JP3534819B2 - Welding gun electrode wear detection method - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a resistance welding technique using servo control, and more particularly to an electrode drive source of a spot welding gun used by being attached to an industrial electric robot. The present invention relates to a method for detecting a wear amount of a welding gun electrode when a servo motor is used as a method. In a conventional resistance welding gun, an electrode is operated by a driving source such as an air cylinder or a motor, and an object to be welded is sandwiched between a pair of electrodes, pressed and held, and a large current flows. We were doing welding by that. Since the paired electrodes gradually wear due to the pressurization and welding heat during the welding, it is necessary to detect the amount of wear of the electrodes during operation of the robot and correct the position of the electrodes. As a method of correcting the electrode position, Japanese Patent Laid-Open No.
In Japanese Patent No. 52771, the case of arc welding is used.
There is disclosed an automatic welding apparatus capable of easily aligning the origin of a welding torch and a workpiece at the start of welding and correcting the position when the welding torch is worn (wearing). This is done by applying the tip of the welding torch to the origin of the work to be welded (workpiece) and setting the position of the welding torch at this time as the origin of the welding torch. ,
The origin of the welding torch is corrected by applying the tip of the welding torch to the workpiece. [0004] However, in this method, the welding torch is directly applied to the workpiece to calculate the amount of wear of the welding torch and to correct the position of the welding torch. When the workpiece is a thin iron plate, there is a problem that the workpiece is deformed. Further, in the publication, there is a problem that the method is complicated even when applied to a welding gun having a plurality of electrodes to be paired, such as a C-shaped welding gun and an X-shaped welding gun. SUMMARY OF THE INVENTION An object of the present invention is to detect a wear amount of an electrode in a welding gun having a pair of electrodes such as a C-type welding gun and an X-type welding gun without causing deformation of a workpiece. Detecting electrode wear for electrode position correction by positioning the electrode based on the amount of wear to minimize deformation of the workpiece caused by displacement of the pressurized point due to electrode wear during welding It is to provide a method. Accordingly, the present invention has solved the problems of the prior art by providing a method for detecting the amount of wear of a welding gun electrode according to the present invention. FIG . 1 and FIG. 2 show an embodiment of the present invention to be described later.
FIG.
The welding gun electrode wear amount detection method according to each reference example
Block diagram and float showing the configuration of an apparatus used for
It is a chart. FIG. 3 is an explanatory view of the operation of the C-shaped welding gun, and FIG. 4 is an explanatory view showing a correction state of the electrode position. 5 and 6 are a block diagram and a flow chart, respectively, showing the configuration of an apparatus used in the method for detecting the amount of wear of the welding gun electrode according to the embodiment of the present invention . Although the welding gun shown in FIGS. 1 to 6 is a C-shaped welding gun, it may be a welding gun having two pairs of electrodes, such as an X-shaped welding gun. First, a reference example will be described. As shown in FIG. 1, an industrial robot controlled by a servomotor with a position detector (not shown) has another servomotor 3 with a position detector 4 at the arm tip 1 as a drive source of a moving-side electrode 6. A C-type welding gun 2 in which only the movable electrode 6 is opened and closed is attached. The moving-side electrode 6 is driven via the ball screw 5 by the servomotor 3 controlled by an electrode driving circuit 14 in the control device. The fixed electrode 7 is attached to the fixed side of the C-type welding gun 2 and moves up and down the C-type welding gun 2 attached to the robot arm tip 1 controlled by the robot drive circuit 12 in the control device. This makes it move up and down. Next, the circuit configuration in the control device will be described. The program data 9 includes robot position data and moving-side electrode position data of each welding point in a state where electrodes are not worn, and detection of total electrode wear. Positions (robot position data and moving-side electrode position data when detecting the amount of electrode wear) are stored in advance. The position data read from the program data 9 by the program data reading circuit 10 is a reference position writing / wear amount detection switching circuit 16.
