Method of controlling wire-cut electric discharge contour machines errors

When cutting an arc or a corner in a workpiece on a wire-cut electric discharge machine, discharge power as required on rectilinear cutting is corrected on the basis of the amount of flexing of a wire electrode during rectilinear cutting and an amount of flexing of the wire electrode permitted in view of a tolerance in arc or corner cutting. The tension of the wire electrode is also adjusted and the speed of relative movement between the wire electrode and the workpiece is controlled. Dependent on whether a convex surface or a concave surface is cut in the workpiece, the rate at which the tension of the wire electrode and the speed of relative movement are proportional to each other is changed.

BACKGROUND OF THE INVENTION 
The present invention relates to a method of controlling a wire-cut 
electric discharge machine to cut a workpiece thereon along an arc or a 
corner with increased accuracy. 
In particular the present invention relates to wire-cut electric discharge 
machines having a pair of upper and lower wire guides and a wire electrode 
extending therebetween and kept taut for applying a voltage across a gap 
between the wire electrode and a workpiece to produce spark discharge 
across the gap, thereby cutting the workpiece with discharge energy. The 
workpiece can be cut to a desired contour by moving the workpiece with 
respect to the wire electrode under cutting command data. As shown in FIG. 
1, when the wire electrode 1 moves in and along a slot 3 in a given 
direction while cutting off the workpiece 2, a pressure is developed 
between the wire electrode 1 and the workpiece 2 due to the electric 
discharge to push back the wire electrode 1 in the direction of the arrows 
which is opposite to the direction in which the wire electrode 1 moves 
along, as shown in FIG. 2. The wire electrode 1 is therefore backed off or 
flexes from the position of the wire guides 4, 4. The cutting acuracy is 
not adversely affected to an appreciable extent by the amount of such wire 
flexing as long as the wire electrode 1 cuts the workpiece 2 along a 
rectilinear slot. However, when the workpiece changes its direction of 
relative movement through, for example, a right angle under a cutting 
command to cut a corner as shown in FIG. 3, the wire electrode has a 
tendency to be dragged inwardly of the corner due to the flexing of the 
wire electrode at a position in which the electric discharge takes place, 
with the result that the contour of the slot 3 as it is cut becomes 
different from a commanded shape as shown by the solid lines and has its 
configuration 3a rendered blunt or beveled as shown by the dotted lines. A 
similar error is also caused when cutting the workpiece along an arc as 
shown in FIG. 4. 
It is known that the blunt shapes of such arcuate or angular corners cut in 
workpieces can be improved by changing discharge conditions. However, 
there has not yet been developed and hence there has been a need for a 
method of effecting optimum corner cutting control under various cutting 
conditions. 
SUMMARY OF THE INVENTION 
Accordingly, it is an object of the present invention to provide a method 
of controlling a wire-cut electric discharge machine for minimzing any 
bluntness of an arcuate or angular corner cut in a workpiece under optimum 
discharge conditions for various cutting conditions. 
According to the present invention, a method of controlling a wire-cut 
electric discharge machine to cut an arc or a corner in a workpiece 
includes the step of correcting discharge power as required on rectilinear 
cutting based on an amount of flexing of a wire electrode on rectilinear 
cutting plus an amount of flexing of the wire electrode permitted in view 
of a tolerance in arc or corner cutting. This correcting step reduces the 
amount of flexing of the wire electrode when it cuts the arc or corner in 
the workpiece, thereby reducing the amount of any bluntness at the arc or 
corner, and improving cutting accuracy. The method also includes the steps 
of increasing a tension to which the wire electrode is subjected, and 
reducing a speed at which the wire electrode and the workpiece move 
relatively to each other. These additional steps serve to decrease the 
bluntness of the cut shape and to minimize an increase in the time 
required to cut the workpiece. The method further has the step of changing 
a rate at which the tension and the relative speed are proportional to 
each other dependent on whether a convex or concave surface is being cut 
in the workpiece. This changing step enables the wire-cut electric 
discharge machine to accurately cut the workpiece to without an 
appreciable amount of bluntness in the resulting contour. 
