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Study on Wire-EDM: Inprocess Measurement of Mechanical Behaviour of Electrode-Wire
Study on Wire-EDM: lnprocess Measurement of Mechanical Behaviour of Electrode-Wire N. Kinoshita ( l ) , M. Fukui and Y. Kimura, University of Tokyo/Japan Summary : It is important to analyse the behaviour of the wire in the gap of Wire-EDM. There are some papers dealing with the existence of the incurvation of the wire and that of the wire-lag behind But in these papers problems were analysed only by static view the position given by NC program. The vibration of wire as well as the above mentioned incurvation or wire-lag has close point. relation to the accuracy of profiled workpiece. A change of direction of programmed path causes the electrode wire to behave complicatedly. In this paper, the mechanical behaviour is observed dynamically in process over a wide range of machining conditions, the difference between programmed path and produced profile is characterized.
1. Introduction Technological aspects of wire-EDM before 1976 were explained in detail on the-key-note-paperE of 26th general assembly of CIRP. 1) Compared with what the technology was, the growth of wire-EDM is very remarkable. For example, the cutting speed has become trebled only in eight years. The sooner the speed of development is, the greater number of problems which should be solved are generated. For improving the accuracy of wire-EDM, it is one of the important problems how to cope with the incurvation of electrode-wire in the working gap. The existence of the incurvation and that of the wire-lag behind the position given by NC-program has alread been pointed out and discussed by some people.2) ,3frr4) Not only the above mentioned incurvation but also the vibration of electrode-wire has close relation to the accuracy of profiled workpiece, and it is important to discuss both incurvation and vibration at a time. In this paper,these mechanical behaviour is observed in process over various conditions,the difference between programmed path and produced profile is characterized, and finally how to provide superior accuracy is discussed.
!P 1(”
Fig.2 Area of Wire-Vibration ( XY-Plane )
I
Fiq.3 Area of W-V. ( FZ-Plane
2. State of Electrode-Wire Fig.1 shows a schema of a electrode-wire which is machining a groove in F-direction. The coordinates X,Y,Z travel with @des,Gl and G2, controlled by NCcontroller of wire-EDM-machine. Statically, the wire is incurved as shown in Fig.1, and dynamically the wire is always vibrating in the shaded area shown in Fig.2 and Fig.3.Considering the front shape of a groove cut by means of wire-EDM, it is possible to approximate the shape of the area to an ellipse on LM-plane as well as on XY-plane. 3. Area of Wire-Vibration As shown in Fig.1, the wire is surrounded by four probes, Pl,P2,P3 and P4. Each probe is moved back and forth along L-axis or M-axis by means of the mechanism shown in Fig.4. The probe is fixed mechanically to a micro-meter screw which is drive,nby a stepping motor,but is isolated electrically from the screw. Each pulse supplied to the stepping motor shift the probe 0.48 pm. Assuming the probe is fixed on some adequate position in LM-plane, the vibrating wire comes into contact intermittently with it. This mechanical
I
Fig.4 Probe Unit L
I
M
Fig.1 Schematic View
->at
T=t2
Fig.5 Probe vs. Area of Wire-Vibration (LM-Plane)
Annals of the CIRP Vol. 33/1/1984
89
contact is detected electrically. Supplying N pulses having peak value of 5V to the probe during Ts sec, it is checked up for every pulse whether an electrical short circuit between the wire and the probe is built up or not. If for n pulses among N nshort" is detected, (%) (1) C = (n/N) x 100 is calculated with micro processor, TK-85 connected to the detecting circuits. As a matter of course the closer the probe is located to the wire,the higher the value of the contact ratio, C is. Monitoring the above mentioned contact ratio on every probe, a micro computer, FM-8, supplies control pulses to the stepping motor of probe unit (Fig.4). Therefore, if the contact ratio, C, is greater than a constant, Co, the probe is retreated from the wire. On the contrary, if C S Co , the probe is advanced to the wire. In this paper the clock frequency for detecting the contact ratio was 614.4 kHz. Repeating preliminary experiments the value of Ts and CO were selected at 0.1 sec and 0 %,respectively. And it was confirmed that the boundary of the area of wire-vibration could be detected both on L-axis and M-axis through the controlled location of the probe without disturbing the motion of wire.
