O R I G I N A L A R T I C L E
Self-tuning fuzzy control with a grey prediction
for wire rupture prevention in WEDM
Received: 18 June 2002 / Accepted: 9 July 2002 / Published online: 10 July 2003 Springer-Verlag London Limited 2003
Abstract Wire rupture in the wire electrical discharge machining (WEDM) process is one of the most trou-blesome problems in practical applications. In this pa-per, the abnormal ratio Rab, defined as the proportion of
abnormal sparks in a sampling period, is taken to rep-resent the gap state in machining. The grey predictor is adopted to compensate the time-delayed Rab caused by
the low pass filter data processing. A gain self-tuning fuzzy control system has been developed to cope with the conditions that often occur with wire rupture in the WEDM process, such as an improper setting of machining parameters, machining the workpiece with varying thickness, etc. Experimental results of several cases show that the proposed controller results in a satisfactory performance. Not only can it immediately suppress transient situation once there is a sudden change of workpiece thickness, but a stable performance can also be achieved during machining a workpiece of constant thickness. As a result, wire rupture problems in most WEDM processes can be successively solved by the proposed control strategy.
Keywords Self-tuning fuzzy controller Æ Grey predictor Æ Wire rupture prevention Æ Wire electrical discharge machining Æ Abnormal ratio
1 Introduction
Wire electrical discharge machining (WEDM) is one of the fastest growing and accepted manufacturing tech-nologies in non-traditional machining processes [1]. In-stead of direct contact, machining is accomplished by a series of discharges between a wire electrode and the workpiece; it is particularly suited for machining diffi-cult-to-cut materials such as die steels. Due to its special material removal mechanism, a long time is generally required for WEDM to complete the entire machining process. Consequently it is imperative that the WEDM process be automated, including unattended operation, automatic wire threading, etc. In order to achieve this objective, it is of great importance to keep the WEDM process stable and efficient.
Wire rupture is the most undesirable event in the WEDM process, because it increases machining time, and deteriorates the quality of final products. There have been diverse efforts to this issue in the past years. Kinoshita et al. [2] found that the percentage of micro short circuit is closely correlated with wire rupture. As a result, they suggested to control the work feed rate by holding this percentage at a certain level. Tanimura and Heuvelman [3] found that wire breaking is associated with the unusual increment of the short-circuit pulses. Liao et al. [4] suggested that abnormal ratio Rab, defined
as the proportion of abnormal sparks in a sampling period, could be taken as a parameter to monitor machining state including wire rupture and machining efficiency. As for controlling wire from rupture, based on the duration of unusual discharges rise prior to the wire rupture, two types of wire rupture are categorised: one is that the duration is in the order of mini-second, for example, at the moment of the restart the machine again [5] or in machining a thin workpiece under high speed [6]. Kinoshita et al. [6] proposed to stop power supply temporarily as soon as the pulse frequency dra-matically increased. By this control strategy, preventing wire from rupture can be achieved but the process
DOI 10.1007/s00170-002-1480-2
W. M. Lee Æ Y. S. Liao
W. M. Lee (&)
Department of Mechanical Engineering, China Institute of Technology,
245 Sec. 3 Academic Road, Nangang, Taipei, Taiwan 11529, Republic of China
E-mail: wmlee@cc.chit.edu.tw Fax: +886-2-27867253 Y. S. Liao
Department of Mechanical Engineering, National Taiwan University,
1 Sec. 4 Roosevelt Road, Taipei, Taiwan 10764, Republic of China
stability and the quality of the product cannot be as-sured. Lawyers et al. [7] developed a thermal model to estimate the temperature distribution of the wire. Con-trol strategies were to provide a temporary reduction or stop of the pulse energy whenever the estimated tem-perature over the wire exceeded a critical value.
