Hole Quality cutting by ecm

8/18/2019 Hole Quality cutting by ecm

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Int J Adv Manuf TechnolDOI 10.1007/s00170-006-0572-9

O RIG IN A L A RTICLE

Dayanand S. Bilgi . V. K. Jain . R. Shekhar .

Anjali V. Kulkarni

Hole quality and interelectrode gap dynamics during pulse currentelectrochemical deep hole drilling

Received: 29 December 2005 / Accepted: 8 March 2006# Springer-Verlag London Limited 2006

Abstract This paper presents the experimental investiga-tion of pulse-current shaped-tube electrochemical deephole drilling (PC-STED) of nickel-based superalloy. Influ-

ence of five process variables (voltage, tool feed rate, pulseon-time, duty cycle, and bare tip length of tool) on theresponses, namely, depth-averaged radial overcut (DAROC), mass metal removal rate (MRR g) and linear metal removal rate (MRR l) have been discussed. Mathe-matical models have been developed to express the effectsof the process parameters on DAROC, MRR g and MRR l.The proposed model permits quantitative evaluation of thehole quality and process performance simultaneously. Theresults have been confirmed for the profile of the drilledhole and MRR l obtained experimentally. In all theexperiments, through holes of 26 mm depth and diametersranging from 2.205 mm to 3.279 mm were drilled. The

results have been explained by the interelectrode gapdynamics prevailing during pulse electrochemical deephole drilling. Optimum parameters determined from theseexperiments can be used to efficiently drill high-qualitydeep holes of high aspect ratio in nickel-based superalloys.

Nomenclature

bi, bii and bij Regression coefficients E Gram equivalent weight, g f i Fraction of total current flowing in side

gap F Faraday’s constant (As) f Tool feed rate (mm/min)

f ke Correction factor for electrolyteconductivity

g Radial overcut (mm)

I Total current (A) I f Frontal gap current (A) I s Side gap current I set Set current (A) I (pk) Total peak pulse current (A) I s (pk) Peak pulse current in side gap (A)κe Specific conductivity of fresh

electrolyte (mho/mm)

κ0

e Equivalent conductivity of

electrolyte (mho/mm) L Bare tip length of tool (mm) Ltd Total drilled depth (mm)n Number of locations

Q s (pk) Peak charge flow in side gapr Radius of hole at any given time (mm)r 1 Outer radius of bare tool (mm)r 2 Radius of drilled hole in workpiece (mm)T t Total time required for drilling a hole

of depth equal to Ltd (s)t m Machining time required to drill a hole

of depth equal to L (s)t off Pulse off-time (μ s)t on Pulse on-time (μ s)t pp Pulse period (μ s)V Voltage (V)x Observed value of hole size at nth location

x1 , x2 , x3, x4, x5 Five process variables y Response under studyρa Density of anode or workpiece (g/mm

3)α

ν Void fraction

Acronyms

ANOVA Analysis of varianceBTL Bare tip lengthCFR Cutting rate to feed ratioDAROC Depth-averaged radial overcut DC Direct current

D. S. Bilgi . V. K. Jain (*) . A. V. KulkarniDepartment of Mechanical Engineering,Indian Institute of Technology,Kanpur, 208 016, Indiae-mail: [email protected].: +91-512-2597916Fax: +91-512-2597408

R. Shekhar Department of Materials and Metallurgical Engineering,Indian Institute of Technology,Kanpur, 208 016, India


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DC-STED Direct-current shaped-tube electrochem-ical drilling

ECD Electrochemical drillingECM Electrochemical machiningEDM Electro-discharge machiningHQF Hole Quality Factor IEG Inter-electrode gapMOSFET Metal oxide semiconductor field effect

transistorsMRR Material removal rateMRR g Mass material removal rateMRR l Linear material removal ratePC-STED Pulse-current shaped-tube electrochem-

ical drillingPECM Pulse electrochemical machiningQPF Quality Performance Factor STDEV Standard deviationSTEM Shaped-tube electrochemical machining

1 Introduction

The cooling holes required in turbine blades are 1 – 4 mmdiameter with high aspect ratio in the range of 40 – 150.Many researchers [1 – 8] have employed shaped-tube elec-trochemical machining (STEM), using direct current (DC),for drilling small diameter deep holes in difficult-to-

machine superalloys. However, STEM with DC, as it iscurrently practiced, suffers from one major shortcoming,i.e., the use of acid electrolytes that cause workpiececorrosion and are difficult to handle [3]. Conventionalelectrochemical machining (ECM) is affected by some

practical problems impeding its further development.Various attempts have been made to improve the dimen-sional control, such as ECM with (1) passivating electro-

