Using Response Surface Methodology of Deep Hole Electrical Discharge Machining Study of Nickel-Base Alloy Inconel-718

: The blades in the high-pressure turbine section of engines of modern aerospace and defense industries need to be drilled for pressurization. The milling and drilling of nickel-base material Inconel-718 are likely to create tool wear and tear, so the drilling process of milling is replaced by deep hole electrical discharge machining (EDM) extensively. However, the EDM creates reaming or overcut phenomenon, so reducing overcut by parameter optimization is an important study. This study used will use response surface methodology to establish the influencing factors of machining parameters in the hole enlargement and machining speed. The experimental results show that the main influencing factor in the nickel-base alloy deep hole EDM is the discharge voltage (V), the secondary factor is the discharge current (I). The hole enlargement of processed hole without optimization is 60um~100um. The DOE is used for hole enlargement measurement and machining speed measurement to design important parameters, and to predict experiment data analysis. The half normal probability graph, Pareto chart and Analysis of variance (ANOVA) are used to learn about the significant factors of parameters and the influence of interaction. The outlet value of optimized parameters is relatively uniform, and the hole morphology is relatively free of residue stacking. Finally, the inlet and outlet results are improved by 17.9% compared with the original parameters. The optimization parameter value predicted by the fitted model is 0.0392mm, and the optimized upper and lower holes validation experiment machining error is 0.0380mm, and the values are quite close, proving that this prediction model is accurate. The model prediction of this DOE can enhance the applied technology of deep hole EDM for nickel-base alloy.


Introduction
The nickel-base high temperature alloy has been used extensively. The nickel-base alloy has good mechanical properties, corrosion resistance, fatigue strength and thermostability at high temperatures, so it can work effectively for long at high temperatures, and it is extensively used in such aerospace parts as turbine blades, combustion chambers, turbine discs, nozzle guides, high-pressure turbine sections, cases and fasteners, as shown in figure 1. However, for long-term existence in the hyperbaric environment of flight, the parts are likely to wear, and the replacement rate is high. The nickel-base superalloy is a material hard to process, the required cutting force is 2~3 times of steels. The milling results in very high temperature and stress of tool tip, and the tool flank wear is very severe. To machine the high pressure section of turbine engine, as it is mostly made of high temperature resistant and hardly cut material, and its exterior is mostly geometrical, wherein there are 200~300 cooling holes, as shown in figure 2. If general milling machine is used for drilling process, the cutting tool will wear considerably, so the deep hole discharge is extensively used for machining at present [1] [2][3] [4].  Figure 2 High-pressure turbine section blade EDM [4] Wright et al. [5] used nickel-base high temperature alloy and general ferrous alloy to study the tool wear property. During the cutting of nickel-base high temperature alloy, at the same speed, the cutting force was twice as high as that of general carbon steel, so the tool tip bore high temperature and high stress. The crater wear was closer to the cutting edge compared with ferrous alloy, the high temperature of tool face resulted in severe tool flank wear, and the tool life was shortened greatly.
Shaw et al. [6] indicated that the cutting of high temperature alloy, e.g. Waspaloy with strong strain hardenability, had groove wear, which often occurred in tool flank cutting depth, forming groove deep wear which extended to the tool face, leading to tool tip breakage during tool cutting. Because the high plastic deformation of cutting edge creates high strain hardening, leading to local high temperature. The higher the material strain hardening is, the more severe is this trend.
Konig et al. [7] used laser heating for hard-to-cut material in the experimental process, and proved this processing mode could reduce tool wear and tear, reduce the processing cost and increase the productivity of processing.
Soni and Chakraverti [8] used 3mm copper-tungsten electrode to study the discharge drilling characteristic of machining depth 10mm of Ti alloy. The paper discussed the influence of two factors, including discharge current and electrode speed, on such processing characteristics as material removal rate and electrode consumption rate. The data were used for statistical analysis by experimental plan and the mathematical model was built, and the machining differences among different electrode motion modes were worked out.
Yan et al. [9] conditioned copper electrodes in different diameters to study microhole EDM of carbide. The paper indicated that the microhole precision and electrode consumption rate after machining were influenced mainly by the polarity, electrode geometry and speed, and when the electrode rotation speed was moderately increased and the electrode geometry had appropriate unilateral notch, the dielectric fluid disturbance was assisted effectively and the removal of machining chips was promoted, the opportunity of secondary discharge of hole wall was reduced, so as to maintain the hole precision after machining.
Huang [10] studied the influence of machining parameters on such processing characteristics as electrode corner consumption and electrode length consumption when the working area was smaller than 50m ㎡ and the machining depth was fixed at 3mm. Based on statistical analysis of ignition delay time, when the number of discharge waves of ignition delay time equal to zero increases, the electrode corner consumption will increase and the material removal rate will decrease, and the working area and the peak current are the major factors influencing the number of this kind of discharge waves.
Peng [11] used 2mm red brass and yellow brass electrode materials to study the discharge drilling of machining depth 12.5mm for SKD11, K10 and conducting ceramic. The paper discussed the processing characteristics of the three materials in material removal rate, electrode consumption rate and surface roughness under different discharge energy supply forms, electrode materials and slipstream pressures, so as to provide the reference for selection and setting of parameters for the processing of various materials.
Yeh [12] used 3mm brass pipe electrode to study discharge perforation of SKD11, discussed the effect of discharge current, capacitance and spindle feedrate parameters on machining, and used aqueous graphite powder solution as dielectric fluid. The paper indicated that when the graphite concentration in the dielectric fluid increased, the carbon layer adhered to the part between two poles in the machining process and the discharge was dispersed, the material removal rate, electrode consumption rate and inlet-outlet diameter difference decreased, and the surface roughness got better.
Cheng [13] proposed a second-order fuzzy logic control method. In Stage 1, the discharge conditions of regular sampling points were established and classified, and the quantity of discharge conditions in the computation period was unified to obtain the discharge condition of each computation period. The second-order fuzzy theory used the periodic discharge condition of previous order as input to deduce the servo feed strategy. The double closed-loop control system for deep hole discharge was designed based on this method. The deep microhole in diameter of 0.1~0.5mm with depth-diameter ratio larger than 10 could be obtained stably by designing the discharge system, and the optimization experiment was proved to be a very effective method for increasing the efficiency of EDM.
Su [14] indicated in the deep hole EDM process, the material removal rate, electrode consumption rate and the ability to complete through hole were influenced as the machining depth changed. The experimental result showed that the material removal rate did not decrease as the machining depth increased, it showed a steady state. The electrode consumption rate was not influenced by machining depth, it remained in a steady state. The ability to complete through hole declined as the machining depth increased. Therefore, the paper proposed an immersion processing method, which could solve the machining problem that the through hole could not be completed smoothly, and could improve the outlet end surface condition after machining. Finally, the information of small diameter deep hole straightness was obtained by using short circuit detection mode. The measurement result showed that the axis wobble increased with the machining depth, and the smaller the electrode diameter was, the larger was the wobble.