4 . Experiments and Discussions
At several machining conditions the area of wirevibration has been measured in process. Both the wire-EDM-machin and the discharge -power-Generator were the same to.our previous papers, 6) , 7 ) and fixed machining conditions are summerized in Table 1. The experimental results and discussions are described below. EXPERIMENT 1 : Shape of the Wire When Discharge Power is "off. ( Preliminary Experiment) Winding electrode-wire at 20 mm/min. without supplying discharge power, the shape or incurvation of the wire was measured on LM-plane using the method described in the previous section. During first 30 seconds, tension of 300 gf was loaded on the wire. Thereafter the value of tension was changed stepwise to 400,500,600,700,800,700,600,500,400,300gf at every 30 sec. Tension=400 gf ~Tention=8OOg f
Fig.5 shows the location of each probe at two different times, tl and t2, on LM-plane. Two ellipses represent the corresponding areas of wire-vibration. Counting the number of pulses sent to the stepping motor during a period, (t2-tl), each shift of the four probes, AL1 or AL2 or AM3 or AM4 is calculated. Here, the following four values are defined : AEL AEM AAL AAM
=
0.5
X
(AL1
-
AL2)
(2) (3) (4) (5)
= 0.5 x (AM3 - AM4) = 0.5 x (AL1 + AL2) = 0.5 x (AM3 + AM4)
Time Duration (min.) Effect of Wire-Tension
Fig.6
Generally speaking, the area of wire-vibration represented by ellipse changes its size, position, and orientation as shown in Fig.5. In this figure Z L and are L- and M-component of shift of the center of the ellipse during a eriod, (t2-tl), ( k l is ) not always respectively. Therefore equal to A E L ( M ) . I f the areaof wire-vibration is a circle, both AEL=AEL and AEM=AEM are true. And if coordinates of the ellipse are parallel to L,Mcoordinates the above mentioned relations are true, too. On the contrary, if the coordinates of the ellipse are not parallel to L,M-coordinates, the above relations are not guaranteed. Fortunately in wireEDM the eccentricity of the ellipse is close to 1.0, therefore it is possible to consider that A E L = m , and that A E M - m In this case, according to the same reason, A A L and AAM in equations (4) and (5) are nearly equal to L-component and M-component of the increment of the amplitude of wire-vibration, respectively, on LM-plane.
Fig.6 shows the time-history of AEL. Increase of AEL means that the wire approaches to Z-axis in Fig.1, in the other words that the radius of curvature of the wire increases. From this result it is clear AEL follows correctly the change of wire-tension with short time lag. If wire-tension is 300 gf, it is too weak to suspend the wire stably, So the trace of AEL plotted on Fig.6 fluctuated considerably. Therefore the data obtained at the wire-tension=300gf is omitted here. 48,
8'
.
,
i i 3 i 5 6 i i 4
'
.
.
.
.
,
.
.
,
Time Duration (min.)' Vsing AEL and AEM the area of wire-vibration is estimated approximately on work-surface defined as XY-plane in Fig.1 through the following equations : Shift of the center (X-component); (6) AEX= (l/L) x AEL Shift of the center (Y-component); AEY= (l/L) x AEM (7) Increment of the amplitude (X-component); AAX= (sin(Ln/S)/sin(Pn/S)) x AAL (8) Increment of the amplitude (Y-component); AAY= (sin(Ln/S)/sin(pn/S)) x AAM (9) where.1 ,L and S were already defined in Fig.3. (1= 31 mm, L=80 mm, S=117 mm). Equations, ( 8 ) and (91, are conducted with the assumption that the wire vibrates with the first natural mode.5). Whether the above four assumptions are true or not is checked through experiments later.
-4
I
FANUC TAPECUT B-Series
Power Generator
RC-relaxation Circuit capacitor : 0.1 F, 0.5 F(Ex.4) resistor : 25 open circuit voltage : 150 V
Workpiece
material : alloy steel (SKD 11) thickness: 20 mm winding speed
:
1
28
1
2
3
4
5
6
7
8
9
Time Duration (min.)
Ea
a 0
Equipment
38
38 28
i0 0'
i
2
1
2
3
i
5
6
7
0
4
Time Duration (min.)