lytes [1], (2) segmented tools [5], (3) mixed electrolytes [4,8, 9] and (4) different control systems. Various methods of tool design and anode shape prediction have also beenapplied [10], but progress has been slow [11]. Pulseelectrochemical machining (PECM) is a new technique,which was first attempted in the 1970s [12] for improvingthe accuracy and quality of electrochemically machinedsurfaces. In PECM, the smaller inter-electrode gap (IEG),the absence of dissolution between voltage pulses, the lowelectrolyte flow rate and the effective flushing of the anodicdissolution products (sludge, evolved gas bubbles andheat) lead to better precision than with ECM with DC.PECM has been exploited for various metal cutting

operations, such as EC sawing and wire-ECM [13 – 15]. Areview of literature shows that a number of investigationsregarding PECM modeling [11], flow characteristics ingaps [12], process characteristics [16 – 19], computer sim-ulation [20], accuracy problems [21, 22], and modeling and

Fig. 1 a Experimental set-upused for deep hole drilling byPC-STED. b Tool feed arrange-ment for deep hole drilling byPC-STED


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3 Design of experiments

Experiments were planned using central composite rotat-able design with half replicate for five variables tominimize the number of experiments [26]. A quadratic

polynomial equation was fitted to the experimental data,and the response surface is given as:

y ¼ b0 þXk i¼1

bi xi þXk i¼1

bii x2ii þ

Xi


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Table 1b. The quadratic response surface equations for evaluating DAROC, MRR g, and MRR l are obtainedseparately by calculating the coefficients of Eq. (2), andthey are given in Tables 2, 3, and 4, respectively.

3.1 Reproducibility, analysis and validationof the model

To check the reproducibility of the PC-STED process, sixexperiments were conducted. The results (Table 5) show

that the DAROC is reproduced within 6.8% (barring

experiments 4 and 6), MRR g within 9.5%, and MRR lwithin 8.2% (barring experiment 6).

Analysis of the results (Tables 2, 3 and 4) shows that theDAROC, MRR g and MRR l models obtained F0 valuesgreater than F0.05, 20, 11=2.65 (critical value) and were withinthe significance level (α =0.05). Furthermore, the singleregressor with P value less than 0.05 contributed significantlyin the model. Regression analysis for the DAROC model(Table 2) indicates that the parameters such as, V, L, t on, γ , andall interaction terms of variables except (t on*γ ), (V * L),(γ * L), contributed significantly. Deleting the insignif-

Table 2 Regression analysis and ANOVA for DAROC

Predictor Coefficient P Predictor Coefficient P

Constant 0.40112 0.000 – – –

x1 0.09447 0.000 x1*x2 −0.04642 0.001

x2 −0.01330 0.136 x1*x3 −0.02225 0.050

x3 −0.02687 0.008 x1*x4 −0.03485 0.006

x4 0.01929 0.040 x1*x5 0.01696 0.122

x5 0.04823 0.000 x2*x3 0.03252 0.008

x1*x1 0.05842 0.000 x2*x4 0.02490 0.032

x2*x2 0.01725 0.042 x2*x5 0.03698 0.004

x3*x3 0.01815 0.034 x3*x4 −0.02049 0.068

x4*x4 0.03626 0.001 x3*x5 0.02937 0.014

x5*x5 −0.00608 0.434 x4*x5 0.00626 0.549

S R -Sq R-Sq (adj)

0.04052 97.0% 91.5%

Source DF SS MS Fo P

Regression 20 0.57856 0.0289 17.62 0.000

Residual Error 11 0.01806 0.0016 – –

Total 31 0.59662 – – –

Table 3 Regression analysis and ANOVA for MRR g


Constant 0.02143 0.000 – – –

x1 0.00348 0.000 x1*x2 0.00006 0.867

x2 0.00038 0.186 x1*x3 0.00039 0.257

x3 0.00014 0.622 x1*x4 0.00033 0.332

x4 0.00260 0.000 x1*x5 −0.00039 0.258

x5 0.00083 0.010 x2*x3 −0.00041 0.239

x1*x1 −0.00153 0.000 x2*x4 0.00039 0.251

x2*x2 −0.00002 0.941 x2*x5 −0.00045 0.199x3*x3 −0.00039 0.140 x3*x4 −0.00023 0.492

x4*x4 −0.00038 0.147 x3*x5 0.00041 0.243

x5*x5 −0.00114 0.001 x4*x5 0.00065 0.074

S R-Sq R-Sq (adj)

0.003515 89.0% 69.0%

ANOVA


Regression 20 0.000601728 0.000030086 17.35 0.000

Residual error 11 0.000019070 0.000001734 –

Total 31 0.000620798 –


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icant terms from the model, DAROC can be approxi-mately evaluated from the equation given below.