The other type is that the duration is in the order of second, for example, machining a workpiece with vary-ing thickness and so on. For problems of this sort, the control strategy can be employed to improve machining efficiency as well as to prevent the wire from rupture. Rajurkar and Wang [8] developed an on-line estimator of the workpiece height. Based on the estimated thick-ness, the optimal reference spark frequency can be determined experimentally. According to a linear model for WEDM process, an integral controller was adopted to adjust the pulse off time to keep the spark frequency at optimal level. Experimental results show that the proposed control system can successfully control the spark frequency at the optimal value without the risk of wire rupture, when cutting a workpiece with variable thickness. However, it is known that the WEDM process is a complex dynamic system and difficult to be mathe-matically modelled. Those model-based control strate-gies [5,8] are inapplicable to the wide range variation of machining condition in WEDM. Yan and Liao [9] proposed a multi-region fuzzy controller to augment the range of the working situation. Liao and Woo [10] developed a DSP-based on-line pulse monitoring system, and both short ratio and discharging energy were taken as controlled variables. Experimental results show that a high machining efficiency as well as system stability can be achieved in machining workpiece of constant thick-ness. The condition where there is a change of workpiece thickness is not taken into account.
In the last two decades, fuzzy logic controllers (FLC) [11,12,13] have been applied successfully to a wide variety of industry applications. Essentially, the FLC offers a method for representing and implementing the engineer’s control strategy by IF-THEN rules. Thus, FLC provides an alternative method for such plants as the WEDM process that is difficult to be mathematically modelled. In general, the conventional FLC with con-stant scaling factors cannot effectively cope with the transient and steady state machining condition at the same time. Specifically, at machining a workpiece with thickness suddenly changing, especially under the high-speed machining, in which the gain should be large en-ough to suppress the transient response, but this high gain will also cause instability during machining a workpiece of constant thickness. Consequently, a gain self-tuning fuzzy controller to further expand the range of the working situation is proposed in this paper.
According to the previous studies of one of the present authors [4], the abnormal ratio Rab can be
taken as a sensing parameter to the gap state in the WEDM control system. Due to the stochastic feature of the WEDM process, and the EMI coming from the adjacent electronic device, there is extreme and random
oscillation exhibited in the measured Rab signal. It is
inappropriate to send the on-line measured Rabdirectly
to the fuzzy controller. Instead, it is usually pre-pro-cessed by a low pass filter. But the filtered signals often have time-delayed problem, especially when it is pro-cessed by a low pass filter having a low cut-off fre-quency. In order to immediately detect the symptom of impending wire rupture, the dramatic increment of the Rab, and let controller take instant control actions to
reduce the risk of wire rupture, the grey predictor [14] was used to compensate the delayed filtered signal. Finally, the simultaneous adjustment of the arc off time, and the servo reference voltage to regulate the Rabat a proper level is adopted to solve the problem of
wire rupture in WEDM process.
2 Experimental setup and monitoring system
2.1 Experimental setup
A flushing-type WEDM machine developed by ITRI (Industrial Technology Research Institute) and CHMER Company, Taiwan, was used as our experi-mental machine. This machine comprises four major subsystems that include an isoenergy power supply, a dielectric regeneration system, a computer numerical control system with a five-axis motion system, and a wire drive system having semiautomatic wire threading function. The discharge power supply system of this machine consists of a low power circuit, and a high power circuit. The low power circuit supplies a 110 V voltage low power to break the insulation in the gap. Subsequently, a 220 V voltage is supplied by the high power circuit to generate the high current discharge and to erode the workpiece. A control circuit board performs the switching of the two power circuits. The peak value of a triangular discharge current waveform can be calculated by a constant slope of 380 A/lsec, and the value of on-time. The workpiece, and electrode were as follows: (1) workpiece (anode)-SKD11 alloy steels, (2) electrode (cathode), /0.25 mm brass wire. The adjust-able parameters of this machine are listed in Tadjust-able 1. These parameters include on-time, off-time, arc on-time, arc off-time, servo reference voltage, wire speed, wire tension, and flushing pressure.