'
20 mm/min. 0
Table 1 Experimental Procedures
3
4
5
6
7
8
9 0
Time Duration (min.) Fig.7 Change of Area of Wire-Vibration (on LM-Plane)
90
From Fig.6 it is judged that the difference between the value of &EL at wire-tension=800 gf and For the purpose of checking the at 4 0 0 gf was 18 pm. reliability of this measuring system, the above mentioned value was optically measured with micrscope, simultaneously. In the latter case the difference was 15 pm. Therefore it was confirmed that this system was very reliable. EXPERIMENT 2
:
EXPERIMENT 4
Effect of Wire-Feed-Rate
Setting the wire-tension at 680 gf a set of experiments described below was carried out with the machining conditions shown in Table 1. 1) During first one minute a groove is cut , feeding the electrode-wire in the direction of '-X" at the constant rate of 0.1 mm/min.. 2) During second four minutes the feed rate is set up to 0.25 mm/min.. 3) During last five minutes the feed rate is re-set to 0.1 mm/min. again. The results are shown in Fig.7. At first, from the top diagram in Fig.7 the following two facts are pointed out : A) If wire-feed-rate increases, the wire is pushed backward (AEL is decreased) by means of greater force caused by repetiting discharqe pulses, because the faster the wire feed is, the more frequent the repetition of discharge is. As described in the introduction this fact is very popular and is called 'wire-lag". But in process mesurment of this value has never been reported. B) It takes very long time (2 or 3 minutes in this experiment) until the wire occupies a stable location against wire-guides. The other three diagrams in Fig.7 shows : C) As a matter of cause, in the direction of "kM" (iY) which is perpendicular to the direction of " t L" (2x1 the wire does not change its location. (see AEM). D ) The amplitude of the wire-vibration measured on LMplane is affected by the wire feed rate as shown by AAL and AAM in Fig.7. It is observed that the faster the feed Is, the smaller the amplitude is. EXPERIMENT 3
:
For the asymmetricity of the positions of thesc nine points around the origin in Fig.8, another reason is considered why the wire fluctuates. The boundary condition suspending the wire is changed corresponding to the wire-feed-direction, especially when a "v"shape groove is used for wire guide. It is important to study this problem for designing better windingsystem in future.
Effect of Feed Direction
:
Corner Machining
In Experiment 3 the effect of the change of wirefeed direction has been surveyed,generally. In this experiment a detailed study on the transient situation of the electrode-wire during machining a groove of "L"-shape is carried out. Selecting wiretension=400 gf and wire-feed-rate=0.20, 0.25 and 0.30 mm/min., the "L"-shape grooves are cut. It is programmed that the electrode-wire is fed constantly in the direction of "-X" during first two minutes, then the direction of feed is changed 90° in the direction of "-Y". In Fig.9 a process of "L"-shape-groove-cutting has been reproduced by computer graphics. In these graphics hollow square is a position of the center of the area of wire-vibration, cross is a programmed position of the center of electrode-wire on the surface of workpiece. The diameter of circle corresponds to the diameter of electrode-wire, 200 um. Ellipse represents a area of wire-vibration calculated with DEL, AAL, AEX, AAX etc., where discharge gap shown in Fig.3 is assumed to be 0. This assumption has a close relation to the value of Co defined in the Section 3. If Co is not equal to 0, the width of gap should be experimentally settled at a special value for the above calculation. In Fig.9 the change of wire-feed-direction was programmed at T=O. The real direction in which the experimented wire advanced did not coinside with the programmed direction until two or three minutes later. Comparing the calculated shape of the above mentioned graphics with the actual shape on the machined workpiece it was confirmed that the difference between both shapes were within a few pm in size. Therefore the assumption described at the end of Section 3 is guaranteed,and it is confirmed that this in process measuring system is very reliable.
During first one minute the electrode-wire is fed at a constant rate, 0.25 mm/min. in the direction of "+XI'. The other machining conditions are the same to Experiment 2. Changing feed-direction 4 5 ' counter clockwise at every one minute, machining of groove is continued. After eight minutes it is expected that the wire returns to the starting position. The above mentioned path of the wire is programmed and controlled with the NC-controller attached to the wire-EDMmachine. At every step the mean value of AEL, AEL* and the mean value of AEM, AEM* are calculated. Thereafter for the purpose of studying the problem on the work-surface, AEX and AEY are calculated substituting those values (AEL* and AEM*) into equations (2) and (3),respectively. The nine sets of (AEX,hEY) obtained by the above calculations are plotted on a plane. Selecting the origin at the mean position of the above nine points, the results were plotted in Fig. 8 . Depending upon the same reason at Experiment 2, the wire is forced to go back and the center of wirevibration had recorded such a wide fluctuation as shown in Fig.8.
