Manufacturing of high quality miniature gears by wire electric discharge machining.
Gupta, K. ; Jain, N.K.
1. Introduction
In recent years the demand for high-accuracy fine pitch miniature
gears has increased and is expected to continue its upward trend in the
future also as the emphasis towards the miniaturization continues. The
gears having outside diameter less than 10 mm are categorized as
miniature gears. Miniature gears can be further subdivided as
micro-gears (outside diameter < 1 mm) and meso-gears (outside
diameter in the range of 1-10 mm). Miniature gears are one of the key
components of the highly accurate miniaturized devices such as miniature
motors and pumps, electronic and home appliances, business machines,
automotive parts, timing devices, measuring instruments, MEMS and NEMS,
etc. used in the scientific, industrial and domestics areas. Functional
characteristics of these miniaturized devices depend on the quality of
the miniature gears used. Therefore, highly accurate and advanced
manufacturing processes are required for fabrication of high quality
miniature gears. The present work is concerned with investigations on
manufacturing of high quality meso-gears by WEDM. Brass, bronze,
aluminium, stainless steel are the most commonly used materials for
these gears (Davis, 2005; Townsend, 2011). Gears made of brass are
primarily used as motion transmitting gears which are fine pitched and
generally run at very high speed. Therefore, accurate motion transfer,
minimum running noise and longer service life are the important
desirable characteristics for these gears.
The conventional processes for manufacturing the miniature gears
include hobbing, stamping, extrusion, die casting and powder metallurgy.
But, these processes suffer from some inherent limitations as mentioned
in the Table 1. Moreover, all these processes manufacture gears of low
quality i.e. Deutsche normen (DIN) quality number is in the range of
9-12 (Bralla, 1998; Davis, 2005; Townsend, 2011). DIN and American gear
manufacturers association (AGMA) are the international standards
defining the quality of the gears in terms of micro-geometry parameters.
Lower DIN number or higher AGMA number indicates better quality of the
gear and vice-versa. Table 2 presents the quality requirements of the
gears for various applications in terms of DIN and AGMA numbers along
with the manufacturing processes used for the miniature gears.
1.1 Micro-Geometry of Miniature Gears
The important micro-geometry parameters of gears affecting their
operating performance and service life include errors or deviations in
the profile, lead, pitch, runout and surface roughness. Fig. 1 depicts
the effects of these micro-geometry parameters on the performance
characteristics of the gears. The profile error affects the noise
behaviour, lead error governs the load carrying capacity while, pitch
error and runout affect the motion transfer characteristics (Fig. 1)
(Goch, 2003; Townsend, 2011). Profile error and lead error are the form
errors while, pitch error and runout are the position or location
errors. Form errors are the deviations from the intended nominal shape
of the gear tooth surface, whereas location errors are related to the
accuracy of location of teeth on a gear. Profile errors or deviations
include form and angle (slope) deviation of the gear tooth profile from
the nominal (intended) involute tooth profile, and are measured
perpendicular to the functional profile.
Lead errors or deviations include lead form deviation and lead
angle (slope) deviation of the gear tooth flank along the face width and
are measured at the middle of the tooth height. Pitch error is the
difference between the nominal angular locations of the gear flanks to
the actual measured locations. Runout is the maximum difference of the
nominal radial position of all the teeth to the actual measured
position. Both pitch errors and runout are measured at the middle of the
tooth height. The geometric inaccuracy of a gear is caused due to the
above said errors.
[FIGURE 1 OMITTED]
Surface roughness refers to short-wavelength and high frequency
closely spaced irregularities on the surface which are caused by the
nature and the actions of the manufacturing processes (Davim, 2010).
Surface roughness affects the fatigue life of the components and this
particularly important for the components subjected to dynamic loading
such as gears. Two most important surface roughness parameters are
average surface roughness '[R.sub.a]' and maximum surface
roughness '[R.sub.t]'. Higher surface roughness (i.e. presence
of nicks, burrs, peaks and asperities) leads to early failure by
occurrence of wear. Therefore, surface roughness should be minimized to
prevent early failure of the gears.
