JPS5930511B2 - automatic welding equipment - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to an automatic welding device, and more particularly to an automatic welding device that uses a torch as a welding line detector (sensor).

The welding torch and the workpiece are mutually controlled in space according to the positional information and control information stored in the storage device,
A playback automatic welding device that automatically performs welding according to a program is well known.

It is known that a sensor is used to cause the welding torch to follow the welding line of the workpiece. However, conventionally, a sensor for detecting a welding line has been attached separately from the torch and in the vicinity of the torch, resulting in a large size around the torch. As a result, the torch or sensor may not be able to enter the deep part of a narrow workpiece.
The sensor does not work effectively when the groove size of the weld line is small. In addition, there were various problems such as the structure being complicated and expensive. Therefore, the present inventors have previously proposed an extremely superior automatic welding device in which the torch itself acts as a sensor. In such a proposed automatic welding device, a detection power source different from a normal welding power source is connected between the torch electrode and the workpiece, and the energization state between the torch, that is, the electrode and the workpiece is detected at this time. It is designed to detect. However, in such a proposed automatic welding device, if a consumable electrode is used as the electrode, the length of the projection from the torch will not necessarily be constant in the sensing mode. In addition, the welding voltage applied between the electrode and the workpiece and the welding current flowing therein are determined depending on conditions such as the thickness of the workpiece, the condition of the groove, and the thickness of the electrode. , is commanded in teaching mode.

However, in the sensing mode, if the protruding length of the electrode is not constant, the voltage and current in this automatic welding mode will be constant (optimal values) because the automatic welding mode is controlled by the information obtained in the sensing mode. It won't be. For example, if sensing is performed while the protrusion length remains short, the resistance of the electrode is small during welding, so
The current becomes large and the voltage becomes small. Therefore, the voltage and current will be different from the optimum voltage and current, and the welding condition or quality may not be as desired. Therefore, the main object of the present invention is to provide a consumable electrode-type automatic welding device that uses a welding torch as a sensor, so that the consumables protrude from the torch during automatic welding, regardless of the protruding length of the consumable electrode during sensing. An object of the present invention is to provide an automatic welding method for maintaining the length of an electrode at a predetermined value.

The invention, in summary, is an apparatus for automatically welding a weld line on a workpiece by means of a workpiece fixture and a consumable electrode torch whose movement and relative position are controlled by control means. In the sensing mode, the control means applies detection power to the electrode, reads mutual positional information between the workpiece and the torch when the electrode tip approaches the workpiece and discharges, and uses this positional information to determine the welding line. It senses the position, and also detects the magnitude of the welding voltage applied to the electrode or the welding current flowing therein in auto mode, that is, automatic welding mode, and the difference between this and the welding voltage or welding current commanded in advance, for example, in teaching mode. This is an automatic welding device that calculates the difference and controls the longitudinal position of the torch in the direction in which this difference should be made zero. The above objects and other objects and features of the invention will become more apparent from the following detailed description with reference to the drawings.

Before describing embodiments of the present invention, an automatic welding apparatus that is a background of the present invention and is effective in carrying out the present invention will be described.

However, it should be pointed out in advance that the present invention is not limited to such embodiments. FIG. 1 is an overall perspective view showing an automatic welding apparatus according to an embodiment of the present invention.

In FIG. 1, this eye movement welding apparatus 100 includes a work W
The torch 10 is configured so that the fixture 105 (not shown) can be moved left and right, front and back, or rotated around the horizontal axis H.
Each of the fixtures 108 of 9 is configured so as to be able to move toward the ground or rotate around the vertical axis L, and
A control box 400 including a general-purpose computer (microcomputer) for automatically controlling the movement and rotational position of the torch 109 is provided. Let me explain in more detail. A first frame 102 is fixed to one side of the L-shaped floor plate 101 in plan view.

A cart 103 that is movable in the left-right direction (X-axis direction in the figure) is provided on the top of the frame 102. The power means (not shown) for this truck 103 is a known motor with a brake equipped with a speed reducer in this embodiment, and the power transmission means (not shown) is a known engagement means (so-called It is a ball screw. In addition, on the top of the trolley 103, there is a
A second frame 104 that is movable is provided. This frame 1
Although the power means and power transmission means of 04 are not shown,
A motor with a brake and a ball screw with a similar speed reducer. The front part of the frame body 104 has an angle of θ in the figure.
An axially rotatable work fixture 105 is provided. Although not shown, the power means of this workpiece fixture 105 is also a known motor with a brake and a reduction gear. A third frame 106 is erected at the other end of the floorboard 101 .