AEY
I 6=270°
+40t
I
I
/
I
-40
I
6=9
I
-8d -80
I
1
-40
0
1
t40
'
+80
AEJ
Fig.8 Fluctuation of Center of Wire-Vibration ( on Work-Surface )
Fig. 9
Reproduction of Process
91
It is very popular to compensate the above mentioned getting out of shape by means of program. For wrighting such program it is needed to collect a great quantity of experimental data and utilize knowhow. But, using this newly developed in process measuring method it is expected to correct program inprocess and to cut more complicated profile with high accuracy. Further, it is considered that the accurate profile can be cut with low wire-tension which makes it to be possible to supply higher discharge power for the purpose of improving the cutting speed of wire-EDM. 5.Conclusion A new in process mesuring method of the area of wire-vibration'& wire-EDM has been developed. For cutting accurate profile, it is very important to estimate the width of the groove which depends upon the behaviour of electrode-wire. If there is a bend in the programmed path of electrode-wire,the transient behaviour of the wire is very complicated. It is not much to say that the correct estimation of the transient behaviour decides the accuracy of wireEDM. The method described here has been approved to solve this problem. Several experiments has affirmed that the method carries out the purpose very reliably.
References 1) A.C.M.Dani6ls : NC Wire Spark Erosion - A Survey. Ann.CIRP, 25/2,1976, p521-525 2) N.Schmidt-Ott : Technik des Funkenerosiven Drahtschneidens. Fertigung, 4 , 1970, p131-135 3 ) F.Balleys : Materialabtrag und Genauigkeit beim Drahterosieren. Pertigung, 5/77, p131-134 4 ) W. Khnig und A.Weiss : Genauigkeitsprobleme Funkenerosiven Sneiden. Industrie Anzeiger, 99(98), 1977, ~1979-1981 S)K.Horio,N.Kinoshita and M.Fukui : Study of Wire Behaviour in Wire-EDM - Explication of Wire Vibration. J.Japan SOC. of Electrical Machining Engineers, 16(31), 1982, pl-13 6) N.Kinoshita,M.Fukui and H.8hichida : Study on EDM with Wire Electrode; Gap Phenomena. Ann. CIRP,25/1, 1976, p141-145 7) N.Kinoshita, M.Fukui and G.Gamo : Control of WireEDM Preventing Electrode from Breaking. Ann.CIRP,31/1
92
1. Introduction Technological aspects of wire-EDM before 1976 were explained in detail on the-key-note-paperE of 26th general assembly of CIRP. 1) Compared with what the technology was, the growth of wire-EDM is very remarkable. For example, the cutting speed has become trebled only in eight years. The sooner the speed of development is, the greater number of problems which should be solved are generated. For improving the accuracy of wire-EDM, it is one of the important problems how to cope with the incurvation of electrode-wire in the working gap. The existence of the incurvation and that of the wire-lag behind the position given by NC-program has alread been pointed out and discussed by some people.2) ,3frr4) Not only the above mentioned incurvation but also the vibration of electrode-wire has close relation to the accuracy of profiled workpiece, and it is important to discuss both incurvation and vibration at a time. In this paper,these mechanical behaviour is observed in process over various conditions,the difference between programmed path and produced profile is characterized, and finally how to provide superior accuracy is discussed.