Depends on the setting status of. The reference position writing / wear amount detection switching circuit 16 can be set to “reference position writing (writing)”, “wear amount detection (detection)”, and a neutral state (a state that is neither “writing” nor “detection”). Like that. Here, the program data reading circuit 10 reads the robot position data and the moving-side electrode position data of each welding point when the reference position writing / wear amount detection switching circuit 16 is in the neutral state.
When the reference position writing / wear amount detection switching circuit 16 selects “write” or “detection”, the electrode total wear amount detection position is read. The robot position data is sent to the robot position command creation circuit 11, and the moving-side electrode position data is sent to the electrode command position creation circuit 13. The electrode position detection circuit 8 reads the electrode position from the position detector 4. Only when the reference position writing / wear amount detection switching circuit 16 is set to “writing” or “detection” and the position data detected by the position detector 4 does not change, the electrode position detection circuit 8 Write electrode position as reference position /
It is sent to the wear amount detection switching circuit 16. Here, the reference position writing / wear amount detection switching circuit 16 is "written".
Is selected, the electrode position at this time is written to the electrode total reference position memory 18 as the electrode total reference position. Conversely, the reference position writing / wear amount detection switching circuit 16 is "detected".
Is selected, the electrode total wear amount and the fixed-side electrode wear amount are calculated from the electrode position at this time, the electrode total reference position, and the electrode wear ratio α.
0 is written to the fixed-side electrode wear amount memory 15. The electrode wear ratio α is a ratio of the wear amount of the fixed-side electrode 7 to the total wear amount of the electrodes, and is a value determined by welding conditions such as the type of the electrode used, the type of the work to be welded, and the time for one welding. It is obtained by actually performing welding several times and measuring the amount of wear of the electrodes. The output timing of the position data stored in each of the electrode total reference position memory 18, the electrode total wear amount memory 20, and the fixed side electrode wear amount memory 15 is as follows.
It depends on the setting state of the reference position writing / wear amount detection switching circuit 16. That is, the electrode total reference position memory 18 outputs data only when the reference position writing / wear amount detection switching circuit 16 is selected as “detection”. The electrode total wear amount memory 20 and the fixed-side electrode wear amount memory 15 output data only when the reference position writing / wear amount detection switching circuit 16 is in the neutral state. The fixed-side electrode wear amount output from the fixed-side electrode wear amount memory 15 as a correction amount is added to the robot position data of the welding point output from the robot position command creation circuit 11 and sent to the robot drive circuit 12. . Similarly,
The electrode total wear amount output from the electrode total wear amount memory 20, which is a correction amount, is added to the moving-side electrode position data of the welding point output from the electrode position command creation circuit 13 and sent to the electrode drive circuit 14. Next , a flowchart shown in FIG. 2 and a flowchart shown in FIG.
By the operation explanatory diagram in the form a welding gun, and more in reference example
A detailed description will be given. First, detection of the electrode total reference position is performed. As shown in FIG. 3A, two unused pairs of electrodes, namely, the movable side electrode 6 and the fixed side electrode 7 are attached to the C-shaped welding gun 2, and a reference position writing / wear amount detection switching circuit is provided. 16 is set to "write" (referred to as a reference position write mode). The moving electrode 6 moves toward the fixed electrode 7 (step 31), and the current position data P of the moving electrode 6 is read by the position detector 4 and the electrode position detecting circuit 8 (step 32). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, as shown in FIG. 3B, the movable electrode 6 comes into contact with the fixed electrode 7 and stops. (Step 33)
Y), stop the rotation of the servo motor 3 (Step 3)
5) Go to step 36. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same value, steps 32 to 33 are repeated (step 3).
4). In step 36, since the reference position writing / wear amount detection switching circuit 16 is in the reference position writing mode (step 36Y), the current position data P is stored in the electrode total reference position memory 18 as the electrode total reference position P1. Remember. Second, the amount of wear of the electrodes is detected.
