Numerical evaluation of transient thermal loads on a ... - Springer Link

Int J Adv Manuf Technol (2010) 48:571–580 DOI 10.1007/s00170-009-2300-8

ORIGINAL ARTICLE

Numerical evaluation of transient thermal loads on a WEDM wire electrode under spatially random multiple discharge conditions with and without clustering of sparks Simul Banerjee & B. V. S. S. S. Prasad

Received: 9 February 2009 / Accepted: 4 September 2009 / Published online: 4 October 2009 # Springer-Verlag London Limited 2009

Abstract Thermal load on wire electrode under randomly located multiple discharge condition is the most important consideration for predicting wire breakage in wire electrical discharge machining process. Sometimes the discharges form clusters as observed experimentally by different researchers and may occur because of inadequate evacuation of the debris generated during each discharge. Formation of clusters is more likely in thick work pieces. Clusters are spread randomly along the wire while sparks in each cluster too are random. Such clustering of sparks enhances the intensity of thermal load on the wire. In the present investigation, a one-dimensional explicit finitedifference thermal model is proposed for estimating the transient temperature distribution along the length of the wire under the conditions of randomly located spatial sparks with and without the formation of clusters. While each of the electric discharges is simulated as a volumetric heat source present within the wire over the discharge channel width, which in turn is calculated from the available literature, the successive sparks and cluster of sparks are located on the wire by means of a random function. The predicted values of maximum wire temperatures indicate the degree of wire rupture risk, which has been found to be different for short and long elapsed times. Accordingly, random pulse and clusters models are suggested for predicting thermal loads while machining thin or S. Banerjee (*) Department of Mechanical Engineering, Jadavpur University, Kolkata 700032, India e-mail: [email protected] B. V. S. S. S. Prasad Department of Mechanical Engineering, Indian Institute of Technology, Chennai 600036, India

thick work pieces, respectively. The effects of work-piece height, power input, pulse frequency, duty factor, wire velocity, wire diameter, and the convective heat transfer coefficient have been reported. The one-dimensional thermal models may be used for setting rules of selection for an expert system for the safe operating conditions of wire electro-discharge machining. Keywords Wire electrical discharge machining process . Thermal load . Clusters model Nomenclature A Cross-sectional area of the wire (m2) c Specific heat (J/kg K) D/Dis Distance along the wire axis (m) EL/l Work-piece width (m) Df Duty factor f: Frequency (kc/s) g Rate of uniformly distributed internal heat generation per unit volume (W/m3) H Enthalpy rate (ρCVwAT) (W) h Convective heat transfer coefficient (W/m2 K) ka Thermal conductivity of work-piece material (W/m K) kw Thermal conductivity of wire material (W/m K) I Work-piece height (m) L/TL Length of wire under consideration (m) NS Counter for the number of sparks in a cluster NSC Number of sparks in a cluster NSP Number of sparks ONt Discharge duration (s) OFt Off-time (s) P Perimeter of the wire (m) q Heat flux (W/m2) r0/Rw Wire radius (m)

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Rd RANF( ) RANF t/t Tb TNS Tt T∞ Vw W/Wav X XC αa αw Δt ΔX/ ΔXG 8w q=q pi ρ te

Int J Adv Manuf Technol (2010) 48:571–580

Discharge channel radius (m) Random number generator between 0 and 1 Time coordinate (s) Boiling point temperature of work material (°C) Total number of sparks Total time (τe) (s) Ambient temperature (°C) Wire velocity (m/s) Average input power to the wire/work piece (W) Length coordinate along wire axis (m) Width of cluster (m) Thermal diffusivity of work-piece material (m2/s) Thermal diffusivity of wire material (m2/s) Time interval (s) Axial grid length for spark position or mesh size (m) Wire diameter (m) Temperature above ambient at the nodal point i at a point of time t =p·Δt (°C) Mass density (kg/m3) Elapsed time (s)