!P 1(”
Fig.2 Area of Wire-Vibration ( XY-Plane )
I
Fiq.3 Area of W-V. ( FZ-Plane
2. State of Electrode-Wire Fig.1 shows a schema of a electrode-wire which is machining a groove in F-direction. The coordinates X,Y,Z travel with @des,Gl and G2, controlled by NCcontroller of wire-EDM-machine. Statically, the wire is incurved as shown in Fig.1, and dynamically the wire is always vibrating in the shaded area shown in Fig.2 and Fig.3.Considering the front shape of a groove cut by means of wire-EDM, it is possible to approximate the shape of the area to an ellipse on LM-plane as well as on XY-plane. 3. Area of Wire-Vibration As shown in Fig.1, the wire is surrounded by four probes, Pl,P2,P3 and P4. Each probe is moved back and forth along L-axis or M-axis by means of the mechanism shown in Fig.4. The probe is fixed mechanically to a micro-meter screw which is drive,nby a stepping motor,but is isolated electrically from the screw. Each pulse supplied to the stepping motor shift the probe 0.48 pm. Assuming the probe is fixed on some adequate position in LM-plane, the vibrating wire comes into contact intermittently with it. This mechanical
I
Fig.4 Probe Unit L
I
M
Fig.1 Schematic View
->at
T=t2
Fig.5 Probe vs. Area of Wire-Vibration (LM-Plane)
Annals of the CIRP Vol. 33/1/1984
89
contact is detected electrically. Supplying N pulses having peak value of 5V to the probe during Ts sec, it is checked up for every pulse whether an electrical short circuit between the wire and the probe is built up or not. If for n pulses among N nshort" is detected, (%) (1) C = (n/N) x 100 is calculated with micro processor, TK-85 connected to the detecting circuits. As a matter of course the closer the probe is located to the wire,the higher the value of the contact ratio, C is. Monitoring the above mentioned contact ratio on every probe, a micro computer, FM-8, supplies control pulses to the stepping motor of probe unit (Fig.4). Therefore, if the contact ratio, C, is greater than a constant, Co, the probe is retreated from the wire. On the contrary, if C S Co , the probe is advanced to the wire. In this paper the clock frequency for detecting the contact ratio was 614.4 kHz. Repeating preliminary experiments the value of Ts and CO were selected at 0.1 sec and 0 %,respectively. And it was confirmed that the boundary of the area of wire-vibration could be detected both on L-axis and M-axis through the controlled location of the probe without disturbing the motion of wire.
4 . Experiments and Discussions
At several machining conditions the area of wirevibration has been measured in process. Both the wire-EDM-machin and the discharge -power-Generator were the same to.our previous papers, 6) , 7 ) and fixed machining conditions are summerized in Table 1. The experimental results and discussions are described below. EXPERIMENT 1 : Shape of the Wire When Discharge Power is "off. ( Preliminary Experiment) Winding electrode-wire at 20 mm/min. without supplying discharge power, the shape or incurvation of the wire was measured on LM-plane using the method described in the previous section. During first 30 seconds, tension of 300 gf was loaded on the wire. Thereafter the value of tension was changed stepwise to 400,500,600,700,800,700,600,500,400,300gf at every 30 sec. Tension=400 gf ~Tention=8OOg f
Fig.5 shows the location of each probe at two different times, tl and t2, on LM-plane. Two ellipses represent the corresponding areas of wire-vibration. Counting the number of pulses sent to the stepping motor during a period, (t2-tl), each shift of the four probes, AL1 or AL2 or AM3 or AM4 is calculated. Here, the following four values are defined : AEL AEM AAL AAM
=
0.5
X
(AL1
-
AL2)
(2) (3) (4) (5)
= 0.5 x (AM3 - AM4) = 0.5 x (AL1 + AL2) = 0.5 x (AM3 + AM4)
Time Duration (min.) Effect of Wire-Tension
Fig.6
Generally speaking, the area of wire-vibration represented by ellipse changes its size, position, and orientation as shown in Fig.5. In this figure Z L and are L- and M-component of shift of the center of the ellipse during a eriod, (t2-tl), ( k l is ) not always respectively. Therefore equal to A E L ( M ) . I f the areaof wire-vibration is a circle, both AEL=AEL and AEM=AEM are true. And if coordinates of the ellipse are parallel to L,Mcoordinates the above mentioned relations are true, too. On the contrary, if the coordinates of the ellipse are not parallel to L,M-coordinates, the above relations are not guaranteed. Fortunately in wireEDM the eccentricity of the ellipse is close to 1.0, therefore it is possible to consider that A E L = m , and that A E M - m In this case, according to the same reason, A A L and AAM in equations (4) and (5) are nearly equal to L-component and M-component of the increment of the amplitude of wire-vibration, respectively, on LM-plane.
Fig.6 shows the time-history of AEL. Increase of AEL means that the wire approaches to Z-axis in Fig.1, in the other words that the radius of curvature of the wire increases. From this result it is clear AEL follows correctly the change of wire-tension with short time lag. If wire-tension is 300 gf, it is too weak to suspend the wire stably, So the trace of AEL plotted on Fig.6 fluctuated considerably. Therefore the data obtained at the wire-tension=300gf is omitted here. 48,
8'
.
