As the trend of miniaturized products, micromachining is a key technique to satisfy functional requirements in various precision industries including automobile, aerospace, electronics, medical implants, biomedicine, robotics, and so on . Microdrilling is become more prominently for fabricating microholes in electronics and computer industries such as printed circuit boards, integrated circuitry masking , and the wafer testing components discussed in this study. The processes must be closely controlled to produce microholes with accurate dimensions, good straightness, small roundness and positional errors, and lengthen tool life.
Mechanical drilling using a microdrill is a cost-efficient method for making microholes in a miniature part . However, some difficulties have to be overcome; for example, a large load cannot be put on the microdrill due to its low strength and rigidity. In addition, owing to the smaller drill flutes, removal of the drilled chips is easy to be obstructed . Hyacinth Suganthi et al.  indicated main factors affecting the size and position of the microholes including the process of microdrilling, tools, speeds and feeds, parallelism, vibration and sound, and positional repeatability. Several researchers have presented their experiences in mechanical microdrilling described as follows.
Cutting force is the principal issue on the drilling by a microdrill. Patra et al.  indicated that downscaling of the conventional drill to a microdrill increases the aspect ratio of the tool and affects the thrust force and radial components. Increasing in the axial cutting force causes the drill bending due to the low stiffness. Anand et al.  presented a force model for the mechanistic microdrilling with considerations of tool edge radius and minimum chip thickness. Kim et al.  developed a tool monitoring system for detecting the thrust force in peck-drilling cycles to improve microdrill life. The thrust force detected was below 3 N in drilling a 250-µm-diameter hole of a plain carbon steel (AISI 1045). Anand and Patra  performed microdrilling experiments of carbon fiber reinforced plastic (CFRP) to investigate the effects of feed and cutting speed on the cutting force components and hole quality. The thrust force was about 4 N in drilling a 0.5-mm-diameter hole. Rahamathullah and Shunmugam  investigated the thrust force in drilling a 320-µm-diameter microhole of carbon fabric laminate composites. The thrust force increases with an increase in feed and a decrease in spindle speed. Actual thrust forces detected were from 2 to 3.8 N.
Run out is one of common and undesired phenomenon in the drilling process. It causes tool breakage, surface damage, or dimensional inaccuracy. Beruvides et al.  believed that run out consists in an eccentric motion of the drill generated by the excessive centrifugal force. Drilling by a high aspect ratio drill needs to be checked carefully. Endo and Marui  said rotational cutting speed is almost zero near the chisel point in the small-hole drilling. At that point, the drill only has a small axial velocity corresponding to the feed motion. Accordingly, the run out easily occurs owing to the small error in the drill size. Chang and Lin  made a center-pilot hole first in the microdrilling process by a short-body drill, to reduce the probability of run out in the inlet stage. Size characteristics of the holes drilled can be controlled effectively. Wang et al.  analyzed the effect of pilot hole in the drilling of CFRP composites. In the drilling of a 4-mm hole assisted by a 1-mm pilot hole, the thrust force was reduced by approximately 55% compared to the none-pilot drilling.
Most literature showed that both cutting speed and feed rate are the principal parameters affecting the cutting force and hole characteristics. Aysal  used Taguchi’s experiment and analysis of variance (ANOVA) method to investigate the effects of drilling parameters (cutting speed, feeds, point angle of the drill) on surface roughness and burr in the drilling of carbon black reinforced polyethylene. Rajmohan and Palanikumar  optimized machining parameters (spindle speed, feed, drill type) in the drilling of hybrid metal matrix composites by Taguchi’s L9 orthogonal array (OA) experiment. The characteristics examined included the thrust force, surface roughness, and torque. Shunmugesh and Panneerselvam  performed microdrilling experiments of CFRP to discuss the parameters of spindle speed, feed rate, and drill diameter by Taguchi’s L27 OA to derive optimum conditions for reducing the delamination factor, circularity, and cylindricity simultaneously. Thanikasalam et al.  developed an online tool-conditions monitoring system to investigate process parameters for surface integrity and hole quality in deep hole drilling of AISI 1045 carbon steel. The control factors in L9 OA were the spindle speed, feed rate, and coolant pressure. Ravisubramanian and Shunmugam  analyzed the thrust force and torque in the drilling of 6061-T6 aluminum alloy by a 0.5-mm-diameter drill. They compared the thrust force and torque in peck-drilling and direct drilling. A maximum reduction of 52% in thrust force was found.