threshold value) for the thin work pieces, however, was attributed to the increase in the presence of contaminants, arising apparently due to faster machining at high powers. Short-circuit pulses before wire rupture, noted by Tanimura and Heuvelman [5], also point to the role of debris/ contaminations. One of the objectives of this paper is to explain these experimental observations by means of a thermal model. The thermal models on WEDM available [2, 6–10] are essentially based on the hypothesis of Jennes et al. [2] that the thermal load on the wire could be simulated by a volumetric heat source uniformly distributed along the wire length in the vicinity of the work piece. Jennes and coworkers [2] considered very long elapsed times and Rajurkar and co-workers [6] performed a quasi-steadystate analysis by dropping the time-dependent term. In practice, however, the WEDM process is transient in nature even though the machining is carried out under “steady” operating conditions. Banerjee et al. [11] suggested a modification to the model of Jennes et al. [2] in that the power will be dissipated mainly over the width of the discharge channel which, in turn, was calculable from the work of Jilany and Pandey [12] and is given as

1 Introduction The wire electro-discharge machining (WEDM) is essentially a thermal process in which the electrodes experience an intense local heating in the vicinity of the ionized channel. The high power density results in the erosion of a part of material from both the electrodes by local melting and vaporization. However, while a better erosion rate of the work piece is a requirement, the removal of the wire material leads to rupture and, hence, is undesirable. This conflict sets a limit on the choice of machining conditions and parameters. An analysis and optimization study by Scott et al. [1] indicated that among different parameters affecting the WEDM process, the discharge current (or power), discharge duration (or duty factor), and pulse frequency were significant control factors, whereas wire speed, wire tension, and dielectric flow were relatively insignificant. Jennes et al. [2] reported a comprehensive experimental study with static pulse generator and analyzer. They particularly noted a sudden increase in the instantaneous power level before wire rupture. Kinoshita et al. [3] and Rajurkar and Wang [4] reported similar observations with a resistor–capacitor circuit as well. However, Rajurkar and Wang [4] made a significant observation that, for a thick work-piece material, wire rupture takes place even without a sudden increase in the frequency/power values once the machining conditions cross the critical frequency/power level. The sudden increase in frequency (above the

Rd tan

Tb ka Rd p 3=2 pffiffiffiffiffiffiffiffiffiffiffi ¼ 4 aa t : W

The growth of discharge channel radius Rd with time t was presented for chromium steel as work-piece material when subjected to different average input power W [11]. The earlier simple model proposed by the authors [11], however, considered a single pulse and the temperature distributions presented were, in principle, for a single pulseon period. On the other hand, in case of single electric discharge, studies of crater morphology/surface texture reveal a crater with raised rim on the electrodes [13]. This ideally would have led to sequential sparking and the resulting surface would have exhibited periodic characteristics. However, morphological studies of electrodes in case of spark train (under normal working conditions) showed random surface characteristics [14]. In order to explain the effect of this randomness, Dekeyser et al. [7, 8] and Kunieda et al. [15] extended the model of Jennes et al. [2] to consider clusters of spark discharges that may vary randomly over the wire length. However, neither the procedure was elaborated nor the effects of different process parameters were reported. Moreover, none of the abovementioned reports considered the transient nature of the locations of sparks occurring in clusters or without forming any cluster and its effect on temperature distribution in the wire electrode. Consideration of this, however,


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will lead to the development of efficient adaptive control systems in which the pulse energy is reduced or stopped based on the distribution of discharge locations measured in process [16]. In the present paper, an improved version of the authors’ previous model [11] has been proposed to consider the transient nature of the process as well as the random nature of the spark train with and without forming clusters. The effects of work-piece height, power input, duty factor, pulse frequency, wire velocity, wire diameter, and the convective heat transfer coefficient on the transient temperature distributions in the wire electrode are closely examined by using the proposed models.

clusters model has been considered for analysis in order to explain the wire rupture while machining thicker work pieces. The governing differential equation of heat flow can be written by considering energy balance over the infinitesimal control volume (Fig. 1).