This frame body 106 has a vertical direction (Z-axis direction in the figure).
A movable arm 107 is provided. The power means and power transmission means of this arm 107 are also a similar motor with a brake and a ball screw, although not shown. The distal end of the arm 107 is arranged around the vertical axis L (
A fixture 108 for a torch 109 is provided which is rotatable in the Φ axis direction in the figure. Although not shown, the power means of this torch mount 108 is also a known motor with a brake and a reduction gear. In addition, the installation position of the torch 109 is
The welding point WP on the extension of the center line of the torch 109 is configured to coincide with the vertical axis L, and the mounting angle is determined depending on the welding mode to be performed (butt welding, fillet welding, etc.) and the workpiece. shall be optimally selected according to the shape of the Further, a current is applied to the torch 109 from a power supply device 200.

The forward rotation, reverse rotation, moving speed, welding current, etc. of the power means (motor with brake with reducer) of each part are automatically controlled in accordance with the program by the above-mentioned leg box 400 and the welding control device 300, and the above-mentioned The mutual positions of the two fixtures 105 and 108 are controlled so that the welding point WP follows the welding line of the workpiece W (not shown) and so that automatic welding can be performed in the position with the best welding conditions. A remote control ("remote control") panel 500 is provided for the purpose of programming or manual operation. In this embodiment, the welding point WP on the extension of the center line of the torch 109 is configured to coincide with the vertical axis L, so it remains constant regardless of the rotation of the fixture 108 in the Φ axis direction. The attitude of the torch 109 with respect to the same welding point can be changed arbitrarily by rotating the fixture 108 (in the Φ-axis direction).

That is, this embodiment is an automatic welding device with five degrees of freedom. Furthermore, the power supply device 200 includes a torch 1.
A consumable electrode supply means 201 for supplying a consumable electrode 209 to the consumable electrode 209 is provided.

The consumable electrode supply means 201 further includes a force device 2 for imparting a bending direction to the consumable electrode 209.
02 is provided. In this embodiment, a flexible tube for guiding a consumable electrode 209 is formed in the force device 202 in a loop shape, so that the tip of the consumable electrode 209 is always bent to a certain degree. Of course, in addition to this embodiment, the force device 202 may be of a type that clamps the consumable electrode with guide rollers to force the consumable electrode into a linear shape. A predetermined voltage is applied to the consumable electrode 209 sent out from the consumable electrode supply means 201 by the voltage application means 203 . The voltage applying means 203 is selectively connected to either a welding power source 205 or a discharge high voltage power source 206 as a detection power source via a changeover switch 204. As is well known, the welding power source 205 is a large current, low voltage power source, and the discharging high voltage power source is a small current, high voltage power source. The welding power source 205 is directly connected to the workpiece w, and the discharge high voltage power source 206 is connected to the workpiece w via a current sensor 207. The current sensor 207 detects a change in current accompanying the discharge of the electrode 209 and provides a signal to the control box 400. Control box 400 controls changeover switch 204 . That is, during normal welding, the changeover switch 204 is set to the welding power source 2.
05 side, and control is performed to switch to the discharge high voltage power source 206 when sensing the weld line. FIG. 3 is a partial vertical sectional view showing in detail a part of the welding torch 109 used in the present invention.

This welding torch 109 has a supply means 201 in its hollow part.
A collect chuck 109a through which a consumable electrode 209 supplied from
9b is fitted into the cylinder 109c, and this cylinder 1
09c, and a pipe 109d for introducing and discharging high-pressure fluid (for example, high-pressure gas in a shield gas cylinder). In FIG. 3, it is assumed that the left side is the torch tip and the right side is connected to the flexible tube 202. The consumable electrode 209 supplied from the consumable electrode supply means 201 is led out to the tip of the torch 109 through the hollow part of the collection chuck 109a. Normally, the piston 109b is biased to the left in the figure by the spring 109e, and the collet chuck 109a is open. Therefore, the consumable electrode 209 can move freely within this welding torch 109. For example, in sensing mode, when it is necessary to clamp the consumable electrode 209, the piston 109b is pushed to the right in the figure by supplying high pressure fluid from the tube 109d. Therefore, collet chuck 109
a is tightened by the inner periphery of the tip of this piston 109b, and the consumable electrode 209 is clamped. In this way, regardless of the protruding length of the consumable electrode 209, the sensing operation is carried out in a constant state.
FIG. 11 is a schematic block diagram showing an electric circuit of an automatic welding apparatus according to an embodiment of the present invention described above.