Applications of ceramic plates with microfeatures are widespread uses for electronic accessories, electrical components, thermal equipment, and catalytic converters . However, the machinability of ceramics is poor due to its brittle behavior and high hardness. To develop an efficient process of ceramic microdrilling is important for controlling the hole’s precision, reducing manufacturing cost, and maximizing productivity. Some researchers devote to the use of ultrasonic vibration-assisted mechanism to overcome the problems of exit chipping and tool wear in the drilling of ceramics [17–19]. Cutting force can be decreased due to dynamic friction and aerodynamic lubrication from the periodical vibration, and obtain better cutting performance . According to the fracture mechanism of drilling engineering ceramics, in the terminal period of drilling, the stress on the periphery of the hole exit is at its maximum and causes a fracture . Liu et al.  used a rotary ultrasonic spindle system to reduce the microchipping or cracking at the exit in drilling of alumina oxide ceramics. The tool wear was decreased. Nevertheless, few studies published are focused on the mechanical microdrilling of ceramics. In our previous study , a two-segment peck-drilling process was proposed to fabricate a 55-µm-diameter microhole. The variation of hole diameter can be controlled within 0.67 µm.
As the literatures mentioned above, the machining characteristics in microdrilling mostly discussed are cutting force [4–9, 11, 13, 16, 17, 21–22] and torque [8, 11, 13, 16]; the hole characteristics include dimensional accuracy [3, 8, 10, 17, 20], circularity or roundness [7–8, 10, 14–15, 20–21], burrs and roughness of hole wall [12–13, 15], and tool wear [15, 19–20]. This is a complicated multi-characteristic problem.
Grey Relational Analysis (GRA) is one of methods widely used to optimize manufacturing process that considers several input factors and multiple responses simultaneously. Some GRA models have been presented to infer the optimal parameters design in mechanical drilling processes. Rajmohan and Palanikumar  applied GRA method to optimize machining parameters in the drilling of hybrid metal matrix composites based on the L9 OA experimental data. The characteristics considered including the thrust force, surface roughness, and torque. Shunmugesh and Panneerselvam  performed the multi-characteristic analysis in the drilling of CFRP. Data of L27 OA experiment were used as the inputs to GRA model for minimizing the delamination factor, circularity, and cylindricity. Thanikasalam et al.  optimized the multi-objective problem of the deep drilling process of a mild steel (AISI 1045) by coupling Taguchi’s L9 OA data and GRA method. Six characteristics were considered such as surface roughness, circularity, cylindricity, hole wall temperature, tool wear, and material removal rate (MRR). Yaşar et al.  presented the use of Taguchi-based GRA method to optimize the machinability characteristics of thrust force and roughness in the drilling of a polypropylene composite based on L27 OA data.
For the experiments on mechanical drilling, several studies [4, 7, 9, 17] analyzed both principal parameters of cutting speed and feed rate by the three-level L9 OA. Nine sets of full-factorial experiments were performed to evaluate the factorial effects on the characteristics examined and derived “preferred factorial level set”. Some literatures [10, 13, 15, 18, 21] added one or two parameters in their experiment, and analyzed them by Taguchi’s fractional-factorial OA such as L9, L16, L18, and L27. Afterward, experimental validations were implemented to confirm the analytical results. Moreover, several researchers [5, 8, 12, 14, 16, 19] increased the number of factorial levels to derive the “optimal factorial level set” by a full-factorial experiment directly. However, when the replicated trials are included, the experimental scale and expense are always huge.
Although Taguchi’s OAs possess orthogonal properties, the interactivities between control parameters/factors are not checked in most study. Experimental errors due to the unknown or uncontrolled factors may affect analytical results . Therefore, interactions between the control factors are suggested to be discussing here, especially in developing a new process.
This study investigated the microdrilling process of a nitride ceramic plate of machining a stepped microhole matched with a spring-loaded needle used in the wafer testing industry. A two-level OA experiment (L8) of a through microhole was first carried out to check the interactions between the peck-drilling parameters analyzed. After interactivity discussion, a three-level OA experiment (L9) of making a stepped microhole was performed to derive the “preferred factorial level set” for minimizing the thrust force and improving the hole characteristics. Furthermore, a Taguchi-based GRA model was built to solve the multi-characteristic problem considering the accuracies of hole diameter, roundness, and positional error simultaneously. Final, the analytical results were showed by experimental validations.