: g @2q @q 1 @q 2 m qþ n ¼ @x2 @x kw aw @t

ð3Þ

where sffiffiffiffiffiffiffiffiffi hP and m ¼ kw A

rcVw n¼ kw

2 Formulation Each individual discharge, acting as a surface heat source, has been simulated by a uniformly distributed internal heat generation (g) in a cylinder of radius equal to that of wire (r0) and height equal to diameter (2Rd) of plasma channel [8, 11].

The boundary conditions as evident from the physical model (Fig. 1) are:

: g¼

@q ¼0 @x

W p r02 ð2Rd Þ

and : g¼0

during discharge duration

during off‐time

ð1Þ

ð2Þ

While the heat source or the discharge channel diameter is time variant, a constant value, corresponding to that at the end of discharge, has been assumed for the entire discharge duration. Considering chromium steel as workpiece material, however, this value of 2Rd is taken directly from the authors’ earlier work [11]. Also, the variation of temperature across the diameter of wire is neglected. Further, in the present study, it is considered that both the wire and the work piece are subjected to the same average power W which means equal apportionment of energy released in each discharge. In order to simulate the effect of spatially random sparking on the wire, a random number generator available as a standard library function on CYBER 120-70 has been used. However, in the present model, the random sparks are considered over the wire of length equal to work-piece height. It has been observed that the discharges form clusters, each consisting of 30 sparks [7, 8]. Clusters are spread randomly along the wire while sparks in each cluster too are random. It is to be mentioned that, for thicker work pieces, wire rupture occurs above a threshold frequency level even without a sharp rise in the frequency [4]. The

q ¼ 0 over the region at

t¼0

on the edges of the region far away from the discharge location at t > 0

ð4Þ

ð5Þ

Using central difference along x-coordinate, the governing Eq. 3 can be written in the following explicit finitedifference form: " # o nΔX aw Δt n p 2 2 q pi þ 1 2 þ m ð ΔX Þ q i1 2 ð ΔX Þ 2 ð ΔX Þ 2 : g aw Δt aw Δt nΔX p q þ 1 þ iþ1 2 kw ð ΔX Þ 2

q pþ1 ¼ i

aw Δt

1þ

ð6Þ The boundary conditions then become qi ¼ 0

over the region at

t¼0

q1 ¼ q2 at x ¼ 0

j on the edges of

qN ¼ q N1 at x ¼ L

j

the region for t > 0

ð7Þ ð8Þ ð9Þ

For the present study, brass is considered as the wire material. Its relevant thermo-physical properties are mass density, ρ=8,568 kg/m3, specific heat, c=0.377×103 J/kg K, thermal conductivity, kw =110 W/m K, and thermal diffusivity, αw =3.4054×10−5 m2/s.

574


Fig. 1 Physical model

x VW

2RW

T = T∞

WIRE WORK PIECE

DIELECTRIC COOLING

B

CURRENT

∆X DIELECTRIC COLLING + DISCHARGE

DIELECTRIC COOLING + DISCHARHE

SUPPLY A

L

h = 10, 000 W / m2 k DIELECTRIC

CURRENT

COOLING T ∞ X VW = WIRE VELOCITY

SUPPLY

(a)

T = T∞

BASIC CONFIGURATION HX + ∆X

TX + ∆X

qX+ ∆X

CONTROL VOLUME

. g

∆X

TX

h

qCONV

T∞

qX X HX

(b)

CONTROL VOLUME FOR ENERGY BALANCE

3 Marching procedure 3.1 Random pulse model A computer program in Fortran-77 is prepared. As the discharge occurs during the on-time, the finite difference Eqs. 6 through 9 at the discrete nodal points in time and space are solved. The calculation is continued during the off-time with g ¼ 0. The exact values of discharge period and the off-time are calculated from the chosen frequency and duty factor conditions. The resultant temperature distributions are thus obtained at the end of the first pulse assuming that it occurs at A (Fig. 1) where the wire first enters the work piece. These are taken as the initial temperature conditions for the second pulse occurring at a randomly generated location. The calculations are repeated for successive random sparks as time progresses. The total time is limited to that required for the wire to cross the work-piece height with chosen wire velocity. As the numerical scheme adopted was explicit in nature, care was taken to ensure the stability of the solution [17]. The numerical solutions are obtained for different values of