In the figure, the control box 400 includes a CPU 4Ol and a ROM
4O2, RAM4O3, interface 404, servo circuits SX, SY, Sθ, SZ, SΦ, and A/D
conversion circuits 405 and 406. In ROM4O2,
Operation programs as shown in FIGS. 5 to 8, which will be described later, are stored. The CPU 4Ol operates according to this operation program. RAM4O3 stores various calculation information and teaching information. Each servo circuit SX
, SY, Sθ, SZ, and SΦ are circuits for respectively driving motors MX, MY, Mθ, MZ, and MΦ for displacing each axis. A/D conversion circuit 405 is given a welding current in automatic welding mode, and converts this welding current value into a digital signal. This digital signal is read into the CPU 4Ol via the interface 404. Similarly, A/D conversion circuit 406 is given a welding voltage in automatic welding mode, and converts this welding voltage value into a digital signal. This digital signal is read into the CPU 4Ol via the interface 404. A switch 204 and a remote control panel 500 are further connected to the interface 404. The sensing operation for using the welding torch as a sensor will be explained below with reference to FIGS. 4 to 7. The operation of automatically controlling the welding point WP from point P6 to point P7 will be described with reference to the flowchart shown in FIG.

First, the computer (not shown) in the pedestal box 400 is set to teaching mode, and by manually operating the operation buttons (not shown) on the panel 500, the welding point WP of the torch 109 is set to points P1→P6→P7 using a known playback method. At point P1, the Φ angle is Φ where the torch is in the XZ plane.
1 and the sensor command at point P6.
At step 7, welding commands are each input into the computer as a user program. Then, the computer is set to auto mode, and a start button (not shown) is manually operated. Then, the contents of the first step of the user program are stored and output.

Its content is as a position command for the torch 109, points P, (X
l, Y,, Zl, Φ1) are commanded. Torch 1 according to
09 and the work w are automatically controlled, the position of the welding point WP of the torch 109 reaches the point P1, and the Φ angle becomes Φ
1, an arrival signal is returned to the computer, and the contents of the next step are stored and output. The contents are torch 1
The next position command after 09 is point P6 (X2, Yl, Z2, Φ1
) and a sensor command. Based on this sensor command, a command to the changeover switch 204 is outputted by a system program that has been separately input into the computer in advance, and the switch 204 is thereby
4 is switched.

Similarly, the system program outputs a command to lower the Z axis, that is, a command to lower the torch 109, and the torch 109 descends. Since a high voltage potential difference is operated between the electrode of the torch 109 and the workpiece W by the power source 206, the tip of the electrode of the torch 109 is at the point P2.
(The maximum distance between the workpiece w and the tip of the electrode is about 2 mm), a spark flies between them. Thus, the sensor 207 detects this current, and based on the signal, Zs of the position information of the current position P2 is taken in, and the computer calculates the difference ΔZ between this value and Z2 of the command information for this step. At the same time, the system program allows the torch 109
is raised by a certain amount (1 to 2 mm) and reaches point P3. Then, the computer shows that the Φ angle is Φ1 and that X1 and
2, the next sensing direction
In the figure, it is determined that the workpiece W is facing rightward (*), a command to move the workpiece W in that direction is output, and the workpiece W moves to the right.

In the same manner as described above, when the electrode and the workpiece w approach each other and a spark flies at point P4, the difference ΔX between the X-direction position Xs of P4 at that time and the command X2 is calculated. Then, the workpiece w is returned by a certain amount to reach a point P. In this way, it is determined that sensing is complete, and based on that information, the previous command to the switch 204 is erased, and the switch 204 returns to its original state. Therefore, the point P6 (X2, Yl, Z2,
The position command to Φ1) is executed, but at this time, the above-determined ΔZ and ΔX are corrected, that is, the point P
6' (X2+ΔX, Yl, Z2+ΔZ, Φ1), and the welding point WP of the torch 109 is located at the welding line WL.
The position is controlled correctly at the starting point. Then, due to the arrival signal similar to that described above, the next step, that is, point P7 (X2,
Similarly, when the command to Y2, Z2, Φ1) is output, Δ
Point P7' (X2+ΔX, Y2, Z2
+ΔZ, Φ, ) is output, and a welding command is also output, and the torch 109 performs welding while moving linearly from point P6 to point P7'.