DAROC mmð Þ¼ 0:4011 þ 0:0945V 0:0270t onþ 0:0193 γ þ 0:0482 L þ 0:0584V V þ 0:0173 f f þ 0:0182t ont on þ 0:0363γ γ 0:0460V f 0:0220 V t on 0:0350V γ þ 0:0325 f t on þ 0:0249 f γ þ 0:0370 f Lþ 0:0294t on L (3)

In the same way, deleting the insignificant terms fromthe model (Table 3), MRR g can be evaluated from theequation given below.

MRR g g =minð Þ¼ 0:0214 þ 0:0035V þ 0:0026γ þ0:0008 L 0:0015V V 0:0011 L L (4)

Drilling speed or MRR l is one of most the important criteria of process capability. Deleting the insignificant terms from the model (Table 4), MRR l can be evaluated asfollows:

MRRl mm=minð Þ¼ 0:5550 þ 0:0271V þ 0:0171 t onþ 0:0429γ 0:0741V V 0:0228 t ont on 0:0391γ γ 0:0216 L Lþ 0:0231V f 0:0256V L 0:0281 f t on 0:0294 f L (5)

To check the validity of the models, two additionalexperiments were conducted (Table 6a). The errors of

Table 4 Regression analysis and ANOVA for MRR l


Constant 0.5553 0.000 – – –

x1 0.0271 0.005 x1*x2 0.0231 0.032

x2 0.0138 0.102 x1*x3 0.0181 0.081

x3 0.0171 0.049 x1*x4 0.0181 0.081

x4 0.0429 0.000 x1*x5 −0.0256 0.020

x5 −0.0129 0.122 x2*x3 −0.0281 0.013

x1*x1 −0.0741 0.000 x2*x4 −0.0081 0.408

x2*x2 −0.0128 0.093 x2*x5 −0.0294 0.010

x3*x3 −0.0228 0.007 x3*x4 0.0094 0.342

x4*x4 −0.0391 0.000 x3*x5 −0.0044 0.652

x5*x5 −0.0216 0.010 x4*x5 0.0106 0.284

S R-Sq R-Sq (adj)

0.03777 95.6% 87.6%

ANOVA


Regression 20 0.341308 0.017065 11.96 0.000

Residual error 11 0.015692 0.001427 – –

Total 31 0.357000 – – –

Table 5 Reproducibility of experiments and error

(a) Machining conditions for six reproducibility experiments

Exp. no. V (volts) f (mm/min) t on (μ s) γ L (mm)

1 to 6 12 0.6 500 0.64 1.1

(b) Experimental error DAROC (mm) MRR g (g/min) MRR l (mm/min)

Exptl. Average Percentage error* Exptl. Average Percentage error* Exptl. Average Percentage error*

0.409 0.424 3.54 0.022 0.021 −4.76 0.564 0.534 −5.62

0.409 3.54 0.020 4.76 0.513 3.93

0.395 6.84 0.021 0.00 0.551 −3.18

0.366 13.68 0.021 0.00 0.578 −8.24

0.421 0.71 0.023 −9.52 0.578 −8.24

0.544 −28.30 0.020 4.76 0.417 21.91

*% age error ¼ Average Exptl:Valueð Þ

AverageValue

100


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prediction of DAROC, MRR g, and MRR l are given inTable 6 b. The results show that there is a small difference inthe experimental and predicted values. Keeping in mind theabove discussion, the results predicted by Eq. (2) (using thecoefficients given in Tables 2, 3 and 4) can be treated as

representative of the experimental results.

4 Analysis of radial overcut

The schematic diagram of ECD is shown in Fig. 3 with twoconcentric electrodes (tool and workpiece). Let r 1 and r 2correspond to the outer radius of bare tool and radius of thehole drilled in the workpiece, respectively. L is bare tip

length of tool and κ0

e corresponds to equivalent conduc-tivity of electrolyte in the side gap, which is given by

κ

0

e ¼

1

2 π L

I s ð pk Þ

V ln r 2

r 1 (6)

where I s (pk) is peak pulse current in the side gap. Is and κ0

e

are both unknown and interdependent. The electrolyteconductivity varies at each point along the flow direction inthe gap and it is difficult to evaluate due to lack of therelated data. To account for the effect of conductivity

variation on the overcut, based on the experimental data, acorrection factor ( f ke) is estimated similar to that explainedin reference [30], and is used to predict radial overcut indeep hole drilling.

