge energy, the electrolyte evaporates at a very high rate, and electrolyte deficiency occurs in the machining zone resulting in a decreasing MRR.It was discovered that an input voltage of 62 V emerged as the breakdown voltage in the selected parametric range in ultrasonic-assisted electrochemical discharge machining under a magnetic field.Beyond 62 V, MRR rises with an increase in vibration amplitude only up to 7 µm.Increasing vibration amplitude above 7 µm shows a decrease in MRR.Magnetic field assistance improves the electrolyte recirculation and decreases film thickness, as revealed by Eq 11.It enhances the discharge quality and gives a better hole surface quality and dimensional accuracy, as seen in Fig. 10.The experimental outcomes in Fig. 11 validate the hypothesis discussed in Fig. 2 that the MFA improves the quality of the discharge and, therefore, the hole surface and machining performance.
Using the formula in Equation 1, the HOC for 58 V at 7 µm vibration amplitude during UAECDM under the magnetic field is 310 µm, and during UAECDM without MFA, it was found to be 420 µm.Therefore, around 35% of HOC can be reduced by implementing a magnetic field to ultrasonic-assisted ECDM.In addition to tool vibration, the magnetic field swerves the departing bubble; therefore, a finer gas layer is produced, which helps reduce hole overcut.However, HOC continues to increase with growing voltage due to the high potency of side discharges and local heating.As per the experimental result shown in Fig. 10, 58 V is the threshold value that gives high MRR with less HOC.MRR increases by around 11%. Although, beyond this voltage, MRR still increases with a lesser rate of increment, as, due to high thermal energy, the tool gets worn out, and the electrolyte vaporizes.The depth of penetration and HOC also increase with growing voltage.However, beyond 62 V, the effect of the vibration amplitude is reversed because of tool wear and limited electrolyte availability at higher depths.DOP in this process increases by around 24% compared to UAECDM without a magnetic field.As the ultrasonic vibration helps to escape the machined material from the confined space at the tool's bottom, and then Lorentz force helps to take it out from side walls effectively, this process with ultrasonic vibration and magnetic effect works collaboratively and provides exceptionally smooth electrolyte flow and stable gas film.Therefore, consistent discharge continues without interruption under the magnetohydrodynamic effect. [60]Better electrolyte circulation at higher voltages makes this process suitable for high DOP with high dimensional accuracy and less thermal damage, as shown in Fig. 12.However, due to elevated temperature in the machining zone, the electrolyte evaporates at a voltage exceeding 62 V. Hence, electrolyte deficiency occurs, and the effect of vibration amplitude becomes counterproductive.
In Fig. 12, the oscilloscope voltage signal also shows that UAECDM under a magnetic field provides a consistent signal with more sparks and more average peak voltage of sparks on different applied voltages.It also shows the microscopic images of the machined hole during UAECDM without and under the magnetic field of intensity 45 Gauss.It is visible that the machined surface with MFA is smoother with less HAZ.During the tool's ultrasonic vibration without a magnetic field, the effect of drag forces on the workpiece surface leads to crack formation. [48]In contrast, no cracks form when a magnetic field is present along with similar input settings.This is because of the presence of stable gas film and smooth electrolyte flow.As shown in Fig. 10 at 58 V with 11 µm Vibration amplitude, HAZ in the hole produced by process UAECDM without a magnetic field is comparably more than the hole made by UAECDM under a magnetic field.Fig. 12 also confirms similar results with evidence of consistent highfrequency discharges that lead to less HOC and better surface quality.
The magnetic field assists in evacuating excess heat available in the machining area, reducing HAZ from the machined surface.However, at higher setup voltage, additional discharge energy produces and increases the electrolyte evaporation that affects the machined surface.In the process of UAECDM without a magnetic field, an increment in voltage damages the hole surface, which can be observed in the microscopic image in Fig. 12.Similarly, from Figs. 10 and 12, it is also clear that, at the same input voltage, under a magnetic field, the process enhanced, resulting in smoother machined holes with higher dimensional accuracy and less thermal damage.However, with further increments in voltage, more magnetic strength may be required to achieve a suitable electrolyte flow rate.
Fig. 13 shows the variation in consistency and intensity of sparks at different voltages without and under magnetic assistance.According to Singh and Appalanaidu, ionization enhances under magnetic field assistance, increasing the machining zone's current density. [60]Enhancement in electrolysis increases the nucleation phenomenon, and more tiny bubbles form and coalesce.Therefore, a stable and fine gas layer forms around the tool surface that upgrades the discharge quality at the tooltip, which results in enhanced MRR and DOP. [61]Magnetic force, in collaboration with the ultrasonic energy of the tool, enhances the electrolysis rate and provides a more stable and fine gas layer that collectively enhances the chemical etching and discharge energy, producing more MRR.It can also be seen in Fig. 13 that during UAECDM without MF, as the amplitude of vibration increases, the spark intensity and frequency both decrease; therefore, less energy is produced and, thus, to enhance the energy at the machining zone, high voltage is needed to build a stable gas film.
FESEM images of both processes show visible surface quality differences in both results.During UAECDM without a magnetic field, the stray bubbles accumulating at the hole's entrance block the electrolyte recirculation path.Therefore, electrolyte deficiency occurs at the tool's tip, and the gas film deteriorates. [60]That shifts the electrical discharge toward side walls; energy channelizes through undesirable non-uniform side discharges, causing stray cutting and hence non-uniform material removal from the workpiece. [62]During the magnetohydrodynamic effect, material removal initiates beneath tool edges, and the wall surface of the machined hole remains smooth, as seen in Fig. 14, inferring uniform discharge energy is channelized toward the center of the hole.Magnetic assistance shows a better response in improving machined surfaces. [60,63]It is clear from Fig. 14 that magnetic field assistance with a low amplitude of vibration gives better surface quality.Similarly, as Figs. 10 from 14, it can be deduced that the magnetic effect reduces the chances of local heating and provides smooth electrolyte flow and consistent electrical discharge, hence a smooth surface and high dimensional accuracy.