In this way, even if the welding line WL deviates from the initially programmed position, the starting point position is detected and the commanded position is moved in parallel to correct it.

In the above description, the relative position of the tip of the consumable electrode with respect to the torch 109 is such that the consumable electrode always protrudes from the torch 109 in the same shape due to the action of the force device 202, and its protrusion length is determined by the clamping during sensing. It will be understood that because of this, the relative positions are always the same, and there is no problem with the above-mentioned function as a sensor.

Note that by flowing gas (for example, CO2) through the torch 109, more stable sensing can be performed. Furthermore, it will be understood that this embodiment can be applied when the angle formed by the two side surfaces constituting the weld line WL is known in advance (in this case, it is a right angle). Next, with reference to FIGS. 6 and 7, another embodiment will be described mainly regarding its differences from the previous embodiment.

Note that this embodiment can be applied when the angle formed by the two side surfaces constituting the weld line WL is not known in advance. The welding line WL in the X-axis direction in this embodiment is a butt welding line having a groove, which is intended to be welded downward, and the torch 109 maintains a vertical posture. The teaching step in this case is to first obtain positional information Xl, Y, .
Input Zl and sensing direction -X (also serves as sensor command).

As a second step, position information Xl, Y2, Zl of point P9 above the terminal end of Y-axis direction welding line WL from the position of point P1 is obtained.
and input the sensing direction -X. As a third step, a command to implement the position information of point P8 sensed in the first step and a sensing completion command are input. Furthermore, in the fourth step, a command for implementing the position information of the point PIO sensed in the second step and a welding command are input. The execution of the above user program will be described below.

First, in the first step, the torch 109 and the workpiece W are
The positions of the torch 1 are mutually controlled, and the torch 1 is placed at the position P shown in FIG.
09 is controlled. Since this step includes a sensor command, a command to the changeover switch 204 is output, whereby the switch 204 is switched and a high voltage is applied between the electrode of the torch 109 and the workpiece W. Then, a command to lower the Z axis, that is, a command to lower the torch 109, is output, and the torch 109 descends. Then, at point P2 (X,, Yl, Z2), a spark flies and the output signal from sensor 207 is input to the computer. In response to this input signal, the computer takes in the position information X, , Yl, Z2 of this point P2 and stores it in a certain predetermined location. Next, since the sensor command is sensing direction -X, determine the sensing direction from that,
(In this case, move the workpiece to the right.) Output the movement command.

Then, a spark flies at point P3 (X2, Y,, Z2), and the signal from sensor 207 is input to the computer. The position information of this point P3 is taken in by this input signal and stored in a certain predetermined location. Next, a command is output to return the workpiece W by a certain amount (appropriately determined depending on the size of the welding line WL) in the opposite direction to the previous movement in the X-axis direction, that is, in this case, the workpiece W moves slightly to the left. When the point P4 (X3, Yl, Z2) is reached, a command to lower the Z axis is output again, and the torch 109 is lowered.

Then, at point P5 (X3, Y,, Z3), the sensor 20
The signal No. 7 is input to the computer, and the position information of this point P5 is taken in and stored in a certain predetermined location. Furthermore, a command to move the workpiece W to the left (in the same direction as the previous movement in the X direction) is output, and furthermore, the signal from the sensor 207 is input to the computer at point P6 (X4, Yl, Z3). Capture location information and store it as well.

In this way, by storing four pieces of position information based on four inputs of the signal from the sensor 207, it is determined that sensing is complete, and the intersection of the line connecting points P2 and P6 and the line connecting points P3 and P5 is calculated, and the point Get P7.

Then, a target position P8 (X5, Y, Z4) of the torch 109 (slightly above the normal point P7) is calculated from the point P7 and stored at a predetermined position. This completes this step. The next step is point P9 (Xl
, Y2, Zl) and includes a sensor command.