2-1 EDM principle
According to the discharge waveform measurability of power system, general deep hole EDM is divided into voltage and current waveforms, as shown in Figure 2-4, the design is divided into iso-energy EDM and iso-frequency EDM.
1. Iso-frequency discharge: each discharge cycle has equal cycle, meaning the arc strike time (Td) discharge period (ON TIME) and discharge off time (Pulse Off-Time) are fixed, i.e. iso-frequency discharge. However, the defect in this power supply is that the discharge period is unfixed, so the discharge energy is different every time, the craters have different sizes and depths after discharge, the machining speed is unstable, and the surface roughness is poor. For the discharge pulse with equal period, the circuit design of waveform generator is relatively simple. Figure 3 shows the schematic diagram of iso-frequency discharge voltage and current waveforms [21][22].
2. Iso-energy discharge: the discharge period of Iso-pulse or Iso energy is a fixed cycle, the discharge cycle is a fixed time, so the discharge energy is fixed. As the discharge period length of iso-energy discharge is fixed, the discharge energy of each pulse is fixed, the craters after discharge have similar sizes, so the machined surface has better roughness. The iso-energy EDM is mostly used in current EDM industry.  The workpiece surface condition after machining is preliminarily observed through optical microscope and the difference between inlet aperture and outlet aperture is measured in this experiment. The brass tube is used as electrode in this experiment, the difference between the weights before and after machining (mg) is measured and divided by machining time (min) to obtain the electrode consumption (mg/min), the electrode consumption rate is divided by material removal rate and multiplied by 100 to obtain relative electrode consumption rate [17].
Empirical equation of hole enlargement: Electrode wear the common wear conditions which create errors in general EDM process are divided into front wear and flank wear, as shown in figure 5.

(1) Front wear
In the deep hole discharge process, as the workpiece and electrode have material removal, the electrode length is shortened as the front end of electrode is worn, leading to insufficient machining depth, as well as errors in the depth of the machined workpiece.

(2) Flank wear
Due to electrode flank wear, the tip is worn into a taper, as shown in Figure 2-13, this condition will create errors in workpiece dimensions, it must be handled when the wear reaches a certain level, or the electrode must be changed.