work-piece height, input power, duty factor, pulse frequency, wire velocity, wire diameter, and convective heat transfer coefficient. 3.2 Clusters model The number of sparks which could occur during the elapsed time is evaluated based on the chosen pulse period (on-time plus off-time). The sparks are then divided into a number of clusters assuming that each cluster consists of about 30 sparks as observed experimentally [7, 8]. The length, over which one cluster occurs, is determined by the product of the number of sparks in one cluster, pulse period, and wire velocity. The temperature distributions at the end of the first cluster is evaluated following the same procedure as in the random pulse model, i.e., restricting the sparks to occur randomly within the length so determined for one cluster. The first cluster, however, has been considered to occur on the wire at the entry zone (starting from position A, Fig. 1) of the work piece. The temperature distribution after the first cluster is taken as the initial condition for the second cluster, sparking in another zone shifted randomly within


the work-piece height. The procedure is repeated for a series of clusters until the chosen total time is elapsed and the final temperature distributions are computed. The marching procedure is conducted with the aid of an algorithm and a computer program having the flow chart shown in Fig. 2.

4 Results The numerical solutions of the governing partial differential equations are presented in Figs. 3 through 13 for the random pulse and the clusters model. 4.1 Random pulse model Figure 3 shows typical transient temperature variations along the wire axis at different points of time during machining with the chosen operating conditions. These Input: TL, EL, VW,

αW, kW, h, RW, Wav, 2Rd, ONτ, OFτ, Tt, ∆X, ∆XG, ∆τ, XC, NSC

. g = Wav /π RW2 (2Rd)

Fig. 2 Flow chart for one-dimensional clusters model

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distributions qualitatively agree with those of Rajurkar and Wang [6], Dekeyser et al. [7, 8], and Banerjee et al. [11]. Apart from the agreement, they also reveal certain differences. The obvious common points with earlier results are: (1) temperature increases with time and (2) the maximum temperature occurs near the exit point B for steady-state operation, i.e., at the end of the total elapsed time. The present results show as to how a temperature distribution for steady-state operation is achievable through a series of transient distributions. For example, under the chosen steady operating conditions in Fig. 3, curve III represents the temperature distribution at the end of a total elapsed time of 15 ms. It is to be noted that this curve need not be identical with the so-called steady-state temperature distribution as computed, for instance, by Rajurkar and Wang [6] by dropping the time-dependent term in the governing equation. The departure between the temperature distributions for the steady-state and the steady operating condition depends on the time constants involved.

576

Int J Adv Manuf Technol (2010) 48:571–580 600

LEGEND

W = 100 Watt f = 10 kc / s

τe millisec

CURVE

Df = 10 %

500

VW = 10 m / min

I

φW = 0.25 mm 2 0 h = 10000 W / m K

5

II

10

III

15

400

III

300

II

200

I

100

W/P

A

VW

B

0 4

6

8

10

12

14

16

DISTANCE ALONG WIRE AXIS, mm

Fig. 3 Transient temperature distributions with the random pulse model for a thin work piece (I=2.5 mm)

In the transient case, the temperature needs not be maximum at B (curves I and II, Fig. 3).The position of maximum temperature gets shifted progressively with time in the direction of motion of wire especially, for thin work pieces. As the work-piece height increases, the wire temperature raises up to certain length, and then becomes relatively flatter; refer to Fig. 4. These observations agree