,
i i 3 i 5 6 i i 4
'
.
.
.
.
,
.
.
,
Time Duration (min.)' Vsing AEL and AEM the area of wire-vibration is estimated approximately on work-surface defined as XY-plane in Fig.1 through the following equations : Shift of the center (X-component); (6) AEX= (l/L) x AEL Shift of the center (Y-component); AEY= (l/L) x AEM (7) Increment of the amplitude (X-component); AAX= (sin(Ln/S)/sin(Pn/S)) x AAL (8) Increment of the amplitude (Y-component); AAY= (sin(Ln/S)/sin(pn/S)) x AAM (9) where.1 ,L and S were already defined in Fig.3. (1= 31 mm, L=80 mm, S=117 mm). Equations, ( 8 ) and (91, are conducted with the assumption that the wire vibrates with the first natural mode.5). Whether the above four assumptions are true or not is checked through experiments later.
-4
I
FANUC TAPECUT B-Series
Power Generator
RC-relaxation Circuit capacitor : 0.1 F, 0.5 F(Ex.4) resistor : 25 open circuit voltage : 150 V
Workpiece
material : alloy steel (SKD 11) thickness: 20 mm winding speed
:
1
28
1
2
3
4
5
6
7
8
9
Time Duration (min.)
Ea
a 0
Equipment
38
38 28
i0 0'
i
2
1
2
3
i
5
6
7
0
4
Time Duration (min.)
'
20 mm/min. 0
Table 1 Experimental Procedures
3
4
5
6
7
8
9 0
Time Duration (min.) Fig.7 Change of Area of Wire-Vibration (on LM-Plane)
90
From Fig.6 it is judged that the difference between the value of &EL at wire-tension=800 gf and For the purpose of checking the at 4 0 0 gf was 18 pm. reliability of this measuring system, the above mentioned value was optically measured with micrscope, simultaneously. In the latter case the difference was 15 pm. Therefore it was confirmed that this system was very reliable. EXPERIMENT 2
:
EXPERIMENT 4
Effect of Wire-Feed-Rate
Setting the wire-tension at 680 gf a set of experiments described below was carried out with the machining conditions shown in Table 1. 1) During first one minute a groove is cut , feeding the electrode-wire in the direction of '-X" at the constant rate of 0.1 mm/min.. 2) During second four minutes the feed rate is set up to 0.25 mm/min.. 3) During last five minutes the feed rate is re-set to 0.1 mm/min. again. The results are shown in Fig.7. At first, from the top diagram in Fig.7 the following two facts are pointed out : A) If wire-feed-rate increases, the wire is pushed backward (AEL is decreased) by means of greater force caused by repetiting discharqe pulses, because the faster the wire feed is, the more frequent the repetition of discharge is. As described in the introduction this fact is very popular and is called 'wire-lag". But in process mesurment of this value has never been reported. B) It takes very long time (2 or 3 minutes in this experiment) until the wire occupies a stable location against wire-guides. The other three diagrams in Fig.7 shows : C) As a matter of cause, in the direction of "kM" (iY) which is perpendicular to the direction of " t L" (2x1 the wire does not change its location. (see AEM). D ) The amplitude of the wire-vibration measured on LMplane is affected by the wire feed rate as shown by AAL and AAM in Fig.7. It is observed that the faster the feed Is, the smaller the amplitude is. EXPERIMENT 3
:
For the asymmetricity of the positions of thesc nine points around the origin in Fig.8, another reason is considered why the wire fluctuates. The boundary condition suspending the wire is changed corresponding to the wire-feed-direction, especially when a "v"shape groove is used for wire guide. It is important to study this problem for designing better windingsystem in future.