The above and other objects, features and advantages of the present 
invention will become more apparent from the following description when 
taken in conjunction with the accompanying drawings in which preferred 
embodiments of the present invention are shown by way of illustrative 
example.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
In FIG. 5, a wire electrode 1 moves with respect to a workpiece with a 
center of the wire electrode 1 following a commanded path illustrated by 
the solid line, cutting a slot having a width .epsilon. on each side of 
the commanded path and defined by boundaries shown by the dot-and-dash 
lines. It is now assumed that when a corner is cut which has an angle 
.theta. and a radius R, there is developed bluntness or error due to 
flexing of the wire electrode at the corner by an amount .delta. as shown 
by the dotted line though the path of movement of the wire electrode 1 has 
been commanded along the solid line. The present inventors conducted 
experiments to determine the relationship between the amount of bluntness 
or error .delta. and the amount of flexing D of the wire electrode 1 under 
a variety of cutting conditions, and found the following approximate 
equation: 
##EQU1## 
D is the amount of flexing of the wire electrode 1 upon corner cutting, 
.epsilon. is the half of the width of the slot which is cut, and K is a 
proportionality constant which ranges from 0.4 to 0.6 when .epsilon. and 
.DELTA.R.sub.T are expressed in mm. 
Study of the equations (1), (2) shows that the angle .theta. and the radius 
R are determined solely by a shape to be cut, and hence the amount of 
bluntness or error .delta. is dependent on the amount of flexing D of the 
wire electrode 1. The wire electrode 1 is caused to flex under the 
pressure of spark discharge produced between the wire electrode 1 and the 
workpiece 2, and the amount of flexing D is proportional to discharge 
power P. Therefore, the following expression can be derived: 
EQU P.delta.D.delta.f(.delta.) (3) 
This expression indicates that the amount of flexing D is proportional to 
the discharge power P, and the amount of bluntness .delta. can be varied 
by controlling the discharge power P. 
When the discharge power P is zero, the amount of flexing D is also zero 
and hence the amount of bluntness .delta. is also zero. However, the fact 
that the discharge power P is zero means that no discharge cutting is 
effected. In practice, since the discharge power P is of a finite value, 
the amount of flexing and the amount of bluntness cannot be nil. 
According to the present invention, a tolerable value .delta.o for the 
amount of bluntness .delta. is first determined, and then the discharge 
power P for the torelable amount is determined. 
More specifically, with the tolerable value .delta.o and the shape data 
(angle .theta. and radius R) being known, an amount of flexing Do of the 
wire electrode 1 for the tolerable value .delta.o is determined from the 
equations (1) and (2). Then, discharge power P1 consumed upon rectilinear 
cutting and an amount of flexing D1 of the wire electrode 1 caused by the 
discharge power P1 are measured. 
The discharge power P1 can be measured by finding a voltage Ve applied to 
the wire electrode 1 and a current flowing therethrough. Although the 
amount of flexing D1 of the wire electrode 1 can be measured by a 
measuring gage, it can also be measured automatically. The automatic 
flexing measurement can be effected by stopping the discharge, moving the 
wire electrode 1 and the workpiece 2 relative to each other, and detecting 
the interval 1 of their relative movement until the wire electrode 1 and 
the workpiece 2 are disengaged. 
The discharge power P1, the amount of flexing D1, and discharge power Po 
for causing the amount of flexing Do as determined by the equations (1), 
(2) have the following mutual relationships: 
##EQU2## 
Accordingly, the discharge power Po can be derived from the equation (4) 
using the discharge power P1 and the amount of flexing D1 which have been 
determined in advance, and the amount of flexing Do which has been found 
employing the tolerable value .delta.o and the shape data. When cutting an 
arcuate slot, the discharge power should be reduced to or below the ratio 
Do/D1 P1 with respect to the discharge power P1 consumed upon rectilinear 
cutting. The discharge power should start being reduced simultaneously 
with the starting of arcuate cutting or slightly before the starting of 
arcuate cutting, and the initial discharge power should be restored at the 
same time that the arcuate cutting is over. It is preferable that the 
discharge power be reduced in increments, but not instantly all the way to 
a reduced level. 