1.2 Introduction to WEDM
High quality finish, better dimensional accuracy, burr-free
surfaces and excellent repeatability are some of the important
characteristics of WEDM (Benedict, 1987; Ho et al., 2004; Jain, 2008;
McGeough, 1988). Therefore, WEDM has been recognized as a potential
substitute to the conventional processes for micromachining and
miniaturization applications (Gupta and Jain, 2013a-b; Hsu, 2008; Qin,
2010). In WEDM, the material is removed by the thermoelectric erosion
process involving melting and vaporization caused due to the electric
spark occurring between the wire and the workpiece material. For spark
generation, the series of electrical pulses generated by the pulse
generator is applied across the inter-electrode gap (IEG) between wire
and workpiece in the presence of a dielectric. In the event of spark
discharge, there is a flow of current across the IEG. Energy contained
in a tiny spark discharge removes a fraction of workpiece material.
Large number of such time spaced tiny discharges between the workpiece
and wire electrode cause the electroerosion of the workpiece material.
Fig. 2 illustrates the working principle of WEDM.
[FIGURE 2 OMITTED]
The main causes of micro-geometry errors in WEDMed products are
irregular shaped craters produced by violent spark at high discharge
energy parameter settings, short circuiting, adherence of wire to the
workpiece surface, and deflection of wire from its path known as wire
lag (Arunachalam et al., 2001; Ho et al., 2004; Liao et al., 2004;
Mingqi et al., 2005; Puri et al., 2003). The wire lag is caused due to
impact of the mechanical forces produced by pressure from the gas
bubbles, the axial forces applied to straighten the wire, the hydraulic
forces induced by the dielectric flushing, the electro-static forces
acting on the wire, and the electro-dynamic forces inherent to the spark
generation.
2. Literature Survey
There are very few references available on manufacturing of
miniature gears by WEDM or EDM-based processes. Takeuchi et al. (2000)
developed a micro-planetary gear system of SKS3 tool steel and WC-Ni-Cr
cermets of 0.03 mm module with the help of micro-EDM. The manufactured
gears were found good in torque transmission performance. Benavides et
al. (2002) manufactured miniature ratchet wheel of different materials
(e.g. 304L stainless steel, nitronic 60, austenitic stainless, beryllium
copper, and titanium) by micro-WEDM with submicron level surface finish,
minimum recast layer and consistent micro-geometry. Di et al. (2006)
machined miniature gears of 40 [micro]m module and having seven teeth,
from stainless steel plate of 1 mm thickness with an accuracy of [+ or
-] 0.2 [micro]m. Ali and Mohammad (2008) reported 1.4 [micro]m as
[R.sub.a] and 7 [micro]m as [R.sub.t] for the miniature copper gear
machined at 1 A discharge current, 8 V voltage and 8 [micro]s pulse-on
time by WEDM. Thereafter, Ali et al. (2010) obtained average surface
roughness ([R.sub.a]), peak-to-valley height ([R.sub.t]) and dimensional
accuracy of 1.8 [micro]m, 7 [micro]m and 2-3 [micro]m respectively for
WEDMed external spur gear of beryllium-copper having 3.58 mm diameter
with seventeen teeth and 6 mm face width. Many attempts have been made
in the recent past on improving the quality of WEDMed components by
using various optimization methodologies (Kanlayasiri et al., 2013;
Kuruvila et al., 2011; Tzeng et al., 2011; Yusup et al., 2012).
The review of past work reveals that no work has been reported on
studying the behaviour of micro-geometry parameters (i.e. profile and
pitch) of miniature gears with WEDM parameters. It can also be concluded
that no literature seems to be available on optimization of parameters
of WEDM for improving the manufacturing quality in terms of minimization
of micro-geometry errors (errors in profile and pitch, and surface
roughness of miniature gears). Also, productivity concept has not been
taken care of in the previous work on WEDM of miniature gears. The
present work bridges this gap by analyzing the behaviour of pitch,
profile, surface roughness and material removal rate with the WEDM
parameters and optimizing them for manufacturing high quality miniature
gears.
3. Objectives of the Research Work
The prime objectives of the present research work were:
1. To explore the capability of WEDM for manufacturing high quality
miniature gears.