Radius (r ) of the hole being drilled, at any time ( t ), can be evaluated from the following equation:

Z r 2r 1

r dr ¼ E f i

2 π F ρa L

Z tm0

I pk ð Þ dt (7)

where I (pk) is total peak pulse current in the gap, E is gramequivalent weight, f i is fraction of the total current going to

Fig. 3 Schematic diagram of electrochemical deep holedrilling

Table 6 Validation experiments of DAROC, MRR g and MRR l

(a) Machining conditions

Exp. no V (Volt) f (mm/min) t on (μ s) γ L (mm)

1 12 0.5 500 0.64 0.7

2 12 0.5 500 0.80 0.7

(b) Percentage error

DAROC (mm) MRR g (g/min) MRR l (mm/min)

Exptl. Predicted Percentage error # Exptl. Predicted Percentage error # Exptl. Predicted Percentage error #

0.489 0.385 21.32 0.018 0.014 21.58 0.400 0.409 −2.22

0.469 0.494 5.08 0.014 0.014 −3.04 0.322 0.318 1.34

#% age error ¼ Exptl:Value Predictedð Þ

Exptl:Value

100


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the side gap, F is Faraday’s constant, ρa is density of anode(workpiece), and t m is drilling time required to drill the holedepth equal to the bare tip length, and can be written as:

t m ¼ L T t

Ltd γ

(8)

where Ltd is total drilling depth (which is equal to 26 mm inthe present study), γ is duty cycle, and T t is total timerequired to drill the hole up to the depth equal to Ltd . Thetotal current being consumed during PC-STED sometimesexceeds the Iset limit. As a result, the tool traverses back.Thus, the time t m estimated by Eq. (8) does not account for this phenomenon; hence, the estimated time becomesapproximate. Theoretically, r 2 ¼ r 1 þ g is the largest radius that should be obtained along the tool axis. In all theexperiments it is observed that, owing to the maximumcurrent limit setting ( I set ), I becomes almost stable once the

tool penetrates the workpiece more than 2 × BTL. Hence, I (pk) is assumed as constant. Also, I s (pk) for simplicity, isassumed as constant and evaluated in terms of radialovercut, g [3, 9, 25] as follows:

I s pk ð Þ ¼ π ρa F

E

g 2r 1 þ g ð Þ Ltd

γ T t

(9)

After substituting I s(pk) in Eq. (6), κ0

e is evaluated, and f κeis obtained from Eq. (10):

f κe ¼κ

0

e

κe

(10)

where κe is specific conductivity of fresh electrolyte.Substituting the value of f κe in Eq. (11), radial overcut (g)during PC-STED can be predicted [3, 9, 25]:

2 E f e e V

F a

t m ¼ g

2 1 þ 13

g r 1

1

12 g r 1

2þ 1

30 g r 1

3 1

60 g r 1

4þ :::

( ) (11)

In Eq. (11), second-order and higher-order terms of ( g / r 1)can be neglected owing to their small magnitude [9, 30].The other terms, except for f ke (which is dependent on t m)and g , are either constant or can be controlled. Comparisonof theoretical (Eq. 11) and experimental DAROC results isshown in Fig. 4. They follow a similar trend, but the

predicted values of DAROC are over-estimated. Theaccuracy of the prediction can be improved by developing

more accurate models for (1) equivalent conductivity inthe side gap k

0

e

and (2) machining time (t m) in the side

gap.

5 Dynamics of IEG

This section will help in understanding the dynamics of thefrontal IEG (or continuous variation of the frontal IEG)during deep hole drilling using the PC-STED process. It isquite different from the DC-STED for two reasons: pulse

power supply and current-sensitive tool feed controller.Any variation in V, f, t on and γ will change the IEG, which

will affect the process performance, as can be seen from thefollowing discussion.

Fig. 4 Comparison of model and experimental results of DAROCduring PC-STED

ton t offtpp

V

t

y

Tool surface

Workpiece surface

Initial

IEG

f < MRRl

Time, t

Fig. 5 Schematic diagram of IEG variation with time during PC-STED with constant tool feed rate


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During PC-STED, electrochemical dissolution takes place during t on, while no dissolution takes place duringt off and the electrolyte carries away the reaction productsand heat from the IEG. Figure 5 shows a change in IEGwith time during PC-STED at constant tool feed rate.During on-time, electrolytic dissolution of anode takes

place, therefore IEG increases. However, during off-timeIEG decreases owing to constant tool travel towards the

anode (workpiece) with no anodic dissolution (MRR l=0).In PC-STED, at no time will the system attain equilibriumcondition because its attempt to attain equilibrium duringt on will be immediately disturbed once t off starts.

As voltage (V) increases, increase in linear materialremoval rate (MRR l) takes place. Consequently, increase inIEG occurs. However, at higher voltage, due to greater gasgeneration in the gap, void fraction (αv ) effect dominates.As a result, κ

0

e decreases leading to decrease in MRR l,,hence IEG decreases. However, during off-time thesereaction products are flushed away from the small IEG andfresh electrolyte enters, causing increase in κ

0

e . This wouldlead to increase in total current ( I ) and hence higher MRR l.