2.2 WEDM discharge frequency monitoring system
The waveforms of the gap voltage and the associated current are shown in Fig. 1. There are three types of discharges namely normal discharge, arc, and short circuit. In order to prevent wire breaking and maintain an appropriate machining performance, it is necessary to develop an on-line monitor to classify these sparks.
From Fig. 1 it is apparent that a normal discharge has a relatively longer ignition delay time than the oth-ers. Based on this observation, a WEDM sparking
frequency monitor system has been developed. Due to the large interference of noises, the voltage level between arc and short circuit is difficult to differentiate. Hence, without loosing too much information for control pur-pose, the short circuits are categorised in the arc pulse group. Accordingly, only two types of pulse namely normal discharge and abnormal discharge (including arc and short circuit) are discriminated in our sparking monitoring system. Details of the discriminating prin-ciples can be found in our previous work [4]. The AX5216 count card in the PC recorded the numbers of discharges, normal pulses, and abnormal pulses. By dividing these numbers by the sampling period yields frequency of total discharge, normal pulses and abnor-mal pulses, respectively. In our system the sampling period ranges from 2 to 65535 ms.
3 Self-tuning fuzzy inferences and grey prediction control systems
3.1 Effects of the tuneable machining parameters on the controlled variable
As mentioned previously, the abnormal ratio Rabhas a
close connection with machining efficiency as well as wire rupture [4]. It is taken as the controlled variable in
the developed WEDM control system, and its on-line measured signal will be used as a feedback signal to reflect the gap state. In this section, effects of the tune-able machining parameters on the controlled varitune-able will be investigated, which can be used to aid the design of the fuzzy controller. Figure 2 shows the effect of arc off-time on the feedrate and the abnormal ratio Rab.
When the arc off-time is set to be a large value, the feedrate and the abnormal ratio Rab is small. Although
the wire rupture in this case will not occur, the machining speed is too low. By stepwise reducing the arc off-time, the machining speed can be improved, but the wire rupture will take place at last. Similar results by changing the tuneable machining parameter, the servo reference voltage, are given in Fig. 3. In summary, the tuneable machining parameters are highly correlated with the Rab and the feedrate, which is in proportion
with the machining efficiency. The higher the machining speed, the more likely the wire rupture would occur. Hence the appropriate setting of the Rabdepends on the
compromise between the ultimate machining speed and
Table 1 Adjustable parameters of the WEDM machine (CW-430F)
Item Range
On-time 1 9steps (unit: 0.1 ls)
Off-time 8 50steps(unit: 1 ls)
Arc on-time 1 5steps(unit: 0.1 ls)
Arc off-time 9 50steps(unit: 1 ls)
Servo reference voltage 30 70 V
Feedrate override 0 310%
Wire feed 1 16 m/min(15 step)
Wire tension 300 1600 gf(15 step)
Flushing 0 20 kg/cm2
(7 step)
Fig. 1 Typical gap voltage and current waveforms of the WEDM process
Fig. 2 Effect of the arc off-time on feedrate and abnormal ratio
Fig. 3 Effect of the servo reference voltage on feedrate and abnormal ratio
the occurrence of wire breaking. Finally, the desired setting of the Rabcan be achieved by concurrently tuning
the arc off-time and the servo reference voltage.
3.2 The compensation of time-delayed signal by the grey predictor
Figure 4 shows the obvious oscillation of the Rabthat is
measured in real time. It is denoted by the original data. In order to attenuate the fluctuation of the original Rab,
a low pass filter is usually employed. The filtered data, also shown in Fig. 4, is processed by the low pass filter having a cut-off frequency of 0.012 times one half of sampling frequency of the original Rab. Compared with
the evolution of the original signal, the filtered signal has an apparent time-delayed phenomenon, and cannot represent the real-time evolution for gap state, hence increases the risk of wire rupture if it is used as the control signal.