2. To analyze the effect of WEDM parameters on micro-geometry,
surface finish and material removal rate of the miniature gears.
3. To optimize the WEDM parameters to minimize the profile error,
pitch error, average roughness, maximum roughness and maximize the MRR.
4. To establish WEDM as a superior alternative process for
manufacturing the high quality miniature gears.
4. Research Methodology
The experimental research was accomplished in three stages namely
pilot, main and confirmation experimentations. Table 3 presents the
objectives, the input parameters, responses, design of experiments (DOE)
approach and number of experiments conducted during each stage along
with the specification of miniature gears manufactured. Pilot
experiments were aimed to bracket the range of WEDM parameters and to
fix the level of cutting speed for further research. Total twenty three
experiments were designed based on one factor-at-a-time approach varying
voltage, pulse-on time, pulse-off time and wire feed rate at five levels
and cutting speed at three levels. The results of the pilot experiments
gave a brief idea about the micro-geometry and surface integrity of
WEDMed miniature gears.
The main experiments were aimed to optimize the quality of the
miniature gears by minimizing the geometric inaccuracy (i.e. profile and
pitch errors), maximizing the surface finish (by minimizing average and
maximum roughness), and the material removal rate (MRR). The main
Experiments were designed using Box-Behnken approach of response surface
methodology (Montgomery, 2009) by varying voltage, pulse-on time,
pulse-off time and wire feed rate at three levels each. The 'Design
Expert 8.0' software was used for regression and graphical analysis
of the data obtained. Total 29 experiments were conducted with two
replicates for the each experiment. Therefore, total 58 gears were
manufactured. The values and ranges of fixed parameters were chosen
based on the preliminary experiments (Gupta and Jain 2013) and the
machine constraints. Analysis of variance (ANOVA) study based regression
analysis was done to analyze the experimental data, to develop the
relation between responses and WEDM parameters and to find the relative
importance of the machining parameters with respect to the measures of
performance (i.e. responses). The optimum values of the selected
variables were obtained by solving the regression equations and by
analyzing, the response surface contour plots. Finally, the confirmation
experiments were conducted to validate the optimized results predicted
by desirability analysis.
5. Manufacturing of Miniature Gears by WEDM
The miniature gears for the present research work were manufactured
on Ecocut WEDM machine from Electronica India. This machine is based on
closed-loop control system and having tolerance of [+ or -] 15 [micro]m.
The machine tool comprises of a main work table (called as X-Y table)
and a wire drive mechanism. The gear blank (5 mm thick copper plate) is
mounted and clamped on the main work table. It moves along X and Y axes,
in steps of 1 micron, by means of stepper motor. A traveling wire which
is continuously fed from wire feed spool is caused to travel through the
plate and goes finally to the waste-wire box. Along its traveling path,
the wire is supported under tension, between a pair of wire guides which
are disposed on both (lower and upper) sides of the gear blank. As the
material removal or machining proceeds, the work table carrying the gear
blank is displaced transversely along a predetermined path (based on the
geometry of the miniature gear) which is stored in terms of linear and
circular elements in the controller via numeric control program and
tries to maintain constant machining gap. While the machining is
continued, the machining zone is continuously flushed with de-ionized
water as dielectric passing through the nozzles on both sides of the
gear blank. An ion exchange resin is used in dielectric distribution
system, in order to prevent the increase in conductivity and to maintain
the conductivity of the water constant.
Part programs for manufacturing of miniature gears on WEDM were
prepared by Elcam software which has a separate segment for gear profile
creation. The gear profile geometry is defined in terms of various
geometrical definitions (lines and arcs) as the wire-tool path elements
on graphical screen. The wire compensation (offset) for wire diameter
and machining overcuts was specified. After the profile is fed to the
computer, all the numerical information about the path is calculated
automatically in terms of geometric and miscellaneous codes (G and M
codes). The entered gear profile was verified on the graphic display
screen with simulation facility. The numeric control program for gear
profile was then transferred to the machine tool by RS 232 cable. The
miniature gears were manufactured from a 5 mm thick rectangular brass
plate using brass wire of 0.25 mm diameter and de-ionized water as
dielectric. The process sequence for manufacturing of miniature gears is
depicted by Fig 3.