Thus off-time serves two functions simultaneously: due to“no-machining period ”, no reaction products are formed,and those present in the IEG are flushed away from the gap.Secondly, entry of fresh electrolyte through the hollow toolwould increase linear as well as volumetric materialremoval rate. However, due to no dissolution during off-time, average MRR l would go down. The extent of achange in MRR l will depend upon the value of the dutycycle (γ ). If the value of the duty cycle is very high then the

process performance will be close to the performance of DC-STED.

Increase in tool feed rate (f) leads to decrease in IEG;hence, more current is drawn. A decrease in IEG is

expected when f > MRR l, and an increase is expected when f < MRR l (Fig. 5). The dynamics of IEG during PC-STEDis more complex than that in DC-STED because of on-time(t on) and off-time(t off ). The relationship between pulse on-time and duty cycle (γ ) is given as:

γ ¼ t on

t on þ t off (12)

The effect of pulse on-time and duty cycle on the IEGdynamics is discussed as follows:

(a) Pulse on-time: At a given γ (Fig. 6a), as t on increases,t off also increases (Eq. 12). During off-time, the toolmoves towards the workpiece without machining, soIEG decreases. When γ t on), thedecrease in IEG is higher than when γ >0.50 (i.e., t off <

t on). Due to a decrease in IEG, the current wouldincrease. Consequently, the machining rate wouldincrease.

(b) Duty cycle ( γ ): At a given t on (Fig. 6 b), increase in dutycycle implies decrease in t off (Eq. 12), resulting in adecrease in pulse period, t pp (= t on+t off );hence, themachining rate increases. At lower γ , t off is high; hence,IEG would be low. This leads to an increase in current during t on, but it decreases average machining rate

because of comparatively higher t off . At higher γ (t off <t on), IEG is comparatively greater due to small t off .Therefore, chances of I > I set (permitted upper limit of current) are low at high γ. When f > MRR l,, decrease inIEG would take place and hence higher I is expected. If

I > I set , closed loop control unit reverses the directionof the stepper motor, thus preventing a short circuit

between tool and workpiece. However, the tool feeddevice, being mechanical in nature, may not be able torespond so quickly to a change in stepper motor direction due to very small t on and t off (μs), and toolretraction would not take place instantaneously.

However, it was observed that “tool was stationary” inmany experiments, due to rapid switching between current on and off pulses. Therefore, total machining time during“tool stationary” condition increases on the side wall of the

workpiece opposite to the bare part of the tool (or BTL). Asa result, peak charge flow (Eq. 13) in the side gap (Q s (pk))due to “tool stationary” condition increases. Increase inQ s (pk) leads to increase in overcut in the region opposite theBTL compared with the region opposite the coated part of the tool, where no dissolution takes place. This variation incharge flow results in non-uniformity of the drilled holediameter, as discussed elsewhere.

Q pk ð Þ ¼ I s pk ð Þ t m (13)

Fig. 6 Relationship between pulse off-time and a pulse on-time and b duty cycle (Eq. 12)


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For any hole to be of good quality, it should haveminimum possible DAROC and minimum possible

STDEV. Minimum DAROC will make the hole a replicaof the tool shape, and minimum STDEV will minimizevariation in the hole diameter along the hole depth. Hence,a hole quality factor (HQF) can be calculated as follows:

HQF ¼ 1

DAROC STDEV (15)

Whichever hole has the highest value of HQF should bethe best-quality hole. Hole 13 yields the highest value,22.8 mm−2. However, experiments 3, 25, 30 and 31 alsohave HQF values close to 22.8.

Nevertheless, if one can obtain a good performance of the process as well as good quality of the hole, it is moredesirable. If the performance of the process (or drilling rateor MRR l) is good but the quality of the hole is not good, or vice versa, then it will not be acceptable. Hence, there is aneed to develop a model to evaluate both these factorssimultaneously. We also know that in direct-current ECM,the best quality of the hole and the best performance of the

process are obtained when the machining is being doneunder the equilibrium condition. However, one can not

obtain equilibrium condition under PC-STED due to the

continuously changing IEG, which is a process character-istic. It is known for experimental observations that under

equilibrium condition in ECM, feed rate ¼ MRRl : In PC-STED, average linear material removal rate MRRl

is

known and the tool feed rate can be externally controlled. If the ratio of these two is equal or very close to 1 then we cansay that the “apparent equilibrium condition” exists. Let this ratio be called cutting rate to feed ratio (CFR).