The discharge power can be changed by varying the peak value of a discharge 
current, or varying intervals of time in which the supply of a current is 
turned on and off. For capacitor discharging systems, the capacitance of 
the capacitor can be changed for varied discharge power. Where a servo 
feed mode in which a constant mean voltage is applied for cutting is 
employed for servo feed control of relative movement of the wire electrode 
and the workpiece, the discharge power and the feeding speed are 
controlled in proportion to each other with the result that no change will 
be caused in the width of a slot being cut. 
The method of the present invention attempts not only to reduce the amount 
of bluntness, but also to improve the shape of a blunt corner which is 
cut. The above-described method is concerned only with how to reduce the 
amount of bluntness, but the workpiece can be cut with higher accuracy by 
improving distortions in shape of other corner portions. 
To this end, the wire electrode 1 is kept under a tension T which 
progressively increases as the discharge power is reduced. FIG. 6 is 
illustrative of the relationship between the tension T and the amount of 
flexing D of the wire electrode 1. Assuming that the tension is expressed 
by T, the distance between the wire electrode guides 4, is L, and the 
width or distance between the opposite surfaces of the workpiece 2 is H, 
the following equations can be set up: 
##EQU3## 
Where N is the force that the wire electrode 1 undergoes due to the 
discharge. 
The above equations show that the amount of flexing D is in inverse 
proportion to the tension T, and henced the amount of flexing D becomes 
reduced and the amount of bluntness becomes smaller as the tension T is 
increased. When the tension T is increased, the magnitude of oscillation 
of the wire electrode is reduced, resulting in a reduced width of a slot 
being cut. Therefore, it is necessary that the feeding speed be reduced in 
proportion to the tension T, or the mean cutting voltage be increased for 
servoed feeding. Since a reduction in the cutting speed which is required 
by an increase in the tension depends on the type of the discharge cutting 
power supply used and other factors, the degree by which the cutting speed 
should be reduced needs to be determined experimentally. 
With the foregoing method, the amount of bluntness cannot be made smaller 
than the tolerable value .delta.o. For cutting with higher accuracy 
required, the radius R should be corrected to correct the shape of a slot 
being cut. 
FIG. 7 is explanatory of a mode of shape correction, in which a corrected 
radius R.sub.l is derived from a radius Ro to be cut. In FIG. 7, the 
radius Rl can be expressed geometrically as follows: 
##EQU4## 
Therefore, 
##EQU5## 
By equalizing (Lo-L.sub.1) to .delta.o, 
##EQU6## 
Hence, 
##EQU7## 
The workpiece should be cut with the radius R.sub.1 thus determined. 
The above method is based on the condition R&gt;.epsilon.. For cutting a 
corner with R&gt;.epsilon., the wire electrode acts only on one side of an 
arcuate slot, resulting in a one-sided discharge condition. For example, 
such a one-sided discharge condition is experienced when cutting a corner 
with R=0 as shown in FIG. 3, with the amount of bluntness .delta. at the 
corner being prevented from exceeding the amount of flexing D. Therefore, 
the discharge power P may be reduced until Do=.delta.o as in the foregoing 
example. This however may result in an instance in which the discharge 
power at the corner is excessively reduced until the relative speed of 
movement becomes 1/10 of the original speed. It is necessary to increase 
the overall time for cutting operation even when the region in which the 
discharge power should be reduced is limited to the corner. To avoid this 
condition, the tension of the wire electrode 1 should be increased at the 
same time that the discharge energy is reduced, as described above. This 
allows the amount of bluntness .delta.o and the tolerable amount of 
flexing Do to have the relationship Do=K.sub.2 .delta.o with K.sub.2 being 
permitted to range from 2 through 5, and hence the amount of flexing Do 
may be greater for the same amount of bluntness .delta.o. The greater 
amount of flexing Do permitted means that the relative speed of movement 
of the wire electrode and the workpiece may be larger, thus improving the 
problem of the reduction in the cutting speed. This also reduces the 
problem of a blunt corner which would be caused by the wire electrode 
displaced in an opposite direction due to the one-sided electric 
discharge. 