Profile error ([F.sub.a]) and pitch error ([F.sub.p]) were measured
on the SmartGEAR CNC gear metrology machine. The measurements were taken
on the left and right flanks of four gear teeth for profile error and on
both the flanks of all the twelve teeth for the pitch error. Profile
error ([F.sub.a]) was calculated by taking average of the mean values of
the deviations in left flank (LF) and right flank (RF) of four gear
teeth. While pitch error ([F.sub.p]) was calculated by taking average of
the maximum differences in angular positions of RF and LF for all twelve
teeth. The surface roughness parameters i.e. average roughness
([R.sub.a]) and maximum roughness ([R.sub.t]) were evaluated using
Surfcom roughness profiler from Accretech, Japan on an evaluation length
of 0.75 mm on gear tooth flank surface along root to tip using 0.25 mm
as cut-off length. For evaluation of the MRR, a weighing scale having
resolution of 10 milligrams is used for taking the weights of the gear
blank (plate of brass) before and after machining, and the machining
time is recorded by a stop watch having least count of 0.01 second. The
following equation was used to determine the MRR value:
MRR = [[M.sub.1] - [M.sub.2]/[rho] x t]([mm.sup.3]/min) (1)
Where, [M.sub.1] and [M.sub.2] are the weights of the gear blank in
grams before and after gear manufacturing by WEDM respectively; [rho] is
the density of the gear material in g/[mm.sup.3] (for brass it is 0.0084
g/[mm.sup.3]); and t is the machining time in minutes.
[FIGURE 3 OMITTED]
6. Results and Discussion
6.1 Results of Pilot Experiments
Keeping in view the objectives of minimizing the total profile
error, accumulated pitch error and surface roughness simultaneously,
5-15V for voltage, 0.6-1.0 [micro]s for pulse-on time, 90-170 [micro]s
for pulse-off time, 9-15 m/min for wire feed rate with 100 % cutting
speed have been bracketed for further detailed investigations (Gupta and
Jain, 2013a-b). The best quality miniature gear manufactured by WEDM
using the combination of 15 V voltage, 1 [micro]s pulse-on time, 170
[micro]s pulse-off time, 9 m/min wire feed rate and 100% cutting speed,
had DIN quality number of 6 for pitch (with pitch error of 11.2
[micro]m), and DIN quality number of 8 for profile (with profile error
of 13.2 [micro]m). The values of average and maximum roughness for this
gear were 1.1 [micro]m and 6.4 [micro]m respectively. The set of
parameters for best quality gear generated crack-free, regular shaped
shallow cratered teeth surfaces. No dominant pattern of microhardness
variation, in case of the best quality gear, with respect to the depth
was noticed. This indicates either the absence or very small thickness
of recast layer and heat affected zone. This gear also had very low
macro-geometry deviations i.e. deviation in span (4 [micro]m), deviation
in chordal tooth thickness (5 [micro]m), deviation in the dimension over
two balls (10 [micro]m). Fig. 4 depicts the SEM images of the this gear
showing (a-b) the uniform burr-free tooth profile (c) defect-free
surface of the gear tooth (d) arrangements of craters on the WEDMed
surface of the tooth of the best gear.
[FIGURE 4 OMITTED]
Results of the experiments proved the capability of WEDM for
manufacturing high quality miniature gears. Main experiments were
conducted for analysing the behaviour of micro-geometry with WEDM
parameters and to improve the quality of the miniature gears.
6.2 Results of Main Experimentation
Twenty nine main experiments were conducted according to
Box-Behnken approach of RSM. Table 4 presents the parametric
combinations and corresponding responses for the different experimental
runs. ANOVA has been used to study the significant WEDM parameters.