FIG. 3C shows a state in which the length of two unused pairs of electrodes changes due to wear. The reference position writing / wear amount detection switching circuit 16 is selected to "detect" (wear amount detection mode). The moving electrode 6 moves toward the fixed electrode 7 (step 31), and the current position data P of the moving electrode 6 is read by the position detector 4 and the electrode position detecting circuit 8 (step 32). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, as shown in FIG. 3D, the movable electrode 6 comes into contact with the fixed electrode 7 and stops. It is determined that the rotation has been performed (step 33Y), the rotation of the servo motor 3 is stopped (step 35), and the process proceeds to step 36. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same value, steps 32 to 33 are repeated (step 34). In step 36, since the reference position writing / wear amount detection switching circuit 16 is in the wear amount detection mode (step 36N), the electrode total wear amount Lt is calculated from the current position data P and the electrode total reference position P1 by Lt. = P
−P1 and stored in the electrode total wear amount memory 20. Further, from the electrode wear ratio α (0 ≦ α ≦ 1), the wear amount Ls of the fixed-side electrode 7 is obtained as Ls = Lt × α and stored in the fixed-side electrode wear amount memory 15. The positions of the movable electrode 6 and the fixed electrode 7 are corrected as shown in FIG. FIG. 4 (a)
Indicates an initial state before the electrodes are worn. FIG. 4B shows a state in which the fixed side electrode 7 is worn by Ls and the movable side electrode 6 is worn by Lm. As shown in FIG. 4C, the position of the fixed-side electrode 7 is determined by the amount of wear Ls of the fixed-side electrode 7 read from the fixed-side electrode wear amount memory 15 in the direction from the fixed-side electrode 7 to the moving-side electrode 6. The correction is made by operating the C-type welding gun 2 by the amount. FIG. 4 (d)
As shown in (2), the position of the movable electrode 6 is such that the servo motor 3 is rotated in the direction from the movable electrode 6 to the fixed electrode 7 by the total electrode wear amount Lt read from the total electrode wear memory 20. To compensate for this. Here, the position correction amount of the moving-side electrode 6 is not the wear amount Lm of the moving-side electrode 6 but the electrode total wear amount Lt. This is because the position correction of the fixed side electrode 7 is performed by operating the C-type welding gun 2.
Since the position of the moving-side electrode 6 also changes by the wear amount Ls of the fixed-side electrode 7, the correction amount of the moving-side electrode 6 is
Is the sum of the wear amount Ls of the moving side electrode 6 and the wear amount Lm of the moving side electrode 6, that is, the electrode total wear amount Lt. As described above, in the reference example, before and after the electrode is worn, the position of the movable electrode 6 when the movable electrode 6 and the fixed electrode 7 are brought into contact with each other is detected.
By calculating the difference between the positions, the total wear of the electrode is determined, and further, the wear of the fixed electrode 7 is determined from the total wear of the electrode and the electrode wear ratio α. Also, the moving side electrode 6
Is determined by subtracting the wear amount of the fixed electrode 7 from the total wear amount of the electrodes. According to this method, the amount of wear of both electrodes can be obtained in a short time only by bringing the movable electrode 6 and the fixed electrode 7 into contact with each other. Next, an embodiment of the present invention will be described with reference to FIGS. In the above-described reference example, in a process in which there are many types of workpieces, it is necessary to calculate the electrode wear ratio α corresponding to the workpieces each time. Therefore, the present onset
In the embodiment described above, the amount of electrode wear is calculated without using the electrode wear ratio α. As shown in FIG. 5, the configuration of the robot body provided with the C-shaped welding gun was described above.