As described above, reduction of the discharge power and tension control 
should be combined for cutting corners and small arcs with 
R.ltoreq..epsilon.. It is most preferable to determine the region in which 
the discharge power is reduced as follows: 
For cutting a corner or a small arc, the discharge power should be reduced 
in a region starting at a position slightly before the area of the corner 
or small arc (that is, the position located ahead 1 to 2 times the 
distance E which is the amount of flexing of the wire electrode) and 
ending at a position in which the wire electrode completely enters the 
next path. For cutting an arcuate corner, the region in which the 
discharge power is to be reduced should extend to a position in which the 
wire electrode moves past the arc into the following path. After the wire 
electrode has entered the region, the discharge power should progressively 
be restored to the original level. 
To provide better cutting precision for substantially eliminating any 
error, there is known a method of changing the cutting path and a method 
of changing the cutting conditions in addition to the method described 
above. The method of changing the cutting path results in a compliated 
corrected path, and hence is practically infeasible. Various processes 
have been proposed for varying the cutting conditions. One of the better 
processes is to change the width of a slot being cut. 
According to the present invention, the speed at which the workpiece and 
the wire electrode are moved relatively to each other is controlled 
dependent on whether the surface to be cut with accuracy is convex (as 
shown at 3a in FIGS. 3 and 4) or concave (as shown at 3b in FIGS. 3 and 
4). More specifically, for the foregoing tension control, the ratio at 
which the tension is proportional to the mean cutting voltage is selected 
to be larger in cutting a convex surface and smaller in cutting a concave 
surface. This allows the speed of the relative movement to be much greater 
when a convex surface is being cut, resulting in a smaller slot width and 
a reduced degree of bluntness at the convex corner. When a concave surface 
is cut, the speed of the relative movement is rendered much smaller, with 
the consequences that the width of the slot becomes greater, and the 
concave surface can be cut deeply to reduce the bluntness of the concave 
corner. 
A wire-cut electric discharge cutting machine for effecting the method of 
the present invention will be described in detail. 
As shown in FIG. 9, the wire-cut electric discharge cutting machine 
comprises an inverted L-shaped column 5 mounted on and projecting upwardly 
from a base 6, the column 5 supporting thereon a capacitor box 7 serving 
as a power supply. A workpiece attachment table 22 is mounted on the base 
6 and movable thereon two-dimensionally by motors for driving the table 22 
in X- and Y-directions. A workpiece 2 is fastened to the workpiece 
attachment table 22 by a clamp 23. A wire electrode 1 is fed along in the 
directions of the arrows while the workpiece is being cut by electric 
discharge. The wire electrode 1 is unwound from a feed reel 8 supporting a 
roll of unused wire electrode and is coiled around a brake roller 9 which 
serves to brake the wire electrode 1 in the direction in which the latter 
is fed or pulled out, for thereby giving the wire electrode 1 a tension T. 
The wire electrode 1 is further trained around a roller 10, a lower guide 
roller 11, an upper guide roller 12, a roller 13, and a feed roller 14 
which is rotatable by a drive motor for feeding the wire electrode 1. A 
pinch roller 15 is positioned adjacent to the feed roller 14 and urged by 
a spring 16 to press the wire electrode 1 against the feed roller 14. The 
wire electrode 1 as it has been used is wound up by a takeup reel 17. The 
column 5 supports on its distal end a movable member 18 on which there is 
mounted a slider 19 movable in a Z-direction and supporting a boring unit 
20 having a boring tool 21 for forming a hole in the workpiece 2 from 
which cutting operation is started. 
FIG. 10 shows in block form a control unit for controlling the wire-cut 
electric discharge cutting machine shown in FIG. 9. The control unit 
comprises an arithmetic and logical unit 25 such as a microprocessor, a 
tape reader 26 for reading cutting command data (such as starting-point 
data, ending-point data and the like) from an NC tape 30, a control panel 
27 for commanding the thickness of a workpiece and the speed of feed 
thereof, a main memory 28 for storing the cutting command data as read 
from the NC tape 30 and a control program, and an interface circuit 29 
connected to a motor 22' for moving the workpiece attachment table 22, the 
brake roller 9 for controllingly tensioning the wire electrode 1, and a 
capacitor 31 for controlling the discharge current flowing through the 
wire electrode 1. The above components of the control unit are connected 
to a bus 24. 