ANOVA study found that all four WEDM parameters significantly
affect the profile error, pitch error, average roughness, maximum
roughness and MRR. Figures 5 and 6 illustrates the variation of the
response surfaces for [F.sub.a] (Fig. 5a and 5b), [F.sub.p] (Fig. 5c and
5d) and [R.sub.t] (Fig. 6a and 6b) with the WEDM parameters. It can be
observed that the minimum values of [F.sub.a] and [F.sub.p] are obtained
in the range of 8-9 volts (Fig. 5a and 5c). This is due to fact that at
very low voltage, high amount of wire lag is caused by high
electrostatic force while, higher values of voltage and pulse-on-time
lead to generation of larger forces caused by violent spark and pressure
of the gas bubbles. It can be seen from Fig. 5b and 5d that there exists
an optimum range for pulse-off time (140-160 [micro]s) and wire feed
rate (12.5-14 m/min). It can be explained by the fact that lower
pulse-off time and wire feed rate causes wire vibrations due to short
circuiting while, their higher values cause excessive hydraulic forces
resulting in wire lag and again increasing errors in profile and pitch.
[FIGURE 5 OMITTED]
It is evident from the Figures 6a and 6b that the optimum ranges of
voltage (6-8 V), pulse-on time (0.6-0.7 [micro]s), pulse-off time
(150-160) and wire feed rate (12.5-14.5 m/min) exist for minimum
[R.sub.t]. While, variation of [R.sub.a] is linear with WEDM parameters
i.e. lowest voltage and pulse-on time (Fig. 7a) and highest pulse-off
time and wire feed rate (Fig. 7b) should be used to minimize [R.sub.a].
It can be explained by as follows. Use of higher voltage, longer
pulse-on time and shorter pulse-off time increases the discharge energy
at the plasma channel, availability of time for transfer of this energy
to the gear tooth surface and decreases the flushing time. While, lower
wire feed rate increases frequency of wire breakage. All these factors
lead to formation of deeper and irregular craters on the gear tooth
surface increasing the surface roughness value.
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Fig. 8 shows the effects of WEDM parameters on MRR. It can be seen
that higher MRR can be achieved using higher voltage, longer pulse-on
time, shorter pulse-off time and lower wire feed rate. Increase in
voltage and pulse-on time leads to increase in MRR because strong
electric field at higher voltage facilitates the ionization of
dielectric and thereby increase in discharge and increase in the period
of transferring of discharge energy to the electrodes which results in
rapid melting and evaporation of large amount of material.
[FIGURE 8 OMITTED]
6.3 Optimization
In order to get precise quality and productivity, the understanding
and control of any process are the prerequisites and can only be
achieved by accurate modelling and optimization of the process and its
parameters. The single-objective optimization of WEDM parameters was
done for minimum values of [F.sub.a], [F.sub.p], [R.sub.a], [R.sub.t]
and for maximum value of MRR.
6.3.1 Desirability analysis
Desirability analysis uses desirability function which is the
geometric mean of the individual desirabilities of all the responses and
tries to find the optimum values of the process parameters to meet the
goal of the desirability function. Each response [Y.sub.i] is converted
into an individual desirability function [d.sub.i] whose value can range
from 0 (when the response is outside the acceptable region) to 1 (when
the response is at its goal or target value). The more closely the
response approaches the goal or target value, the closer is the
desirability to 1. Equation (2) presents the generalized equation of the
desirability function for the ith data:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
Where, n is number of responses; [d.sub.ij] is the desirability of
the jth response for the data with 0 [less than or equal to] [d.sub.ij]
[less than or equal to] 1.
In the present case there are five responses [F.sub.a], [F.sub.p],
[R.sub.a], [R.sub.t] and MRR. For each response the optimized values of
WEDM parameters were predicted by desirability approach. The individual
desirabilities for [F.sub.a], [F.sub.p], [R.sub.a], [R.sub.t] and MRR
for the ith data were calculated by following equations (Montgomery,
2009):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
[([d.sub.MRR]).sub.i] = [[MRR.sub.i] - [MRR.sub.min]/[MRR.sub.max]
- [MRR.sub.min]] (7)
Where, i is the value of i th response obtained min and max are the
minimum and maximum values of the responses.
6.4 Confirmation Experiments
The optimum values of the WEDM parameters obtained through
desirability analysis for each response were standardized based on
machine constraints and are given in Table 5. On these standardized
optimum values of WEDM parameters, the confirmation experiments were
conducted to validate the predicted results. Very close agreement found
between the experimental results and those obtained by the desirablity
analysis.