The description is omitted because it is the same as FIG. 1 in the reference example . As shown in FIG. 5, the program data 9 includes robot position data and moving-side electrode position data of each welding point in a state where the electrodes are not worn, and the electrode total wear amount detection position (total electrode wear). The robot position data and the moving-side electrode position data when detecting the amount) and the moving-side electrode wear amount detection position (the robot position data and the moving-side electrode position data when detecting the moving amount of the moving-side electrode) are stored in advance. Have been. The position data read from the program data 9 by the program data reading circuit 10 is based on the total detection /
It depends on the setting state of the moving side detection switching circuit 21 and the reference position writing / wear amount detection switching circuit 16. The total detection / moving side detection switching circuit 21 can be set to “total detection (total)” and “moving side detection (moving side)”. Here, when the reference position writing / wear amount detection switching circuit 16 is in the neutral state, the program data reading circuit 10 reads the robot position data and the moving-side electrode position data of each welding point. When the wear amount detection switching circuit 16 is selected as “write” or “detection” and the total detection / moving side detection switching circuit 21 is selected as “total”, the electrode total wear amount detection position is read. . Further, the reference position writing / wear amount detection switching circuit 16 is selected as “writing” or “detection”, and the total detection / moving side detection switching circuit 2 is selected.
When 1 is selected as "moving side", the moving side electrode wear amount detection position is read. The robot position data is sent to the robot position command creation circuit 11, and the moving-side electrode position data is sent to the electrode command position creation circuit 13. The electrode position detecting circuit 8 reads the electrode position from the position detector 4. The electrode position detection circuit 8 selects the reference position writing / wear amount detection switching circuit 16 to “write” or “detection”, and only when the position data detected by the position detector 4 does not change, The electrode position is sent to the reference position writing / wear amount detection switching circuit 16 via the total detection / moving side detection switching circuit 21. A total detection / moving side detection switching circuit 21
Is selected as “total” and the reference position writing / wear amount detection switching circuit 16 is selected as “writing”, the electrode position at this time is stored in the electrode total reference position memory 18 as the electrode total reference position. Written. Conversely, when the reference position writing / wear amount detection switching circuit 16 is selected as “detection”, the electrode total wear amount is calculated from the electrode position at this time and the electrode total reference position, and is stored in the electrode total wear amount memory 20. Written. Similarly, the total detection / moving side detection switching circuit 2
1 is selected as "moving side" and the reference position writing / wear amount detection switching circuit 16 is selected as "writing", the electrode position at this time is set as the moving side electrode reference position as the moving side electrode reference position. The data is written to the position memory 19. Conversely, when the reference position writing / wear amount detection switching circuit 16 is selected as "detection", the fixed-side electrode wear amount is calculated from the electrode position at this time, the moving-side electrode reference position, and the electrode total wear amount. The data is written to the fixed-side electrode wear amount memory 15. The output timing of the position data stored in each of the electrode total reference position memory 18, the electrode total wear amount memory 20, the moving side electrode wear amount memory 19, and the fixed side electrode wear amount memory 15 is based on the reference position writing. / It depends on the setting of the wear amount detection switching circuit 16. That is, the electrode total reference position memory 18 and the moving-side electrode reference position memory 1
No. 9 outputs data only when the reference position writing / wear amount detection switching circuit 16 is selected as "detection". The electrode total wear amount memory 20 and the fixed-side electrode wear amount memory 15
Outputs data only when the reference position writing / wear amount detection switching circuit 16 is in the neutral state. The robot position data output from the robot position command generation circuit 11 is added with the fixed-side electrode wear amount output from the fixed-side electrode wear amount memory 15 as a correction amount, as in the above-described reference example, and the robot is driven. The signal is sent to the circuit 12. Similarly, the electrode total wear amount output from the electrode total wear amount memory 20 as a correction amount is added to the moving-side electrode position data output from the electrode position command creation circuit 13,
It is sent to the electrode drive circuit 14. Next , the flowchart of FIG. 6 and C in FIG.
According to the operation explanatory view of the welding gun, the embodiment of the present invention is described.
A more detailed explanation will be given. First, detection of the electrode total reference position is performed. As shown in FIG. 3A, two unused pairs of electrodes, that is, the moving side electrode 6 and the fixed side electrode 7 are attached to the C-shaped welding gun 2, and the total detection / moving side detection switching circuit 21 is provided. "Total" is selected (set to the total detection mode) (step 51Y), and the reference position writing / wear amount detection switching circuit 16 is selected to "write" (set to the reference position writing mode). The moving electrode 6 moves toward the fixed electrode 7 (step 53), and the current position data P of the moving electrode 6 is read by the position detector 4 and the electrode position detecting circuit 8 (step 54). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, as shown in FIG.