In order to compensate this associated time-delayed problem, a grey predictor [14] is applied to the filtered data. By the theory of grey prediction and associated data generating, the compensated value of ^yyð Þ0 ðkþ pÞ,
through grey model GM (1,1), can be calculated by [15]
^
yyð Þ0ðkþ pÞ ¼ 1 eð cÞ yð Þ0 ð Þ 0 b c
ec kþpð Þ ð1Þ
where p is the compensated step size, y(0) is a filtered data sequence, c and b are the development coefficient and the grey input, respectively [14].
An appropriate compensated step size p can be determined by the following off-line signal process. Firstly, the objective signal, which stands for the instantaneous evolution of the Rabbut has no apparent
fluctuation, is obtained by the moving average with 50 steps to attenuate the fluctuation. Then moving 25 steps ahead is conducted to cope with the delay problem, caused by the previous moving average calculation. By
considering the various combination of the compensated step size of the grey predictor, and the cut-off frequency of the low pass filter, the optimal parameters can be obtained, in the sense of the least square error in Eq. 2. Table 2 shows the optimal compensated step size in different cut-off frequency. It is found that the smaller the cut-off frequency, the longer the compensated step size is required. When the cut-off frequency is taken too large and then the more frequency component is in-cluded, the compensated result was not well on the contrary and the resulting error is very large. The opti-mal combination is that the cut-off frequency for the 2nd order low pass digital Butterworth filter is 0.012 times one half of sampling frequency of the original data, and the compensated step size for the grey predictor is 37 steps in our case. These parameters are adopted in this paper. As a result, the compensated data, shown in Fig. 4, has good synchronism with the progression of the original signal.
error p; xð cÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N XN k yð Þ yk p;xc k ð Þ 2 v u u t ; ð2Þ Where
y*: the objective signal
y: the signal previously processed by low pass filter and then grey predictor
N: the total number of sampling data
3.3 The gain self-tuning fuzzy controller
In order to prevent wire rupture under different machining conditions, a gain self-tuning fuzzy controller is proposed. Figure 5 is the configuration of the pro-posed self-tuning fuzzy inference with grey prediction control system, in which the PI-type Fuzzy Logic Con-troller (FLC) is involved. In order to keep the Rab at a
desired level, the inputs to the controller including the error e and the change of error ce, are described as follows:
e kð Þ ¼ Rð abÞref Rð abÞpð Þk
ce kð Þ ¼ Rð abÞpðk 1Þ Rð abÞpð Þk
Fig. 4 The original, filtered and compensated Rabdata
Table 2 The optimal compensated step size in different cut-off frequencies
2*cut-off frequency/ sampling frequency
Compensated step size Error
0.010 46 1.07e)2 0.012 37 0.98e)3 0.015 27 1.03e)2 0.020 17 1.19e)2 0.030 6 1.40e)2 0.050 1 1.74e)2 0.100 1 4.70e)2
E¼ e kð Þ Ge ð3aÞ CE¼ ce kð Þ Gce ð3bÞ Where (Rab)ref is the reference of the abnormal ratio,
(Rab)f is the abnormal ratio processed by the low pass
filter from the original Rab, and (Rab)p is the abnormal
ratio compensated by the grey predictor from the (Rab)f.
Ge and Gce are input scaling factors and in our cases their values are Ge=5 and Gce=40 respectively. E and CE in Eq. 3a and 3b are corresponding fuzzy variables. Each fuzzy variable is quantified into seven term sets: NB-Negative Big, NM-Negative Medium, NS-Negative Small, ZE-Zero, PS-Positive Small, PM-Positive Med-ium, and PB-Positive Big. The triangular membership functions for each fuzzy term set and the universes of discourse for each fuzzy variable, including input and output variable, are shown in Fig. 6.