Therefore, in the same way as in the previous step, the aiming position PlO(X6, Y2
, Z5) is calculated and stored. Furthermore, in the next step, the position information of point P8 stored in the first step is called up and executed.

At this time, since the sensing completion command is also included, the previous command to the changeover switch is erased, the switch 204 returns to its original state, and a welding voltage is applied between the torch 109 and the workpiece w. In the next step, the second
Since the point PIO memorized in step is given a position command and a welding command is given, the workpiece w moves in the Y-axis direction, that is, the torch 109 moves relatively from point P8 to PIO while performing welding. Move and perform automatic welding.

According to this embodiment, even if the weld line WL is formed by a groove of an undefined shape, the intersection of the side surfaces is calculated and the groove shape is determined, thereby achieving the best welding result. It is possible to determine the target welding position.

Further, although this embodiment has been described with respect to a straight welding line WL, even if the welding line WL is bent,
All the aiming positions of the torch 109 at the starting point, each bending point, and the ending point may be calculated in advance, and each point may be sequentially executed by PTP control. After sensing the welding line in this manner, the automatic welding mode is subsequently entered.

In the automatic welding mode, as shown in the flowchart of FIG. 8, control is performed to generate an arc between the ablation electrode 209 of the torch 109 and a workpiece (not shown). If no current flows between the consumable electrode and the workpiece at this time, it is determined that the welding is abnormal, and an alarm is used to notify the welding process, for example. Furthermore, when the welding current flows, the welding voltage at this time is first sampled and read into the CPU 4Ol included in the control box 400. After this welding voltage sampling operation, CPU4Ol and ROM4
A microcomputer composed of O2 and RAM4O3 functions as a voltage/current detection means, a comparison means, and a longitudinal position control means. Further, the CPU1 determines whether the sampled welding voltage is approximately close to a predetermined value, that is, a value preset in the teaching mode. For example, a preset voltage is 20V, and it is determined whether the sampled welding voltage is within ±5V of this set voltage. If the welding voltage is within a predetermined value range, the welding current is then sampled and C
Read into PU4Ol. The CPU 4O1 accordingly determines whether the sampled welding current is within the taught predetermined value range. For example, a preset current is 250A, and it is determined whether the sampled welding current is within a range of ±50A from this set current. If the welding current is also within a predetermined value range, welding is continued, and upon completion of welding, the process proceeds to the next step. If the welding voltage is outside the predetermined value range, the CPU 4Ol subsequently determines whether it is larger or smaller than the predetermined value.

Similarly, if the welding current is outside the predetermined value range, it is determined whether it is above or below the predetermined value. When the welding voltage is less than a predetermined value and when the welding current is more than a predetermined value, sensing is performed while the tip of the torch is too close to the workpiece, and this result indicates that the position is being controlled. , CPU4Ol moves the torch by, for example, 2 mm in the (-) direction of the torch axis. In other words, since the tip of the torch is too close to the work, the torch is controlled to move away from it. In addition, when the welding voltage is above a predetermined value and when the welding current is below a predetermined value,
In other words, this indicates that the tip of the torch is too far away from the workpiece. Therefore, the CPU 4Ol controls the torch to move, for example, 2 mm in the (+) direction of the torch axis. That is, the tip of the torch is controlled to move in a direction closer to the workpiece. When the torch movement control in the (1) direction or (+) direction is completed, the welding voltage or welding current is sampled again to determine whether it is within a predetermined value range.

In this way, the welding voltage or welding current in the automatic welding mode is regulated within the range of the welding voltage or welding current value set in advance in the teaching mode. This means that the welding voltage set by the protrusion length of the consumable electrode,
This means that automatic welding is performed with the current approximately close to a satisfactory value. In addition, in the above-mentioned example,
The flow and discharge of the high pressure fluid through the pipe 109d may be performed manually by operating a switching valve (not shown), or the switching valve may be automatically switched by a signal from a program.

Furthermore, in the embodiment described above, the welding power source 205 and the detection high voltage power source 206 are connected by a mechanical changeover switch 204.
Although the switching is performed according to the above, an embodiment as shown in FIG. 9 or FIG. 10 may also be considered.