CFR ¼ MRRl

f

PC STED

(16)

Analysis of Table 1b reveals that the HQF has highvalues in those experiments where CFR has the value veryclose to 1 (nos. 13, 14, 19, 25, 27, 30 and 31). Thisindicates that to some extent both these factors havecorrelation with each other. It can also be seen that wherever CFR>1, HQF value comparatively low.

The value of CFR ≥ 1 is desirable only when the value of HQF is also quite high. Thus, to have high quality of thehole and at the same time high performance of the process,

25.0

22.5

20.0

17.5

15.0

12.5

10.0

7.5

5.0

2.5

0.0-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

Radial distance (mm)

H o l e d e p t h

( m m )

A

B

C

D

E

F

G

H

Sr. No.30

Fig. 9 Hole profile produced by PC-STED (experiment no. 30) at applied voltage=12 V, f =0.6 mm/min, t on = 500 μ s, γ=0.64,L=1.1 mm

Fig. 10 Hole profile produced by PC-STED (experiment no. 31) at applied voltage=12 V, f =0.6 mm/min, t on = 500 μ s, γ=0.64, andBTL= 1.1 mm


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the value of the quality performance factor (QPF) should beas high as possible.

QPF ¼ CFR HQF (17)

Analysis of Table 1b indicates that hole 13 gives thehighest value of QPF followed by holes 30, 31, and 25.

Hence, the cutting conditions of this experiment 13 can betaken as the appropriate cutting conditions for getting highquality of the hole as well as high performance of the

process.Thus, it can be concluded that the quality of a hole can be

evaluated from HQF, performance of the process can beevaluated from CFR, and both quality of the hole and

process performance at the same time can be evaluatedfrom QPF. It is always desirable to have higher values of these factors. Further, the taper observed at the punctured

bottom can be completely eliminated by the use of adummy workpiece.

6.2 Depth averaged radial overcut

6.2.1 Voltage

Equation (3) and Fig. 11a show that the voltage has asignificant effect on DAROC. At a tool feed rate of 0.4 mm/min, DAROC increased by more than 210%1

(0.356 mm to 1.105 mm) as voltage is increased from 6 Vto 18 V. In case of 0.8 mm/min tool feed rate, initiallyDAROC decreased by about 34% (0.674 mm to 0.444 mm)and attained a minimum; however, as voltage increasedfrom about 6 V to 12 V, it increased by about 53%

(0.444 mm to 0.681 mm). The variation in DAROC can beexplained with respect to Q s(pk) (Fig. 12a). DAROC andQs(pk) have similar trends of variation.

At lower tool feed rate ( f ) of 0.4 mm/min, machiningtime at a point in the side gap is greater than at the higher value of tool feed rate. As a result, increase in Q s(pk) isexpected. Increase in voltage also increases Q s(pk). There-fore, as voltage increases, Q s(pk) increases (Fig. 12a);consequently, DAROC also increases (Fig. 11a). At hightool feed rate of 0.8 mm/min, IEG decreases rapidly,leading to the ‘stationary tool’ condition. Therefore,machining time in the side gap increases until IEG andcurrent adjust. Consequently, Q s(pk) increases (Fig. 12a);

hence, a large DAROC is obtained.As voltage increases, dissolution of metal in the front gap as well as the side gap increases. This leads to increasein IEG in the front gap, and hence a lower probability of approaching the ‘stationary tool’ condition, leading tosmall adjustment time for IEG and current. Consequently,Q s(pk) decreases (Fig. 12a) and DAROC is reduced. Due tohigh tool feed rate and high voltage (beyond 12 V), voidfraction (αv ) would increase in the IEG. This would lead todecrease in conductivity (κ) and decrease in MRR l. Due to

this fast-changing dynamics of the IEG, the condition of ‘stationary tool’ would approach, resulting in higher Q s(pk)(Fig. 12a) and higher DAROC.

6.2.2 Pulse on-time

Curves in Fig. 11 b show the effect of pulse on-time on

DAROC at high and low duty cycle. The relationship between Qs(pk) and pulse on-time (Fig. 12 b) shows a similar pattern. At lower duty cycle ( I set .When I > I set , ‘stationary tool’ condition may approach,which would lead to increase in both Q s(pk) and DAROC.Thus, at lower duty cycle, as pulse on-time increasesDAROC increases. However, at higher duty cycle (0.8),void fraction (αv ) effect predominates. This causes adecrease in κ which leads to a decrease in Q s(pk) (Fig. 12 b)

and hence a decrease in DAROC.