According to Lee [11], the rule bases can be derived from a dynamic system response. A typical response of the Rabin WEDM process is shown in Fig. 7, where the
dash line stands for the desired set point. For the point a, the Raberror, E, is PB and the change of the Rab, CE,
is ZE and then the change of control action dU, the arc off-time, should be reduced to improve the machining speed. This linguistic control strategy can be described in fuzzy inference, as
IF E is PB and CE is ZE, THEN dU is NB
In the same way, the other points such as b, c, d.... can be described and the rule bases are summarised in Table 3. In addition, from Figs. 2 and 3, the effect on the Rab by adjusting arc off-time is the same as that by
the servo reference voltage. Consequently, the rule bases for arc off-time can be directly applied to those for the servo reference voltage without any modification. As a result, the design procedure of the controller can be greatly simplified.
Through the height defuzzification method [12], the crisp output of fuzzy inference dU can be obtained. The actual increment control actions in Eq. 5a and 5b, the change of arc off-time and the change of servo reference voltage, can be calculated by multiplying the scaling factors, Gu and Gv, respectively. The actual control actions at the kth sampling instant are calculated by
u kð Þ ¼ u k 1ð Þ þ du kð Þ ð4aÞ
Fig. 5 Self-tuning fuzzy logic and grey prediction control system
Fig. 6a,b Membership function of a E, CE and b dU
Fig. 7 A typical example of the Rabresponse for WEDM processes
Table 3 Rule bases of the FLC
CE E NB NM NS ZE PS PM PB PB ZE NS NM NB NB NB NB PM PS ZE NS NM NB NB NB PS PM PS ZE NS NM NB NB ZE PB PM PS ZE NS NM NB NS PB PB PM PS ZE NS NM NM PB PB PB PM PS ZE NS NB PB PB PB PB PM PS ZE
v kð Þ ¼ v k 1ð Þ þ dv kð Þ ð4bÞ where du kð Þ ¼ dU kð Þ Gu ð5aÞ dv kð Þ ¼ dU kð Þ Gv ð5bÞ Gu¼ Ku ej jU a; E; CEð ÞW ol; dpf ð6aÞ Gv¼ Kv ej jU a; E; CEð ÞW ol; dpf ð6bÞ Uða; E; CEÞ ¼ g1 þ g2 f CE; 5 Eð Þ ð7Þ W ol; dpf ¼ ol 1 þ 100:0 dpf e <0:01 ð8Þ u(k), u(k)1): arc off-time at the kth, (k)1)th sampling
instant respectively
v(k), v(k)1): servo reference voltage at the kth, (k)1)th sampling instant respectively
du(k): increment of arc off-time at the kth sam-pling instant
dv(k): increment of the servo reference voltage at the kth sampling instant
dU(k): crisp output of fuzzy inference at the kth sampling instant
Gu: output-scaling factor for the arc off-time Gv: output-scaling factor for the servo
refer-ence voltage g1¼ 0:5 1:0 þ að Þ g2¼ 0:5 1:0 að Þ
f x;ð aÞ ¼1 exp a xð Þ
1þ exp a xð Þ: hyperbolic tangent function ð9Þ dpf ¼ Rð abÞp Rð abÞf
Ku, Kv: the global gain about control actions a: III region tuneable parameter ol: overloading parameter sampling time Dt = 40 ms
Each of the tuneable output-scaling factors, Gu and Gv, has three factors: (1) The Raberror, |e|, is called the
attraction-causing factor. Its function is to attract Rabso
that it can reach and remain at the set-point, (Rab)ref.(2)
The overshoot-attenuating factorF(a,E,CE) which will attenuate impending overshoot or undershoot by reducing control actions in regions I and III (referring to Fig. 7). Instead of tuning the massive rule bases [13], this factorF(a,E,CE) in Eq. 7, is synthesised by a hyperbolic tangent function given in Eq. 9. Since a few parameters would be tuned, the task of design can be apparently simplified. The smaller the parameter a and the more the level to be attenuated. But too small a value will reduce the system response. (3) The overloading factorY(ol,dpf)
which will suppress the overloading phenomenon by enhancing the control actions once the Rab
apparently exceeded the safety level. For instance at the instant of sudden change of workpiece thickness during machining, the dpf in the Y will increase drastically
and accordingly enhance control actions to prevent the wire from breaking. Effect of Ku and Kv is similar to the gain of a general controller where a larger gain results in faster but unstable response. The relative magnitude between Ku and Kv will determine which control action will be dominantly tuned. For instance, when Kv is chosen larger, the servo reference voltage is mainly reg-ulated.