qualitatively with those of Rajurkar and Wang [6] and Dekeyser et al. [7, 8], calculated for thick work pieces of over 20 mm. Referring to Figs. 3 and 4, the values of maximum temperature for thick work pieces are typically 240°C lower than those for the thin work pieces for the same operating conditions. The lower temperatures for the case of thicker work piece may be attributed to (1) the higher heat capacity due to longer wire length within the work piece and (2) the lower rate of sparking per unit length (S*); for example, the rates are 4,000 and 500, respectively for curve III in Fig. 3 and curve II in Fig. 4. On the other hand, sudden peak temperature more than the value near B is observed for a thick work piece; curve I of Fig. 4. No such sudden peak is discernable in Fig. 3 for thin work piece. The reason for the sudden peak may be due to large local variations of the parameter S*. These variations are likely to be larger on longer wire when sparks occurred successively in a narrow zone and subsequently shifted to a relatively far-off location. The resulting sudden peak in temperature is likely to cause wire rupture without an apparent signal such as increased frequency (due to the presence of debris, say, for thin work pieces [4]). Figure 5 shows the effect of input power on the wire temperature distribution. As expected, the wire temperature increases with increasing power at all positions along the wire length. It is obvious that while larger powers are preferred for better machining speeds, they are restricted by the increase in the maximum temperature value. In practice, however, larger powers are used with lower duty factors. 1000

LEGEND

f = 10 Kc / s Df = 10 %

500 W = 100 Watt f

400

900

LEGEND τe -2 CURVE x10 sec

= 10 kc / s

Df = 10 %

I

10

VW = 10 m / min

II

12

φ W = 0.25 mm

I

50

φW = 0.25 mm

II

100

III

200

τe = 15 millisec

700

X – BEST FIT POLYNOMAL OF CURVE II

2 0 h = 10000 W / m K

VW = 10 m / min 2 0 h = 10000 W / m K

800

W, Watt

CURVE

III

600 300

500 400

200

II

300 I II

100

200

I

II X

0

X W/P

A

12

22

32

100

VW

B

42

I

52


W/P

A

0 4

6

8

VW

B

10

12

14


Fig. 4 Transient temperature distributions with the random pulse model for a thick work piece (I=20 mm)

Fig. 5 Effect of input power on the temperature distribution

16


577

Figure 6 is obtained to show the effect of variation in duty factor for the chosen values of power and frequency by changing the discharge duration. It is to be noted that this situation is possible only in machines with pulse generators. However, the same model can be used to accommodate the variations of duty factor in other EDM generators for the purpose of simulation. As the duty factor increases, the maximum temperature of the wire increases. One has to, however, exercise caution in choosing the optimum values of power and duty factor for better machining yet without risking wire rupture. The temperature distributions, obtained for different values of operating frequency by keeping the power and duty factor values constant, are shown in Fig. 7 for three values of frequency; f=5, 10, and 20 kc/s. In other words, the numbers of sparks are 75, 100, and 300, while the discharge durations are 20, 10, and 5 μs, respectively. It is evident that the effect of increase in the number of sparks is to increase the temperature values, whereas the effect of decrease in the discharge duration is to decrease the temperature. As a net effect, therefore, with increasing values of frequency, the temperature values first registered an increase and then a decrease. As the numbers of sparks are large for high frequency, the randomness of the pulses causes mild fluctuations in the temperature. Figure 8 indicates that there exists a critical value of frequency at about 10 kc/s for the chosen work piece length of 2.5 mm along with the other conditions. This inference particularly

1200 LEGEND

W = 50 Watt

1100

VW = 10 m / min φ W = 0.25 mm

1000

h = 10000 W / m

2 0

K

D f = 10 %

CURVE

VW = 10 m / min

250

φ W = 0.25 mm 20

h = 10000 W / m

K

τ e = 15 millisec

800

5

II

10

III

20

200

II

150 I

100 III

50 W/P A

0

4

6

VW

B

8

10

12

14

16


Fig. 7 Effect of pulse frequency on the temperature distribution

is in agreement with the experimental observations of Rajurkar and Wang [4] for the same work-piece length. Figure 9 shows the effect of wire velocity on the temperature variation. In contrast to the present research, the results of previous investigators [2, 7] indicate that this effect is negligible. However, the machining practice demands higher velocities to reduce wire rupture risks, though restricted otherwise by wire vibration. This apparent contradiction is essentially due to the fact that the

I II

10 20

III

50

180 l = 2.5 mm W = 50 Watt Df = 10 % VW = 10 m / min φW = 0.25 mm h = 10000 W / m2 0K τe = 15 millisec