Conclusion
The present research highlights the impact of a magnetic field on the UAECDM process mechanism and performance.The machining behavior was investigated using experiments performed on the developed UAECDM facility.The implications of varying input parameters (voltage, vibration amplitude, and magnetic field intensity) were discussed, keeping machining efficiency and accuracy in focus.UAECDM under a magnetic field significantly improvises the process and enhances the performance.Some key conclusions are listed below-• Lorentz's force enhances the tool's surface coverage and promotes the formation of a thin and stable gas layer around the tool.High-frequency consistent discharge signals support this phenomenon under a magnetic field.An applied voltage of 58 V, a vibration amplitude of 11 µm, and a magnetic field intensity of 45 Gauss resulted in high MRR and DOP, with lesser HOC.• On increasing the voltage, MRR and HOC increased.The highest DOP achieved with a magnetic field with lesser HOC is around 955 µm at an applied voltage of 58 V and vibration amplitude of 11 µm.• On increasing vibration amplitude, HOC was reduced.
However, increasing the amplitude by more than 11 µm affects the hole's surface quality and results in crack formation.• The MFA in UAECDM aids in reducing the gas film thickness and promotes stability and, therefore, generates moderate intensity consistent discharge.Electrolyte recirculation in the hydrodynamic zone also shows improvement due to the magnetohydrodynamic effect.Hence, the machining of borosilicate glass through UAECDM under a magnetic field provides better dimensional accuracy and a high machining rate over UAECDM without a magnetic field.• Ultrasonic electrochemical discharge machining under a magnetic field process has higher MRR and DOP, with 11% and 24% rise compared to without a magnetic field, respectively.It also reduces HAZ, taper angle, and HOC and provides a damage-free surface without crack formation.
• From experimentation, it has been found that at 58 V, 7-10 µm tool vibration amplitude, 45Gauss magnetic field, 20%wt.NaOH electrolyte and 3:1 pulse ON: OFF ratio resulted in a smooth surface with less HOC and 120 mg/min MRR.Based on these specific parameters, it can be deduced that the performance of UAECDM under a magnetic field has been prominently enhanced.

Figure 2 .
Figure 2. (a) Top view of electrolyte gas film under w/p during UAECDM under magnetic field (b) Single bubble attached to tool electrode during UAECDM (c) Single bubble attached to tool electrode during UAECDM under magnetic effect.

Figure 4 .
Figure 4. Single bubble attached to tool electrode, (a) without magnetic field, (b) under 45 Gauss magnetic field &; (c) direction of Lorentz force.

Figure 5 .
Figure 5.The effect of set-up voltages on (a) MRR, (b) HOC (c) DOP in the UAECDM process.

Figure 6 .
Figure 6.Microscopic images of the drilled hole at 60 V on the different amplitudes of ultrasonic vibration.

Figure 7 .
Figure 7. Discharge mechanism in discharge regime (a and b) and hydrodynamic regime (c and d).

Figure 8 .
Figure 8.Effect of varying magnetic field in machining area on MRR, DOP, and HOC (machining condition applied voltage 58 V, 11 µm amplitude of vibration).

Figure 9 .
Figure 9. Voltage signal from Oscilloscope at different magnetic field values (machining condition applied voltage 58 V, vibration amplitude 11 µm).

Figure 10 .
Figure 10.Microscopic images of machined holes at constant parametric settings of Voltage 58 V.

Figure 12 .
Figure 12.Microscopic view of a machined hole at different Voltage and discharge quality without magnetic field and under magnetic field at a constant vibration amplitude.

Figure 13 .
Figure 13.Voltage signals on different voltages with and without magnetic field with three sets of ultrasonic vibration in the tool.

Figure 14 .
Figure 14.FESEM images of machined holes showing surface quality at applied voltage 60 V.

Table 1 .
Process parameters and their range used for experimentation.