Fig. 9 depicts SEM images of the miniature gears manufactured at
optimal parameters. It is clear that miniature gears have burr-free
uniform tooth profile.
[FIGURE 9 OMITTED]
7. Conclusions and Future Scope
As the demand of the miniaturized devices continues to grow, the
requirement of high quality miniature gears is ever increasing. The
results of the present work would be very useful to engineers and
manufacturers for manufacturing of high quality miniature gears by wire
electric discharge machining. This chapter reported about the
investigations on the effects of WEDM parameters on the profile error,
pitch error, average roughness, maximum roughness and material removal
rate of miniature gears. This chapter also describes the single
objective optimization of WEDM parameters for minimization of profile
error, pitch error, average roughness and maximum roughness, and
maximization of MRR. Following conclusions can be drawn from the present
work:
1. Voltage, pulse-on time, pulse-off time and wire feed rate were
found to be highly significant parameters.
2. Main reasons of errors in profile and pitch, and surface
roughness are irregular shaped craters created due to violent sparks
having high discharge energy, short circuiting and adherence of wire on
gear tooth surface, and wire-lag due to various forces generated during
machining.
3. It was also found that WEDMed miniature gears had burr-free
uniform profile, defect free surfaces and very thin recast layer.
4. optimization was done to improve the quality and productivity of
WEDMed miniature gears. Confirmation experiments revealed very close
agreement between predicted and experimental results of optimization.
5. The optimized values of profile (11.1 [micro]m) and pitch (8.4
[micro]m) categorize the gear in high quality i.e. DIN quality number 7
and 5 respectively, which are superior than the other existing
conventional processes of miniature gear manufacturing.
6. The results of the present work prove the superiority and
capability of WEDM to manufacture high quality miniature gears for the
miniaturized devices.
Similar work can also be done for miniature gears of different
materials such as stainless steel, bronze, aluminium and other metallic
materials. Wires of different materials and types can be used to
manufacture miniature gears and effect of the same can be analyzed on
the quality of miniature gears. High end WEDM machine tool having
minimum constraints can be used to analyze the effect of other WEDM
parameters such as current, wire tension, flushing pressure etc. on the
quality of miniature gears.
8. Acknowledgements
Authors wish to acknowledge the cooperation from Carl Zeiss
technology centre, Pune (India) for the surface roughness measurements
of the miniature gears by surface profiler Surfcom
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Authors' data: Gupta, K[apil]; Jain, N[eelesh] K[umar],
Discipline of Mechanical Engineering, Indian Institute of Technology
Indore, 453446, MP, India, kapil@iiti.ac.in, nkjain@iiti.ac.in
This Publication has to be referred as: Gupta, K[apil] & Jain,
N[eelesh] K[umar] (2013) Manufacturing of High Quality Miniature Gears
by Wire Electric Discharge Machining, Chapter 40 in DAAAM International
Scientific Book 2013, pp. 679-696, B. Katalinic & Z. Tekic (Eds.),
Published by DAAAM International, ISBN 978-3901509-94-0, ISSN 1726-9687,
Vienna, Austria
DOI: 10.2507/daaam.scibook.2013.40
Tab. 1. Limitations of conventional processes for
manufacturing of miniature gears with corresponding
DIN quality
Miniature gear Limitations DIN
manufacturing quality
process number
Hobbing * Replicates tool marks on gear teeth 9
* Needs subsequent polishing operation
for high quality gears
* Requires long set-up time.
Stamping * Necessitates shaving operation for 10
final finishing of gears
* Cannot manufacture gears with higher
tooth thickness
* Wear & Tear of die and punch is a
problem in stamping.
Die-Casting * Cannot be used where extreme accuracy 11
is needed
* Subsequent trimming operations are
necessary after the gear has been
removed from the die.
Extrusion * Requires secondary drawing operation 12
for improving accuracy of gears
* Wear of die is a major problem.
Powder * De-binding of part from mould is 10
Metallurgy difficult
* Arrangement of fine metal powder of
all types is difficult
* Not suitable for gears other than
spur type.