τe = 15 millisec

900

f, kc / s

I

Df, %

CURVE

f = 10 kc / s

LEGEND

W = 50 Watt

III

160

700 600

140

500 400

120

II

300 200

100

I

100 A

4

6

VW

W/P B

0 8

10

12

14


Fig. 6 Effect of duty factor on the temperature distribution

16

80

0

5

10

15

20

FREQUENCY, k c / s

Fig. 8 Variation of maximum temperature with pulse frequency

25

578

Int J Adv Manuf Technol (2010) 48:571–580 300 f

= 10 kc/s

CURVE

Df = 10 %

250

350

LEGEND

W = 50 Watt

φW = 0.25 mm h = 10000 W / m2 0K

VW m / min

W f Df

τe m sec

I

10

15

II

15

10

III

20

7.5

300

= 50 Watt = 10 kc / s = 10 %

LEGEND CURVE

φW, mm

VW = 10 m / min

I

0.20

φW = 0.25 mm

II

0.25

III

0.30

2 0

h = 10000 W / m

K

τe = 15 millisec

200

250

I

150

I

200

100

II

II

150

III

III

50

100

A

0

4

6

W/P

8

B

10

VW

12

14

50

16


W/P

A

Fig. 9 Effect of wire velocity on the temperature distribution

0

4

VW

B

6

8

10

12

14

16


Fig. 10 Effect of wire diameter on the temperature distribution

are not too high (about 25%) in view of the change in the value of h from 4,000 to 15,000 (275%). This is because the Biot number will have relatively less influence on the temperature distribution for small elapsed times. That is due to the low values of Fourier number [18], as with low 350

LEGEND

W = 50 Watt f

300

= 10 kc / s

CURVE

h, W / m2 0K

Df = 10 %

I

4000

VW = 10 m / min

II

10000

φW = 0.25 mm

III

15000

τe = 15 millisec

250

TEMPERATURE 0C

calculated temperature distributions in references [2, 7] considered only the so-called convective effect due to wire velocity and keeping the elapsed time at a constant value, irrespective of the work-piece height and wire velocity. Figure 9 shows the effect of wire velocity when a thin work piece is used. It is evident from the figure that, at lower wire velocities, the value of maximum temperature is higher and vice versa. It is worth noting that the present results represent the combined effects of the convection effects as well as the number of sparks, although the effect of the former is relatively insignificant. Figure 10 shows the temperature variation along the wire axis for three different wire diameters. For the given input power, the maximum temperature decreases with increase in wire diameter. Thus, wires with smaller diameter are prone to easy rupture. A wire with smaller diameter, on the other hand, is generally preferred for better profile accuracy. However, in the machining process, the wire diameter does not remain uniform due to erosion. The effective diameter varies along the work-piece height from the inlet to outlet (A to B). Since the effect of wire diameter is apparently significant (Fig. 10), it is recommended that the calculations should be carried out based on the average nominal values of inlet and effective outlet diameter. The effect of varying convective heat transfer coefficient is examined in Fig. 11. The values of h are chosen between 4,000 and 15,000 according to the references [2, 6]. It is found that the difference in maximum temperature is about 25% of the peak temperature in the chosen range of h. This implies that h has a reasonable influence on the wire temperature distribution. Flushing conditions, therefore, affect the thermal load on the wire. However, these changes

200 I II

150

III

100

50

A

0

4

6

W/P

8

VW

B

10

12

14

16


Fig. 11 Effect of convective heat transfer coefficient on the temperature distribution


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Fourier number (typically 0.087 with pulse-on time 10µs and wire diameter of brass 250µm) the storage of heat is so fast that very less heat could be transferred from the surface of the wire to the surrounding dielectric medium during a single discharge. Moreover, neglecting the wire velocity effect, the time constant is estimated as 20 ms (with h=10,000 W/m2 K) while only 15 ms is taken by the wire to cross the thin work piece.