In FIG. 9, a welding power source 205 is applied to a voltage applying means 203, that is, a depletion electrode 209, through a unidirectional element 205a such as a diode. The detection power supply 206 is connected to the output side of this diode 205a. Here, the detection power supply 206 uses, for example, an oscillator that generates a high frequency voltage, and is activated or activated in the sensing mode. Therefore, in the example of FIG. 9, in the sensing mode, the voltage from the welding power source 205 and the detection power source 206 are
is applied to the consumable electrode 209 in a superimposed manner. Note that in the welding mode, the power source 206 may be disabled. In the embodiment shown in FIG. 10, the welding power source 205 is connected to the voltage applying means 203 via a current limiting resistor 206a.

A changeover switch 204a is connected in parallel to this current limiting resistor 206a. In the welding mode, this switch 204a is closed to shunt the current limiting resistor 206a. Therefore, the consumable electrode 20
9 receives the output from the welding power source 205 as is. In the sensing mode, the changeover switch 204a is opened and the current limiting resistor 206a is enabled. Therefore, in this sensing mode,
A voltage from the welding power source 205 is applied to the consumable electrode 209 via the resistor 206a. Due to the action of this current limiting resistor 206a, only an extremely smaller current flows in the sensing mode than during welding. As described above, according to the present invention, the welding current and welding voltage are detected in the automatic welding mode after the sensing mode, and compared with set values to control the distance between the tip of the torch and the workpiece. Even if the protruding length of the consumable electrode in the sensing mode is not constant, the protruding length of the consumable electrode in the automatic welding mode is constant, and the welding voltage and welding current can be kept at optimal values.

Therefore, the finish of welding is extremely good.

[Brief explanation of the drawing]

FIG. 1 shows an overall perspective view of an automatic welding apparatus according to an embodiment of the present invention. FIG. 2 is a partially illustrative view relating to the consumable electrode supply means. FIG. 3 is a partially enlarged sectional view showing details of the welding torch 109. FIG. 4 is an illustrative view showing one form of a weld line sensed by the present invention. FIG. 5 is a flow diagram showing the sensing operation in the case of FIG. FIG. 6 is an illustrative view showing another form of the weld line sensed by the present invention. FIG. 7 is a flow diagram showing the sensing operation in the case of FIG. FIG. 8 is a flow diagram showing one embodiment of the present invention. FIG. 9 and FIG. 10 are schematic diagrams showing other embodiments for switching to a welding power source and a detection power source, respectively. FIG. 11 is a schematic block diagram showing an electric circuit of an automatic welding device according to an embodiment of the present invention. In the figure, 100 is an automatic welding device, 10
7 is an arm, 105 is a workpiece fixture, 109 is a torch, 20
1 is a consumable electrode supply means, 204 is a changeover switch, 205
is a welding power source, 206 is a detection power source, 207 is a current sensor, 209 is a consumable electrode, 109a is a collection chuck,
109b is a piston, and 109c is a cylinder.

Claims (1)

[Claims] 1. A consumable electrode type torch including a consumable electrode supplied from a supply means and a workpiece mount for attaching a workpiece, and configured to be switchable between a sensing mode and an automatic welding mode, wherein the sensing mode Then, when a power source is connected to the consumable electrode and the tip of the consumable electrode is close to the workpiece and energized, the position of the welding line of the workpiece is sensed based on the comprehensive positional information of the workpiece and the torch. In the automatic welding mode, the automatic welding apparatus automatically welds the weld line of the workpiece by controlling the relative positions of the consumable electrode type torch and the workpiece fixture, and in the automatic welding mode after the sensing, , voltage/current detection means for detecting at least one of the welding voltage applied to the consumable electrode and the welding current flowing through the electrode, and a voltage/current detection means for detecting at least one of the welding voltage applied to the consumable electrode and the welding current flowing through the electrode; Comparing means for comparing a reference voltage value or a reference current value; and a longitudinal position control means for controlling a longitudinal position of the torch with respect to a mounting position of the workpiece based on a comparison result of the comparing means.
Automatic welding equipment. 2. The above-mentioned comparison means calculates a difference between the welding voltage or welding current detected by the voltage/current detection means and the preset reference voltage value and reference current value. Automatic welding equipment according to scope 1. 3. The automatic welding apparatus according to claim 2, wherein the longitudinal position control means is configured to control based on the difference in a direction in which the difference should be made zero.