2-3 Response surface methodology
The response surface methodology (RSM) is a method assisted by statistical method to compute the relation between multiple independent variables in unknown function and a response variable, it is combined with DOE and regression analysis [18]. The required response value and the corresponding input parameter position are obtained in the preset input parameter space by DOE. Generally, the RSM is represented graphically, aiming to provide a set of effective analysis and solution for product design optimization, process optimization and system optimization problems in the process.
The application has the following two constraints: (1) applicable to continuous system, assuming that the measurement graduation of all response values and independent variables is continuous; (2) the independent variables influencing the system are measurement (controllable and uncontrollable variables). Under the assumption of RSM and the constraints of application system, the optimal experimental values or activity variable values can be obtained effectively [19].
In experimental analysis of RSM, if the input parameters influencing the response value y are x 1 , x 2,. . , x p , and x is the independent variable, the unknown function (dependent variable) is 12 ( , ,.., )  The RSM is a sequential procedure. When the response surface is far from the optimal condition point, as shown in

Experimental plan and process
According to the deep hole machining influencing factor graph, there are seven main classes of factors which influence the deep hole machining accuracy: (1) control system (2) discharge system (3) electrode system (4) setup environment (5) mechanism system (6) working fluid (7) workpiece. The controllable parameter in the machining process is discharge system. The factor parameters influencing the precision machining in the discharge system includes (1) ON TIME, (2) OFF TIME, (3)

4-1 Deep hole discharge parameters screening experiment
This study uses eight factors and two levels to plan the discharge drilling process conditions, the electrode is brass

4-2 Analysis of influential parameters according to inlet-outlet difference and electrode wear
According to the aforesaid inlet and outlet screening experiment, the OFF-Time, current I, voltage V and capacitance CF are significant factors. When the machining time is short, the material removal rate is relatively high, and the required energy is higher, so the electrode consumption is increased, the parameters of significant factors will be discussed. When the off time is changed, the experimental result is shown in Figure 13, there is slight difference in hole enlargement and inlet and outlet error value (difference value is about within 0.01mm), so the off time has less effect on hole enlargement and outlet. When the off time is before 70us, the electrode consumption will increase with off time. When the off time is 84us, as the off time is too long, the energy decreases, so that the electrode consumption decreases. When the current of machining parameters is changed, the experimental result is shown in Figure 14, the discharge is effective until the energy is I=12A, under different current conditions, the hole enlargement and inlet and outlet error value are changed obviously. In low current region, the generated energy is lower and unstable, so the electrode size consumption is large. When the current exceeds I=14.5A, the electrode size consumption is smaller, but the workpiece error is markedly increased, the first cause is the increase in discharge energy.

Pareto Chart of the Standardized Effects
(response is OverCut, Alpha = .05) enlargement and inlet and outlet error is similar to voltage state, because higher capacitance will generate higher instantaneous voltage. The electrode wear shows that the capacitance has greater effect, it is observed when the capacitance CF=2, the electrode consumption is lower (difference is about 0.2g).  Table 4.

4-4 Actual machining validation
The original parameters and optimized parameters are used to process 10 holes continuously in the validation experiment, the original parameters are the company recommended parameters, the average errors of 10 holes are shown in figure   18. The hole morphology, hole edge morphology and carbon residue level are observed after discharge in the experiment on the original parameters, the outlet observation shows the discharge ring is larger, the crater phenomenon (residue stacking) is relatively apparent, the numerical error of outlet is larger and unstable.

Conclusion
This study built a prediction model for electrode wear and upper-lower hole error, the principle is DOE. The optimization and parameter validation of significance of hole enlargement, electrode wear and upper-lower hole error are concluded below.
(1) In different conditions of off time, the difference in hole enlargement and inlet and outlet error value is slight (difference value is about within 0.01mm), so the off time has less influence on hole enlargement and outlet factors. Before 70us of off time, the electrode consumption increases with off time. When the off time is 84us, the off time is too long, the energy decreases, so that the electrode consumption decreases.
(2) In different current conditions, the difference in hole enlargement and inlet and outlet error value is relatively significant. In smaller current state, the generated energy is lower, and the electrode size is relatively small, so about before 14.5A, the error amount changes slightly. When this value is exceeded, the error increases as the energy increases.
In smaller current state, as the energy is lower, the discharge is unstable, the electrode wear is too large, the discharge is effective until the energy is 12A.
(3) Under different voltage conditions, the hole enlargement and inlet and outlet error change significantly, the optimum parameter values shall be found out using the advantages of DOE. The hole enlargement will vary with the inlet and outlet error. Before 55V discharge voltage, the electrode consumption is relatively stable (difference is about 0.01g), the consumption will have positive effect in this region. When the voltage is 60V, the energy increases, the consumption, hole enlargement and inlet and outlet error increase accordingly.
(4) Under different capacitance conditions, the trend of hole enlargement and inlet and outlet error is close to different voltage conditions, because the higher capacitance will generate higher instantaneous voltage. According to the electrode wear, the capacitance has great effect, when the capacitance is 2, the electrode consumption is lower (difference is about 0.2g). According to robust experiment, the inlet-outlet difference of optimized parameters is improved by 17.9% compared with the original parameters, so this experimental model is correct.