In recent years, alumina as a substrate is being explored in the field of radio-frequency (RF) micro-electro-mechanicalsystems (MEMS) and microsystems packaging. Alumina as a substrate offers superior electrical insulation (>10 14 -cm), excellent wear resistance, hardness (15.7 GPa) , and higher thermal conductivity (35 W/mK). In high frequency (>2 GHz), the electrical insulation helps in reducing the substrate loss and thus, results in faster signal transmission. Despite having clear advantages over silicon in the first-level microsystems packaging, alumina has not been used a lot. Due to the hard and brittle nature of alumina, the formation of microfeatures such as blind/through holes, channels by the conventional contact-based method is a very challenging task. Plasma etching has a very low etch rate and requires a thick masking layer to protect the desired area. Due to the residuals formed during the plasma etching, the chamber needs to be frequently cleaned. Ultrasonic machining to etch alumina remains a slower process and requires harder abrasive particles (B4C, polycrystalline diamond) and also has issues of tool erosion. Abrasive jet machining process has a possibility of nozzle chocking and poor surface quality. Only, the laser ablation process has limited success in creating micro features in alumina; however, laser ablation requires expensive infrastructure, which may not be readily available. Hence,
In recent years, alumina as a substrate is being explored in the field of radio-frequency (RF) micro-electro-mechanicalsystems (MEMS) and microsystems packaging. Alumina as a substrate offers superior electrical insulation (>10 14 -cm), excellent wear resistance, hardness (15.7 GPa) , and higher thermal conductivity (35 W/mK). In high frequency (>2 GHz), the electrical insulation helps in reducing the substrate loss and thus, results in faster signal transmission. Despite having clear advantages over silicon in the first-level microsystems packaging, alumina has not been used a lot. Due to the hard and brittle nature of alumina, the formation of microfeatures such as blind/through holes, channels by the conventional contact-based method is a very challenging task. Plasma etching has a very low etch rate and requires a thick masking layer to protect the desired area. Due to the residuals formed during the plasma etching, the chamber needs to be frequently cleaned. Ultrasonic machining to etch alumina remains a slower process and requires harder abrasive particles (B4C, polycrystalline diamond) and also has issues of tool erosion. Abrasive jet machining process has a possibility of nozzle chocking and poor surface quality. Only, the laser ablation process has limited success in creating micro features in alumina; however, laser ablation requires expensive infrastructure, which may not be readily available. Hence, 48th SME North American Manufacturing Research Conference, NAMRC 48 (Cancelled due to there is a need to reduce the cost of micromachining and to improve the etching performance of ceramic materials. The process capability to produce high aspect ratio micro-holes through non-conductive ceramic materials can open up several applications in various fields such as biomedical, MEMs, and energy sectors.
In recent decades, electrochemical discharge machining (ECDM) has emerged as a simple, economical, and faster approach to fabricate the micro-scale parts in a wide range of non-conductive materials such as glass, fused silica, and quartz, etc. [1, 2] . ECDM is the combination of electrical discharge machining (EDM) and electrochemical machining (ECM) processes and removes the material by the combined action of localized melting and high-temperature assisted chemical etching [3] . Although the ECDM has already been reported for glass micromachining by various researchers across the globe, there is limited literature on the etching of alumina, which has a much higher melting point (2030 C) than glass (1400 C). [4] . Tsutsumi et al. attempted the high-quality machining of alumina using the combined process of ultrasonic drilling and ECDM. The authors observed that ultrasonic core drilling performs better in the drilling of holes; however, the hole diameter was more than a millimeter. The authors obtained a material removal rate of 0.1 mm/min for hole formation at a machining voltage of 70 V using 20% NaOH electrolyte [5] . Bhattacharyya et al. used a copper electrode of 2 mm diameter and 20%-30% NaOH electrolyte with a pulsed DC power supply [6] . Jain and Chak obtained a maximum hole depth of 1.35 mm within 70 minutes using copper wire ( 1.5 mm) as a tool electrode [7] . Jain et al. used an abrasive tool electrode to achieve further improvement in the ECDM process in terms of higher material removal rate and higher machining depth [8] . Wang et al. investigated the machining performance of alumina using ECDM assisted diamond wire sawing and found improvement in material removal rate compared to stand-alone diamond wire sawing operation [9] . Ji et al. proposed an electrochemical dischargebased scanning process for machining of zirconia ceramic and obtained better machining efficiency and accuracy using a notched electrode [10] . Instead, Biswas et al. used a fiber laser-based milling process for micro-channel fabrication through zirconia ceramic and achieved a maximum channel depth of around 373 µm in 5 passes [11] .