6.2.3 Duty cycle

Equation (3) indicates that the effect of duty cycle(Fig. 11c) is significant. At maximum BTL of 1.5 mm,DAROC decreases by about 35% (from 0.555 mm to0.473 mm) as duty cycle increases from 0.48 to 0.64. Afurther increase in duty cycle (i.e., from 0.64 to 0.80)increases DAROC by about 55% (from 0.473 mm to0.682 mm). As duty cycle increases, off-time decreases,and chances of I > I set decrease. Consequently, Q s(pk)

decreases, hence DAROC decreases. Beyond 0.64 dutycycle, due to increase in machining rate, Qs(pk) increases(Fig. 12c); hence, DAROC increases.

6.2.4 Bare tip length

Figure 11d shows the effect of bare tip length (BTL) onDAROC. At high voltage (18 V ), it increased more than110% (0.635 mm to 0.964 mm) as BTL increased from0.7 mm to 1.5 mm. As BTL increases, circumferential areaincreases; hence, more current flows in the side gap. Inaddition, increase in BTL increases time of machining in

the side gap. Therefore, Q s(pk) increases (Fig. 12d); hence,DAROC increases with increase in BTL. However, themagnitude of increase in DAROC is different at different voltages.

6.3 Metal removal rate

6.3.1 Voltage

Equation (4) and the curves in Fig. 13a show that the effect of voltage on MRR g is significant. At a tool feed rate of 1 % age increase or decrease ¼ Initialvalue Finalvalueð Þ

Initialvalue

100


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0.8 mm/min it increased by more than 175% (from 0.009 g/ min to 0.024 g/min) as voltage is increased from 6 V to18 V. Initially, MRR g increased sharply up to 12 V. Beyond12 V, the rate of increase in MRR g decreases and finallytends to be independent of voltage. Faraday’s law of electrolysis states that MRR g is directly proportional toaverage current ( I ). Figure 14a shows the experimentalvariation of I with voltage, which shows a trend very similar to that in Fig. 13a. The nature of the curves at the higher voltage can be attributed to the decrease in conductivity of the electrolyte due to marked gas evolution at theelectrodes.

6.3.2 Pulse on-time

MRR g increases by about 25% (from0.012 g/min to0.014 g/min) as pulse on-time increases by ten times(from 50 μ s to 500 μ s), and it remains almost constant

beyond 500 μ s (Fig. 13 b). This shows that the pulse on-time has little effect on MRR g.

6.3.3 Duty cycle

At BTL of 1.5 mm, increase in MRR g is about 169% (from

0.009 g/min to 0.025 g/min) when duty cycle increases

Fig. 11 Effect of various pro-cess parameters on DAROCduring PC-STED

Fig. 12 Relationship betweencharge (Q s) in the side gapand various process parametersduring PC-STED


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from 0.48 to 0.80 (Fig. 13c). The main reason for increasein MRR g with increase in duty cycle is due to (1) increasein machining time due to increase in on-time, and hence (2)increase in total current.

6.3.4 Bare tip length

Figure 13d and Eq. (4) show that BTL has little effect onMRR g compared with voltage. At high voltage (18 V),MRR g increases by about 26% (from 0.018 g/min to

0.022 g/min) as BTL is increased from 0.7 to 1.1 mm, and beyond 1.1 mm BTL, it decreases by about 19.7% (from

0.022 g/min to 0.018 g/min). These variations are smaller than the 175% variation in voltage effect.

6.4 Linear metal removal rate

6.4.1 Voltage

Equation (5) expresses that the effect of voltage on MRR l issignificant (Fig. 15a). At high tool feed rate (0.8 mm/min),MRR l attained a maximum value at about 12 V, and beyond

this, it started decreasing. The increase in MRR l is about 500% (from 0.089 mm/min to 0.525 mm/min), while the

Fig. 13 Variation of MRR gwith a change in the process parameter during PC-STED

Fig. 14 Variation of total aver-age current ( I ) during PC-STED


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decrease is about 27% (from 0.535 mm/min to 0.387 mm/ min). The variation in MRR l can be attributed to averagecurrent flow in the front gap ( I f ). The trend of variation of I f (Fig. 16a) with voltage is similar to that shown in Fig. 15a.Initially, I f increases with increase in voltage from 6 V to12 V (Fig. 16a). At higher voltage, void fraction in thesmall IEG increases and conductivity decreases. Therefore,

beyond 12 V, I f decreases. Consequently, at high voltagesMRR l decreases.