4 Experimental results and discussion
In order to verify the feasibility of the self-tuning fuzzy control with grey prediction proposed in the paper, four cases where wire rupture often occurs are tested. They are: (1) improper setting of machining parameters, (2) machining of a thick section workpiece, (3) machining of a workpiece with varying thickness, and (4) machining of a workpiece with a hole. In the following experiments, Fig. 8 shows the cross-section of workpiece used and Table 4 gives the corresponding machining parameters initially set. The fuzzy control algorithms are imple-mented in the PC using C language. A RS485 interface card installed in the PC is used for the data communica-tion between the PC and the machine. The sampling time used in the experiments is 40 ms. Table 5 shows the parameters of the controller for the four cases under study.
4.1 Case1—improper setting of machining parameters
The WEDM process is characterised by many machining parameters. An improper setting of machining parame-ters may be occurred, especially to a beginner. Figure 9a
shows the time variations of Rabwhen a 50 mm thickness
SKD11 workpiece shown in Fig. 8a is machined under the machining conditions of case no. 1 in Table 4. The fluctuating signal of Rabin Fig. 9a indicates the original
on-line measured Rab, while the solid line stands for the
filtered and compensated one. Form Fig. 9a, it is ob-served that the compensated Rab is continuously above
60%. Because of too many abnormal discharges, the wire electrode endured about 55 seconds and ruptured at last. Figures 9b and 9c show the control actions and the resulted time record of the Rab respectively, under
the same machining condition as that of Fig. 9a. The associated parameters of the controller are given in Table 5 (case no.1). As shown in Fig. 9b, when the machining parameters are set improperly and hence the Rab is over the safety level, the proposed controller can
rapidly lengthen the arc off-time and the servo reference voltage to improve the gap state. By so doing, Rab is
promptly controlled and remained around the set point in Fig. 9c. As a result, not only can the chance of wire rupture be eliminated, the allowable machining can be also achieved by employing the developed control strategy.
4.2 Case 2—the machining of a workpiece with a thick section
Machining thick section of a workpiece is often re-quired in industry applications. However, in this cut-ting condition wire rupture is likely to occur due to the poor flushing condition resulted from the nature of the thicker workpiece. This experiment is conducted to test the proposed controller in this situation. A workpiece of 100 mm thickness in Fig. 8b is tested in this case and the corresponding machining parameters are listed in Table 4 (case no. 2). Fig. 10a shows the same phe-nomenon as Fig. 9a but it lasts for a shorter duration before wire breaking because of the poor flushing condition. Figs. 10b and 10c show the control actions and the resulted time record of Rab, respectively for the
same machining condition as Fig. 10a. The associated parameters of the controller are given in Table 5 (case no.2). Similar to case 1, through the concurrent adjustments of the arc off-time and the servo reference voltage, Rab can be controlled around the set
Table 4 Machining parameters
in the experiments Case no. On-time Off-time Arc on-time Arc off-time Servo voltage Wire speed Wire tension Flushing pressure 1 6 15 4 13 35 4 10 2 2 6 15 4 15 40 4 10 2 3 6 15 4 30 40 4 10 2 4 6 15 4 35 45 4 10 2
Table 5 Parameters in the controller
Case no. Ge Gce a ol Ku Kv (Rab)ref
1 5 40 0.7 2.0 0.06 0.03 0.6
2 5 40 0.7 2.0 0.06 0.03 0.6
3 5 40 0.7 2.0 0.08 0.16 0.42
4 5 40 0.7 3.0 0.07 0.14 0.42
Fig. 9 a A wire rupture phenomenon-abnormal ratio without control actions b the control actions, the arc off-time and the servo reference voltage and c abnormal ratio with control actions under the improper machining parameter setting
point. Comparing Fig. 10b with Fig. 9b, it is noted that larger control actions are automatically tuned in this case.