It is clear from the literature review that etching of alumina is much more difficult than the glass material, which is due to two reasons, i.e., higher melting point and lower chemical reactivity with an alkaline electrolyte. Creating a deep microhole through alumina ceramic still remains a challenging task for the research fraternity. In this work, the authors aim to develop a cost-effective ECDM process capable of etching >300 µm deep micro-holes through alumina substrate using a simple steel tool electrode. As maintaining a constant gap between tool electrode and alumina substrate is very important, this experimental investigation aims to understand the rate of tool consumption and appropriate tool feed rate at different machining voltages. Further, the combined feed mechanism was adopted to achieve a deep micro-hole (>300 µm) through alumina substrates. Numerical simulation was carried out to find the crater depth of alumina at various process parameters. These simulated results were compared with the experimental results.
All the experiments were performed in an in-house developed ECDM setup, whose schematic is shown in Fig. 1 . Pulsed DC power supply was used as an energy source where the machining voltage, pulse frequency, and duty cycle can be regulated as per the requirement. Alumina substrate (25×25×3 mm 3 ) was used as workpiece materials whose properties have been listed in Table 1 . Mirror finished alumina substrate was mounted in the center of an auxiliary electrode in the machining chamber. High carbon steel needles were used as tool electrodes, which had an average tip size of 150 µm. The effect of machining voltage and tool feed rate on the depth, overcut of the micro-holes, and tool electrode consumption have been investigated. The machining voltage directly controls the thermal energy, which is supplied to the workpiece in the form of discharge pulses. The experimental setting of control parameters has been listed in Table 2 . During the preliminary experiment conducted at a 70% duty cycle, it was observed that at a machining voltage of 45 V, the discharge energy was not sufficient enough to remove any significant amount of alumina material. When the experiments were carried out at a machining voltage of more than 60 V, the depth of micro-holes in the alumina substrate was not significant. It was due to severe tool wear that occurred at higher machining voltage. Therefore, machining voltage was varied at three different levels, i.e., 50 V, 55 V, and 60 V. Further, the tool feed rate was varied at three different levels, i.e., 0.25 µm/s, 0.50 µm/s and 1 µm/s. A total of 27 experiments were performed for all combinations of machining voltage and tool feed rate. Each experiment was repeated three times to ensure the repeatability of the ECDM process. 2 shows the V-I graph obtained for 30% NaOH electrolyte and the alumina substrate. The acquired V-I characteristics were similar to one obtained with the fused silica substrate by the authors [12] . In the overvoltage region (ab), a negligible amount of current flow between the electrodes indicates that no electrolysis occurs in this region. However, bubbles formation takes place in the ohmic region (bc), and the current is linearly increasing with an increase in voltage. Further, a similar trend between current and voltage is observed in limiting the current region where bubbles coalesce take place. Then, the instability region was detected where the value of current suddenly decreases with an increase in applied voltage, which indicates the formation of the gas film around the tool electrode. When the voltage exceeds the specified value known as critical voltage, a discrete discharge pulse is detected, which is known as electrochemical discharge. From Fig. 2 , it can be observed that the V-I characteristics are independent of the material to be etched, but these are majorly affected by the electrolyte type and its concentration. Further, it can be noted that electrical discharge only occurs after a critical voltage of 40 V. This finding is found to be useful to determine the minimum voltage, which is required for machining of alumina substrate.
A finite element method (FEM) was used to predict the depth of the crater formed on the alumina substrate. The FEM simulation was carried out using COMSOL5.4 software. The boundary conditions used for simulation are demonstrated in Fig. 3(a) . Gaussian heat flux was considered as a source of thermal energy in the discharge zone. The top surface of the workpiece was exposed to the convective heat transfer, whereas other surfaces were thermally insulated. In this simulation, the deformation induced by thermal loads was not considered. The geometry meshed with a tetrahedral element. The discharge zone was further refined using maximum and minimum elemental mesh size of 4 µm and 0.1 µm, respectively, as shown in Fig. 3(b) . Several complex phenomena, such as bubble generation, film formation, and spark generation, are involved in the ECDM process [13] . The following assumptions were taken into consideration to simplify the thermal model.
a) The material properties such as specific heat, thermal conductivity, and density are assumed homogeneous and isotropic and temperature independent. b) Electrochemical discharges follow a Gaussian distribution of heat flux, and only a fraction of heat energy termed as energy partition (Ep) is transferred to the substrate. c) Every subsequent spark at a particular spot of the tool was repeated only when the sparks had already been generated from other remaining locations. d) Regions with a temperature higher than the melting temperature (Tm) of alumina substrate (2303 K) is assumed to be removed.