6.4.2 Duty cycle

Curves in Fig. 15 b show a significant effect (Table 4) of duty cycle on MRR l. At high BTL (say, 1.5 mm), MRR lincreases by about 186% (0.163 mm/min to 0.467 mm/ min) as γ increases from 0.48 to 0.72. Beyond 0.72 dutycycle, it decreases by a small amount, about 10%. This can

be explained with the help of average current flow in thefront gap ( I f ). Figure 16 b shows that the I f variation andMRR l variation (Fig. 15 b) are similar. At lower γ, tooltravel during t off would decrease IEG. When γ increases

from 0.48 to 0.64, t off decreases (Fig. 6 b). As a result, timeof machining increases, which leads to an increase in IEG.Consequently, the chances of occurrence of ‘stationarytool’ condition reduce and the tool moves towards theanode (workpiece), causing an increase in frontal current, I f (Fig. 16 b). However, beyond 0.64 duty cycle, due to further decrease in pulse off-time (Fig. 6 b), effective flushing of reaction products does not take place; hence, the conduc-tivity of the electrolyte in the IEG decreases, leading todecrease in I f (Fig. 16 b).

7 Conclusions

The following conclusions can be drawn from the aboveResults and discussion.

1. DAROC varies significantly with applied voltage, baretip length, pulse on-time and duty cycle. Tool feed ratehas moderate effect on DAROC. Trends of DAROC

predicted by the proposed model and experimentalresults are similar in nature. However, the proposedmodel over-estimates DAROC. Further, minimumDAROC is produced whenever linear metal removalrate is equal to the tool feed rate.

2. The hole quality and process performance evaluationfactor (QPF) can be used to evaluate both the quality of a hole and performance of the process at the same time.However, HQF can be used to evaluate the quality of the hole and thus determine the machining parametersfor the best quality hole.

Fig. 15 Variation of MRR lduring PC-STED

Fig. 16 Variation of averagefrontal current ( I f ) duringPC-STED

Direction

(1)

Variable

Frequency

Clock

(2)

Motor

Control Unit

(6)Current

Sensing and

Direction

Deciding

Circuit

(3)

Motor

Drive Unit

(4)

Stepper

Motor

Controlling

Tool Feed

(5)

ECM Cell

for Deep

Hole

Drilling

Fig. A1 Block diagram of closed control of ECM deep hole drillingmachine


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14. Maeda R, Chikamori K, Yamamoto H (1984) Feed rate of wireelectrochemical machining using pulsed current. Precis Eng 6(4):193 – 199 Oct

15. Chikamori K, Yamoto H, Madea R (1984) Wire ECM with pulsed current. Proc of 5th Int Conf on Production Engineering,Tokyo, pp 407 – 412

16. Kozak J, Lubkowski K (1979) The basic investigation of characteristic in the pulse electrochemical machining. Proc of 20th IMTDR conf pp 625 – 630

17. Datta M, Landolt D (1981) Electrochemical machining under

pulse current conditions. Electrochem Acta 26(7):899 – 90718. Kozak J, Lubkowski K, Abdel Mahboud AM (1988)

Characteristics of the pulse electrochemical machining(PECM). Prod Engg Division, PED-Vol. 34, ASME Winter Annual Meeting, Chicago, pp 189 – 197

19. Rajurkar KP, Kozak J, Wei B (1993) Study of pulse electro-chemical machining characteristics. CIRP Ann 42:231 – 234

20. Kozak J, Rajurkar KP, Ross RF (1991) Computer simulation of pulse electrochemical machining (PECM). J Mater ProcessTechnol 28:149 – 157

21. Kozak J, Lubkowski K (1981) Accuracy problems of the pulseelectrochemical machining. Proc of 22nd IMTDR Conf, pp 353 – 363

22. Rajurkar KP, Zhu D, Wei B (1998) Minimization of machiningallowance in electrochemical machining. CIRP Ann 47:163 – 165

23. Rajurkar KP, Wei B, Kozak J (1995) Modelling and monitoringinterelectrode gap in pulse electrochemical machining. CIRPAnn 44:177 – 180

24. Wei B, Rajurkar KP, Talpallikar S (1997) Identification of interelectrode gap in pulse electrochemical machining.J Electrochem Soc 144(11):3613 – 3619 Nov

25. Bilgi DS (2004) Electrochemical deep hole drilling in super

alloys, PhD thesis, I.I.T., Kanpur, India26. Cochran WG, Cox GM. Experimental designs. Asia Publishing

House, Bombay, pp 334 – 35327. Montgomery DC (2001) Design and analysis of experiments,

5th edn. Wiley (Asia)28. De Silva AKM, Altena HSJ, McGeough JA (2000) Precision

ECM by process characteristic modelling. CIRP Ann 49(1):151 – 155

29. Thorpe JF, Zerkle RD (1969) Analytical determination of theequilibrium electrode gap in electrochemical machining. Int JMachTool Des Res 9:131 – 144

30. Bilgi DS, Jain VK, Shekar R, Mehrotra S (2004) Electrochem-ical deep hole drilling in super alloy for turbine application.J Mater Process Technol 149:445 – 452

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