Effect of Feed Direction
:
Corner Machining
In Experiment 3 the effect of the change of wirefeed direction has been surveyed,generally. In this experiment a detailed study on the transient situation of the electrode-wire during machining a groove of "L"-shape is carried out. Selecting wiretension=400 gf and wire-feed-rate=0.20, 0.25 and 0.30 mm/min., the "L"-shape grooves are cut. It is programmed that the electrode-wire is fed constantly in the direction of "-X" during first two minutes, then the direction of feed is changed 90° in the direction of "-Y". In Fig.9 a process of "L"-shape-groove-cutting has been reproduced by computer graphics. In these graphics hollow square is a position of the center of the area of wire-vibration, cross is a programmed position of the center of electrode-wire on the surface of workpiece. The diameter of circle corresponds to the diameter of electrode-wire, 200 um. Ellipse represents a area of wire-vibration calculated with DEL, AAL, AEX, AAX etc., where discharge gap shown in Fig.3 is assumed to be 0. This assumption has a close relation to the value of Co defined in the Section 3. If Co is not equal to 0, the width of gap should be experimentally settled at a special value for the above calculation. In Fig.9 the change of wire-feed-direction was programmed at T=O. The real direction in which the experimented wire advanced did not coinside with the programmed direction until two or three minutes later. Comparing the calculated shape of the above mentioned graphics with the actual shape on the machined workpiece it was confirmed that the difference between both shapes were within a few pm in size. Therefore the assumption described at the end of Section 3 is guaranteed,and it is confirmed that this in process measuring system is very reliable.
During first one minute the electrode-wire is fed at a constant rate, 0.25 mm/min. in the direction of "+XI'. The other machining conditions are the same to Experiment 2. Changing feed-direction 4 5 ' counter clockwise at every one minute, machining of groove is continued. After eight minutes it is expected that the wire returns to the starting position. The above mentioned path of the wire is programmed and controlled with the NC-controller attached to the wire-EDMmachine. At every step the mean value of AEL, AEL* and the mean value of AEM, AEM* are calculated. Thereafter for the purpose of studying the problem on the work-surface, AEX and AEY are calculated substituting those values (AEL* and AEM*) into equations (2) and (3),respectively. The nine sets of (AEX,hEY) obtained by the above calculations are plotted on a plane. Selecting the origin at the mean position of the above nine points, the results were plotted in Fig. 8 . Depending upon the same reason at Experiment 2, the wire is forced to go back and the center of wirevibration had recorded such a wide fluctuation as shown in Fig.8.
AEY
I 6=270°
+40t
I
I
/
I
-40
I
6=9
I
-8d -80
I
1
-40
0
1
t40
'
+80
AEJ
Fig.8 Fluctuation of Center of Wire-Vibration ( on Work-Surface )
Fig. 9
Reproduction of Process
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It is very popular to compensate the above mentioned getting out of shape by means of program. For wrighting such program it is needed to collect a great quantity of experimental data and utilize knowhow. But, using this newly developed in process measuring method it is expected to correct program inprocess and to cut more complicated profile with high accuracy. Further, it is considered that the accurate profile can be cut with low wire-tension which makes it to be possible to supply higher discharge power for the purpose of improving the cutting speed of wire-EDM. 5.Conclusion A new in process mesuring method of the area of wire-vibration'& wire-EDM has been developed. For cutting accurate profile, it is very important to estimate the width of the groove which depends upon the behaviour of electrode-wire. If there is a bend in the programmed path of electrode-wire,the transient behaviour of the wire is very complicated. It is not much to say that the correct estimation of the transient behaviour decides the accuracy of wireEDM. The method described here has been approved to solve this problem. Several experiments has affirmed that the method carries out the purpose very reliably.
References 1) A.C.M.Dani6ls : NC Wire Spark Erosion - A Survey. Ann.CIRP, 25/2,1976, p521-525 2) N.Schmidt-Ott : Technik des Funkenerosiven Drahtschneidens. Fertigung, 4 , 1970, p131-135 3 ) F.Balleys : Materialabtrag und Genauigkeit beim Drahterosieren. Pertigung, 5/77, p131-134 4 ) W. Khnig und A.Weiss : Genauigkeitsprobleme Funkenerosiven Sneiden. Industrie Anzeiger, 99(98), 1977, ~1979-1981 S)K.Horio,N.Kinoshita and M.Fukui : Study of Wire Behaviour in Wire-EDM - Explication of Wire Vibration. J.Japan SOC. of Electrical Machining Engineers, 16(31), 1982, pl-13 6) N.Kinoshita,M.Fukui and H.8hichida : Study on EDM with Wire Electrode; Gap Phenomena. Ann. CIRP,25/1, 1976, p141-145 7) N.Kinoshita, M.Fukui and G.Gamo : Control of WireEDM Preventing Electrode from Breaking. Ann.CIRP,31/1
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