The temperature distribution in the alumina substrate was obtained by solving a transient 3D heat conduction differential equation expressed by Eq. (1):
Where k, ρ, cp are the thermal conductivity, density, and specific heat of the workpiece, respectively. The properties of the alumina substrate used during the simulation are listed in Table 1 . In the beginning, the temperature of the entire domain at the ambient temperature, i.e., T0 = 298 K. The top surface was exposed to a Gaussian heat flux (q) given by Eq.
(2). In contrast, all the remaining surfaces were thermally insulated. 2 
Where Rs is the spark radius (20 μm) expressed by Eq. (3) [14] , ton is the pulse-on time, Ep is the energy partition (5%), h is the convective heat transfer coefficient of the electrolyte (10000 W/m 2 K), V is ECDM machining voltage, and I is the mean current flowing through the circuit for different electrolytes [15, 16] . The pulse-on time was determined to be 70 μs, while the pulse-off time was 30 μs for a given duty cycle (70 %) and pulse frequency (10 kHz). It was assumed that the spot size for each electrochemical discharge was 1 μm 2 ; therefore, the subsequent spark for tool tip diameter of 150 μm would occur at a particular location only after 1.75 sec. Fig. 4 shows the temperature distribution obtained after the second spark. The maximum surface temperature was more than 4000 K, and the predicted crater depth was 5.7 μm. 5 shows the cross-section of the crater obtained after the different numbers of sparks at a particular location. After each spark, the material having temperature >2303 K was removed, and the subsequent heat flux was applied on the modified top surface. The crater depth showed an increasing trend with an increase in discharge duration. The thermal energy transferred into the workpiece increases with an increase in discharge duration resulting in higher crater depth. The simulation results obtained have been validated experimentally and discussed in section 4.4.
Higher discharge energy in the ECDM process results in more severe tool wear and also affects the surface quality of the machined component. The machining voltage has a significant influence on tool electrode consumption during the ECDM process. A small change in dimension of the tool can change the gap between the tool electrode and the alumina substrate, thereby affecting the performance of micro-hole. The effect of the ECDM process parameter on the micro-hole formation in the alumina substrate has been discussed in the following section.
The electrode consumption was determined by the weight loss method using a precise weighing balance (Mettler Toledo -MX5) having an accuracy of 1 µg. The effect of machining voltage on electrode consumption at different feed rates and machining voltage has been shown in Fig. 6 . An increase in machining voltage tends to increase the discharge energy and thus increase the tool consumption. Further, tool wear was decreasing with an increase in tool feed rate (f) for all specified values of machining voltage. This behavior could be explained by the fact that at lower feed, the tool was allowed for a comparatively longer time to remove the material and also remain in contact with the electrolyte for a longer duration. Hence, tool consumption increases. At higher feed rate, the tool was allowed to remove the material for a relatively shorter time and also remain in contact with electrolytes relatively for a shorter time; hence a small amount of tool material was consumed during the ECDM process. An increase in the machining voltage tends to increase the discharge intensity during ECDM, hence resulted in severe tool wear, as shown in Fig. 7 . As the discharge pulse strikes the surface of the tool below the plasma channel, the substrate receives intense thermal energy, which is quite enough to melt and evaporate the tool material [17] . The increasing trend of electrode wear along with machining voltage, has been demonstrated in Fig. 7(b) , 7(d) and 7(f). Initially, the tool tip which was immersed in the electrolyte eroded due to a hightemperature discharge pulse, as shown in Fig. 7(b) . Then, neck formation started at the vicinity of the tool tip due to an increase in discharge energy at a higher machining voltage of 55 V, as shown in Fig. 7(d) . Further, with an increase in machining voltage up to 60 V tends to breakdown the tool tip where necking formation was started as indicated in Fig. 7(f) . 
The machining voltage, along with the combination of the duty cycle, is the main influencing factor of the ECDM process. It is directly related to the thermal energy transferred to the alumina substrate for the removal of material by spark erosion and electrochemical dissolution. In ECDM, ceramic material like alumina is removed mainly due to etching of grain boundary in the presence of high-temperature electrolyte [18] . For better discharge stability, the duty ratio of 70% was maintained constant. From Fig. 8 , it was observed that the depth of the micro-hole formed on the alumina substrate was decreasing with an increase in the machining voltage. This behavior could be better explained by the fact that a slight increase in the machining voltage drastically changes the dimension of the tool electrode, which has already been explained in section 4.1. The change in electrode shape and geometry can increase the gap between tool and workpiece. A slight change in the gap between tool and workpiece drastically influences the performance of the ECDM process. That's because the higher the gap between tool and workpiece in the ECDM process resulted in a decrease in discharge intensity, which in turn significantly reduced the depth of micro-hole formed on an alumina substrate, as shown in Fig. 8 . Further, it was also observed that the change in tool dimension could reduce the effect of increased tool feed at machining voltage of 50 V and 55 V. Therefore, the depth of micro-hole was decreasing with an increase in the tool feed. But, at a higher voltage of 60 V, the effect of feed rate on micro-hole depth was less significant due to the breakage of tool tip after neck formation, as shown in Fig. 7(f) . The graphical representation of micro-holes formed on the alumina substrate has been shown in Fig. 9 , which indicates that the best quality of micro-hole was obtained at machining voltage of 50 V and tool feed rate of 0.25 µm/sec, whereas other control factors were maintained constant as reported in Table 2 . Fig. 9 . Graphical representation of micro-holes with different tool feed rate and applied voltage.