Figure 12 compares the results of temperature distributions calculated by (1) the random pulse model and (2) the clusters model. Work-piece height was chosen to be 2.5 mm and the number of clusters is limited to five. It is clear that there is no qualitative difference between the temperature distributions obtained at the end of the elapsed time by the random pulse model and the clusters model. However, the number of clusters would be larger for a thicker work piece (found to be 40 in the present case under chosen conditions) and correspondingly there are several temperature peaks which are above the random model (Fig. 13). The maximum temperature peak of about 400°C occurs after the 16th cluster, i.e., after 48 ms; curve II Fig. 13. The reason for this appears to be the occurrence of a specific combination of clusters. Thus, there is a

700 = 10 kc / s

Df = 10 % VW = 10 m / min

600

φW = 0.25 mm h

2 0

= 10000 W / m

K

500

CURVE

τe millisec

I II III IV V

3 6 9 12 15

0.0 – 0.5 2.0 – 2.5 0.5 – 1.0 2.0 – 2.5 1.5 – 2.0

X

15

RANDOM PULSE

LAST CLUSTER POSITION ON W / P mm

X

100

5

7

I II

3 48

φW = 0.25 mm

III

120

40

X

120

RANDOM PULSE

h

= 10000 W / m2 0K

500

9

II

300 III I

200

100

X

A

0 12

W/P

22

VW

B

32

42

52


Fig. 13 Temperature distributions computed by clusters model for a thick work piece (I=20 mm)

B

II

200

W/P

1 16

VW= 10 m / min

(a) Transient analysis for short elapsed times is essential for estimating thermal loads of wire EDM, especially while machining thin work pieces. (b) An optimum combination of power and duty factor as well as a critical value of frequency seemed to exist for better machining without wire rupture risks. (c) For long elapsed time under multiple spark conditions, increase in wire velocity reduces the maximum temperature.

X

A

Df = 10 %

600

IV III

I

CURVE

A transient thermal analysis for the determination of temperature distribution in the wire of a WEDM process under multiple discharge condition is reported by using an explicit finite-difference method. Two thermal models are proposed: (1) the random pulse model, which seems to be more appropriate for short wire lengths for machining thin work pieces, and (2) the clusters model for thicker work pieces. The following important conclusions could be made from the present parametric study.

V

0

= 10 kc / s

5 Conclusions

400

300

f

possibility for the random model to predict lower maximum temperature and hence less wire rupture risks. The clusters model is preferable, therefore, to the random pulse model for thicker work pieces.

LEGEND

W = 100 Watt

LEGEND τe LAST CLUSTER millisec NUMBER

W = 100 Watt

400

4.2 Clusters model

f

700

VW

11

13

15


Fig. 12 Temperature distributions computed by clusters model for a thin work piece (I=2.5 mm)

580

(d) While there is a qualitative agreement between the temperature distributions obtained by the random pulse model and clusters model, the latter predicts higher values of maximum temperature for thicker work pieces. (e) The one-dimensional thermal models can be used for setting rules of selection for an expert system for the safe operating conditions of WEDM. For example, parametric combinations, spatial distributions of sparks like clustering and arcing conditions shall be appropriately chosen without risk of wire rupture, in view of the fact that maximum average temperature of wire is kept below a safe limit.

References 1. Scott D, Boyina S, Rajurkar KP (1991) Analysis and optimization of parameter combinations in wire electrical discharge machining. Int J Prod Res 29(11):2189–2207 2. Jennes M, Snoeys R, Dekeyser W (1984) Comparison of various approaches to model the thermal load on the EDM-wire electrode. Ann CIRP 33(1):93–98 3. Kinoshita N, Fukai M, Gamo G (1982) Control of wire-EDM preventing electrode from breaking. Ann CIRP 31(1):111–114 4. Rajurkar KP, Wang WM (1991) On-line monitor and control for wire breakage in WEDM. Ann CIRP 40(1):219–222 5. Tanimura T, Heuvelman CJ, Veenstra PC (1977) The properties of servo gap sensor with wire spark-erosion machining. Ann CIRP 26(1):59–63

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