Tab. 2. Quality requirements of the gears for various
applications in terms of DIN and AGMA standards (Bralla,
1998; Davis, 2005; Townsend, 2011)
Application Typical AGMA DIN
type examples quality quality
number number
Commercial Hand tools, 3
applications Pumps, Clocks,
Slow speed
machineries, 4 12
Various
appliances
5 11
6 10
7
Precision Aircraft 8 9-10
applications engines,
Turbines, 9 8-9
Cameras,
Automatic
transmission 10 7-8
systems,
Instruments, 11 6-7
High speed
machineries 12-13 4-6
Ultra- Precision 14 3-4
precision instruments,
applications Military 15 1-2
navigations
Application Typical Corresponding manufacturing
type examples or finishing process
Commercial Hand tools, Plaster-mold casting, Permanent-mold
applications Pumps, Clocks, casting
Slow speed
machineries, Investment casting, Injection
Various molding *, Extrusion *
appliances
Die casting *
Milling, Cold drawing, Stamping *,
Powder metallurgy *
Rolling, Broaching
Precision Aircraft Rolling, Shaping, Hobbing *
applications engines,
Turbines, Rolling, Shaving, Honing, Lapping,
Cameras, Grinding
Automatic
transmission Shaving, Honing, Lapping, Grinding
systems,
Instruments, Shaving, Grinding
High speed
machineries Grinding
Ultra- Precision Grinding
precision instruments,
applications Military Grinding with extra care
navigations
* used for manufacturing of the miniature gears
Tab. 3. Details of different stages of the experimentation
Experimentation Objectives Input parameters
stage with levels
Pilot * To analyse the 1. Voltage (V):
Experiments behaviour of 5-10-15-20-25
microgeometry
parameters with 2.Pulse-on time ([micro]s):
WEDM parameters. 0.6-0.8-1-1.2-1.4
* To bracket the 3.Pulse-off time ([micro]s)
range of WEDM 90-130-170-210-250
parameters
for further 4.Wire feed rate:
investigations. 3-6-9-12-15 (m/min)
* To fix the 5. Cutting speed
cutting speed for (%)*: 50-75-100
further
experimentation.
* To analyse the
surface integrity
of miniature gears.
Main * To analyse the 1. Voltage (V):
Experiments effect of WEDM 5-10-15
parameters and
interactions 2. Pulse-on time
between them on ([micro]s): 0.6-0.8-1
the responses.
3. Pulse-off time
(Ls): 90-130-170
* To further
facilitate the 4. Wire feed rate:
optimization 9-12-15 (m/min)
Confirmation * To validate Optimized
Experiments the optimum WEDM parameters
results predicted
by desirability
analysis.
Experimentation Responses DOE
stage approach (No.
of experiments)
Pilot Profile error ([micro]m) One factor
Experiments at-a-time
(23)
Pitch error ([micro]m]
Avg. roughness ([micro]m]
Max. roughness ([micro]m]
Microstructure
Micro-hardness
Main Profile error ([micro]m] Box-
Experiments Behnken of
RSM (29)
Pitch error ([micro]m]
Avg. roughness ([micro]m]
Max. roughness ([micro]m]
MRR ([mm.sup.3]/min)
Confirmation Profile Error ([micro]m] (5)
Experiments Pitch Error ([micro]m]
Avg. roughness ([micro]m]
Max. roughness ([micro]m]
MRR ([mm.sup.3]/min)
Fixed parameters: Wire material: brass; Wire diameter: 0.25 mm; Wire
tension: 1200 grams, Dielectric: de-ionized water; Dielectric
conductivity: 20 [micro]S/cm; Dielectric pressure: 7 kg/[cm.sup.2]
Miniature gear specifications: Material: brass; Profile: involute;
Type: external spur gear; Pressure angle: 20[degrees]; Module: 0.7 mm;
Outside diameter: 9.8 mm; Number of teeth: 12; Face width: 5 mm.
* Cutting speed was fixed during main and confirmation experiments.
Tab. 4. Experimental runs and corresponding responses for
main experimentation
Expt. Input Parameters
No.