The effect of machining voltage on the overcut of microhole is shown in Fig. 10 , which indicates that overcut was increasing with an increase in the machining voltage. This behavior can be explained by the fact that at higher machining voltage, discharge intensity will increase, which in turn produces a more aggressive discharge pulse compared to low voltage discharge pulse, hence formed comparatively large size hole on alumina substrate as shown in Fig. 7(e) . On the other hand, at a lower machining voltage, the discharge pulse is more concentric due to low thermal energy hence produce comparatively smaller and deeper micro-holes, as shown in Fig. 7(a) . Further, it was also observed that the effect of tool feed rate on hole overcut is not significant at a lower machining voltage of 50 V; however, it has some influence on machining performance at a higher machining voltage (>50 V) as shown in Fig. 10 . The cross-sectional profile of micro-hole formed at the tool feed rate of 0.25 µm/sec has been shown in Fig. 11 , which indicates that with an increase in applied voltage from 50 V to 55 V, the depth of micro-hole is slightly decreased; however, hole overcut is severely increased due to an increase in discharge energy followed by aggressive discharge pulse. Fig. 11 . A cross-sectional profile of micro-hole formed at a different voltage.
In the current study, a micro-hole depth of 228 µm is achieved at a machining voltage of 50 V and a tool feed rate of 0.25 µm/sec, as shown in Fig. 7(a) where the tool was allowed to travel only 300 µm. Beyond 300 µm, the electrochemical discharge machining is not significant due to the insufficient availability of electrolytes at higher depth [19] . A combined feed mechanism has been attempted to overcome this issue and to achieve a deeper micro-hole in the alumina substrate. Initially, the tool is allowed to travel at a higher feed (0.5 µm/sec), then the tool feed is reduced to 0.25 µm/sec once it reaches to 350 µm. The combined feed mechanism is first attempted for lower machining voltage (50 V). But, it was observed that machining is not significant beyond 250 µm due to inadequate discharge energy followed by insufficient availability of electrolyte at higher depth. Then, experiments were conducted at higher machining voltage (55 V). A micro-hole depth of 425 µm was obtained after a tool travel of 500 µm in -Z direction, as shown in Fig.  12 (a). The tool electrode was initially allowed to travel a distance of 350 µm at a feed rate of 0.50 µm/s, and then next 150 µm was attempted at a feed rate of 0.25 µm/s. The crosssectional profile of deep micro-holes (>300 µm) through the alumina substrate has been illustrated in Fig. 12(b) , which explores the potential of the ECDM process for microfluidic application. Fig. 13 indicates the numerical validation of the experimental crater depth obtained at machining voltage of 50 V, followed by different discharge duration. The crater depth showed an increasing trend with an increase in discharge duration. Due to an increase in discharge duration, the total heat flux transferred to the alumina substrate increases, resulting in an increase in material removal as well as crater depth. The predicted crater depth showed a good matching trend with experimental values. A marginal difference in values could be due to the assumptions considered in the numerical model, i.e., constant flushing efficiency and partition energy. 
The present study mainly focuses on the fabrication of the deep micro-hole in hard non-conductive materials like alumina for radio-frequency MEMS and microfluidic application. High carbon steel needles of tip size 150 µm were used to create micro-hole on alumina substrate using the ECDM process. The experiments were performed to study the effect of machining voltage and tool feed rate on the depth of micro-hole, overcut, and tool consumption. It was observed that machining voltage of 50 V and feed rate of 0.25 µm/s produced an optimum quality micro-hole in terms of hole depth of 228 µm, lower overcut of 270 µm and lower electrode consumption of 360 µg. Tool tip breakage after neck formation was observed beyond 55 V that drastically increase the gap between tool and workpiece, and significantly affect the machining performance of micro-hole formed on the alumina substrate. Further, the combined feed mechanism was adopted, which helped in achieving deeper micro-hole (425 µm) in the alumina substrate. Also, the results obtained with numerical simulation depicted a good agreement with experimental values.