In operation, the cutting command data are read by the tape reader 26 and 
stored together with the data commanded by the control panel 27 into the 
memory 28. The arithmetic and logical unit 25 is controlled by the control 
program stored in the memory 28 to control rotation of the motor 22' 
through the interface circuit 29 based on the data stored in the memory 
28. At this time, the arithmetic and logical unit 25 reads the value of a 
discharge current i.sub.1 and the value of a tension T1 preset at the time 
of rectilinear cutting out of the memory 28, and controls the capacitor 31 
housed in the capacitor box 7 and the brake roller 9 through the interface 
circuit 29 based on the read data. 
Under the control of the control program stored in the memory 28, the 
arithmetic and logical unit 25 effects the steps of carrying out the 
arithmetic operations expressed by the equations (1), (2) and (4) to 
compute a discharge current, increasing the tension T to increase the 
speed of feed in response thereto, and carrying out the arithmetic 
operation of the equation (12). Stated otherwise, the control program 
comprises instructions for executing the above steps. 
In response to a command for cutting a corner or arc in the workpiece, the 
arithmetic and logical unit 25 reads cutting command data for the cutting 
command out of the memory 28 to compute corner angle data .theta.. Then, 
the arithmetic and logical unit 25 determines a radius R from the cutting 
command data, reads a slot width .epsilon., a proportionality constant k, 
and a tolerable amount of bluntness .delta.o from the memory 28, and 
carries out the arithmetic operations given by the equations (1), (2) to 
compute a tolerable amount of flexing Do of the wire electrode. 
Thereafter, the arithmetic and logical unit 25 reads the value of 
discharge current i.sub.1 and the amount of flexing D1 of the wire 
electrode stored in the memory 28 at the time of rectilinear cutting, and 
effects the arithmetic operation (4) to compute a discharge current io 
required when cutting the corner of the arc. To cut a corner or a small 
arc that needs tension control, the arithmetic and logical unit 25 added a 
fixed value .DELTA.T to the given tension T to compute the increased 
tension (T+.DELTA.T), and furthermore carries out an arithmetic operation 
to reduce the speed .upsilon. by .DELTA..upsilon. which corresponds to the 
tension increase .DELTA.T. When controlling the speed at the convex and 
concave surfaces, the speed reduction .DELTA..upsilon. should be varied 
dependent on the contour of the convex and concave surfaces. When it is 
necessary to make a radius correction, the arithmetic and logical unit 25 
reads the radius R, the amount of bluntness .delta.o and the angle 
.theta., and executes the arithmetic operation expressed by the equation 
(12) to find a corrected radius R.sub.1. In this manner, the arithmetic 
and logical unit 25 effects necessary arithmetic operations each time a 
command for cutting an arc or a corner is provided, and supplies data on a 
discharge current to the capacitor 31, data on a tension to the brake 
roller 9, and data on a radius and a speed to the motor 22' via the 
interface circuit 29 prior to initiating arc or corner cutting, for 
thereby controlling the discharge power consumed by the wire electrode 1, 
the tension thereof, and the movement of the workpiece attachement table 
22 for improved cutting accuracy at the arc or corner. 
With the method of the present invention, as described above, the discharge 
power as consumed on rectilinear cutting is corrected on the basis of the 
amount of flexing of the wire electrode on rectilinear cutting plus an 
amount of flexing thereof allowed in view of a tolerance in cutting an arc 
or corner in a workpiece. The wire electrode when cutting an arc or corner 
therefore flexes to a smaller amount, thus reducing the amount of 
bluntness at the arc or corner and increasing the cutting accuracy. This 
permits electric discharge cutting operation to find a wider range of 
applications. The method of the present invention can reduce the corner or 
arc bluntness to a much smaller degree and minimize an increase in the 
cutting time by increasing the tension of the wire electrode and at the 
same time reducing the speed of relative movement between the wire 
electrode and the workpiece. The present invention is also of high 
practical advantage in that convex and concave surfaces can be cut in a 
workpiece with high accuracy and without appreciable bluntness or error 
through changing the rate at which the tension and the speed of relative 
movement are proportional to each other as they are increased. 
Although certain preferred embodiments have been shown and described in 
detail, it should be understood that many changes and modifications may be 
made therein without departing from the scope of the appended claims.