V [T.sub.on] [T.sub.off] W
(Volts) ([micro]s) ([micro]s) (m/min)
1 15 0.8 130 15
2 10 0.8 90 9
3 5 1.0 130 12
4 10 0.8 130 12
5 15 0.6 130 12
6 5 0.8 130 9
7 5 0.8 170 12
8 10 1.0 130 9
9 15 0.8 130 9
10 10 0.8 170 15
11 15 0.8 170 12
12 15 1.0 130 12
13 10 0.8 130 12
14 10 0.8 130 12
15 10 0.8 130 12
16 15 0.8 90 12
17 10 0.8 170 9
18 10 1.0 90 12
19 5 0.8 90 12
20 10 0.8 130 12
21 10 0.6 90 12
22 10 0.6 170 12
23 10 0.8 90 15
24 10 1.0 130 15
25 5 0.6 130 12
26 10 0.6 130 9
27 10 1.0 170 12
28 5 0.8 130 15
29 10 0.6 130 15
Expt. Responses
No.
'[F.sub.a]' '[F.sub.p]' '[R.sub.a]'
([micro]m) ([micro]m) ([micro]m)
1 14.20 30.20 1.70
2 14.50 41.00 2.00
3 14.00 29.40 1.80
4 13.10 12.40 1.40
5 14.00 24.20 1.44
6 14.40 32.10 1.70
7 13.00 19.20 1.35
8 14.60 44.50 1.82
9 14.80 38.60 1.76
10 13.10 18.10 1.28
11 14.40 35.00 1.71
12 15.20 40.80 1.92
13 12.80 16.25 1.65
14 12.50 11.80 1.70
15 13.10 15.00 1.60
16 14.80 35.70 1.87
17 13.80 32.40 1.68
18 13.90 38.00 1.97
19 14.30 34.00 1.61
20 13.00 18.20 1.76
21 14.20 28.35 1.63
22 11.70 8.30 1.40
23 13.50 25.10 1.55
24 14.00 27.00 1.74
25 13.30 20.65 1.14
26 13.50 25.00 1.49
27 14.60 32.80 1.65
28 13.00 22.40 1.25
29 12.00 16.00 1.18
Expt. Responses
No.
'[R.sub.t]' MRR
([micro]m) ([mm.sup.3]/min)
1 7.40 38
2 9.20 42.5
3 8.72 25.68
4 7.23 28
5 7.14 25.46
6 8.00 31.4
7 6.87 17.8
8 8.85 35.58
9 8.55 38
10 7.01 27.6
11 7.30 28.2
12 8.90 42.42
13 7.00 30.5
14 6.78 34
15 6.90 27.8
16 8.70 36.4
17 7.80 25.54
18 9.80 40.73
19 8.20 28
20 7.11 32
21 7.30 28.16
22 7.00 24
23 8.23 32.45
24 8.70 37.17
25 6.72 16.08
26 7.45 30.64
27 7.90 28.8
28 6.75 22
29 6.90 20.26
Tab. 5. Comparison of optimum values with the results of
confirmation experiment for [F.sub.a], [F.sub.p], [R.sub.a],
[R.sub.t] and MRR
Responses WEDM parameters
Optimized
V [T.sub.on] [T.sub.off] W
[R.sub.a] 6.31 0.61 164.01 14.47
[R.sub.t] 7.61 0.61 149.86 14.13
[F.sub.a] 8.14 0.60 165.36 12.99
[F.sub.p] 8.71 0.64 154.15 12.87
* D:0.983
MRR 14.8 0.83 97.14 9.18
Responses WEDM parameters
Standardized
V [T.sub.on] [T.sub.off] W
[R.sub.a] 6 0.6 165 15
[R.sub.t] 8 0.6 150 14
[F.sub.a] 8 0.60 160 13
[F.sub.p] 9 0.65 150 13
* D:0.983
MRR 15 0.85 100 9
Responses Values of response from
Desirability Confirmation
analysis Experiments
[R.sub.a] 1.07 1.10
[R.sub.t] 6.48 6.40
[F.sub.a] 11.58 11.10
[F.sub.p] 8.91 8.4
* D:0.983
MRR 42.81 42.97