4.3 Case 3—the machining of a workpiece having varying thickness
Figure 11a shows the phenomenon of wire rupture during machining of a workpiece having varying thick-ness shown in Fig. 8c. Machining parameters are also listed in Table 4 (case no. 3). At the instant of a sudden change of workpiece thickness in machining, there is an abrupt rise of abnormal discharge and this would result
in the burnt out of wire electrode instantaneously. Apparently, the larger the change of workpiece thick-ness, the lower the safety level of Rab should be set to
avoid wire rupture. But too low a reference level of Rab
will sacrifice the machining efficiency. Taking these into consideration, it is found from our experiments that the proper level of Rab for the 20 mm step increase in
workpiece thickness is 42%. Figs. 11b and 11c show the control actions and the resulted time record of Rab,
respectively under the same machining condition as that of Fig. 11a. The associated parameters of the controller are given in Table 5 (case no.3). Viewing from these figures, it is noted that there are excessive abnormal discharges as soon as the wire electrode contacted the
Fig. 10 a A wire rupture phenomenon-abnormal ratio without control actions b the control actions, the arc off-time and the servo reference voltage, and c abnormal ratio with control actions in machining a thick section workpiece
Fig. 11 a A wire rupture phenomenon-abnormal ratio without control actions b the control actions, the arc off-time and the servo reference voltage and c abnormal ratio with control actions in machining a workpiece having a step change of thickness
step change wall of the workpiece. The arc off-time and the servo reference voltage were quickly elongated to suppress the fast increasing Raband hence avoid the wire
rupture which may occur as that shown in Fig. 11a.
4.4 Case 4—the machining of a workpiece with a hole
Machining a workpiece with a hole as shown in Fig. 8d may be encountered in manufacturing industries. Although the upper and lower flushing pressure can be maintained at a constant level during machining, the centre part of wire undergoes poor flushing condition due to the impediment of the upper and lower part of the
workpiece. Similar to the case 3, there is an abrupt rise in Rab as shown in Fig. 12a as soon as the wire electrode
contacts the internal wall of the workpiece. Machining parameters and associated parameters of the controller for this case are also listed in case no. 4 of Tables 44 and 5, respectively. The control actions and the resulted time record of Rab, respectively under the same machining
condition as that of Fig. 12a are displayed in Figs. 12b and 12c. Once again, as Rab suddenly rises due to the
workpiece geometric discontinuity, controller can rap-idly respond and the arc off-time and the servo reference voltage are adjusted accordingly to overcome the poor gap condition. By so doing the appropriate machining can be maintained in the following cutting process.
5 Conclusions
With the objective of preventing wire rupture in the WEDM process, a gain self-tuning fuzzy controller has been developed. It provides a solution to the control system for the WEDM process. The proposed tuning algorithm consists of three factors including the attrac-tion-causing factor, the overshoot-attenuating factor, and the overloading factor. The output scaling factor of the fuzzy controller can be adaptively tuned in a wide variety of machining conditions. Experimental results show that not only can it immediately suppress transient situation once there is a sudden change of workpiece thickness, a stable performance can be also achieved during machining a workpiece of constant thickness. In the proposed control system, the grey predictor is adopted to compensate the time-delayed Rab caused by
the low pass filter data processing, and hence the gap state can be reflected in real time. By the concurrent adjustment of the arc off-time and the servo reference voltage, the controlled variable Rab can be regulated at
the proper level. As a result, the problems of wire rupture in most WEDM processes can be successively solved by the proposed control strategy.
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