Is determined to have stopped by contacting the fixed-side electrode 7 (step 55Y), the rotation of the servomotor 3 is stopped (step 57), and the routine proceeds to step 58. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same, steps 54 to 55 are repeated (step 56). In step 58, the total detection / moving side detection switching circuit 21 enters the total detection mode (step 58Y),
Since the reference position writing / wear amount detection switching circuit 16 is in the reference position writing mode (step 59Y), the current position data P is stored in the electrode total reference position memory 18 as the electrode total reference position P1. . Second, the detection of the reference position of the movable electrode is performed. As shown in FIG. 3E, two unused pairs of electrodes, namely, the movable side electrode 6 and the fixed side electrode 7 are attached to the C-shaped welding gun 2 and a total detection / movement side detection switching circuit 21 is provided.
Is selected as "moving side" (moving side detection mode), and the reference position writing / wear amount detection switching circuit 16 is "written".
(Reference position writing mode). Total detection /
Since the moving-side detection switching circuit 21 is selected as “moving-side” (step 51N), the robot is moved so that the jig is arranged at a preset position between the moving-side electrode 6 and the fixed-side electrode 7. (Step 52). When the movement of the robot is completed, the movable electrode 6 moves toward the fixed electrode 7 (step 53), and the current position data P of the movable electrode 6 is read by the position detector 4 and the electrode position detection circuit 8 (step 53). 54). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, the moving-side electrode 6 comes into contact with the jig and stops as shown in FIG. (Step 55Y), the rotation of the servo motor 3 is stopped (Step 57), and the routine proceeds to Step 58. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same, steps 54 to 55 are repeated (step 56). In step 58, the total detection / moving side detection switching circuit 21 is in the moving side detection mode (step 58N) and the reference position writing / wear amount detection switching circuit 16 is in the reference position writing mode (step 58N). 63Y), the current position data P is stored in the moving-side electrode reference position memory 19 as the moving-side electrode reference position P2. Third, the total amount of electrode wear is detected. FIG. 3C shows a state in which the length of two unused pairs of electrodes changes due to wear. The total detection / moving side detection switching circuit 21 is selected as “total” (to be a total detection mode) (step 51Y), and the reference position writing /
The wear amount detection switching circuit 16 is selected as "detection" (wear amount detection mode). The moving electrode 6 moves toward the fixed electrode 7 (step 53), and the current position data P of the moving electrode 6 is read by the position detector 4 and the electrode position detecting circuit 8 (step 54). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, as shown in FIG. 3D, the movable electrode 6 comes into contact with the fixed electrode 7 and stops. It is determined that the rotation has been performed (Step 55Y), the rotation of the servo motor 3 is stopped (Step 57), and the process proceeds to Step 58. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same, steps 54 to 55 are repeated (step 56). In step 58, the total detection /
The moving side detection switching circuit 21 is set to the total detection mode (step 58Y), and the reference position writing / wear amount detection switching circuit 1
6 is in the wear amount detection mode (step 59).
N), from the current position data P and the electrode total reference position P1, the electrode total wear amount Lt is obtained by Lt = P-P1,
It is stored in the electrode total wear amount memory 20. Fourth, the amount of wear of the moving-side electrode is detected. FIG. 3G shows a state in which the length of two unused pairs of electrodes changes due to wear. Total detection /
The moving side detection switching circuit 21 is selected as "moving side" (moving side detection mode), and the reference position writing / wear amount detection switching circuit 16 is selected as "detection" (wear amount detection mode). . Since the total detection / moving side detection switching circuit 21 is selected as “moving side” (step 51N), the moving side electrode 6
The robot moves so that the jig is arranged at a preset position between the and the fixed-side electrode 7 (step 52). When the movement of the robot is completed, the moving side electrode 6 moves to the fixed side electrode 7 side (step 53), and the current position data P of the moving side electrode 6 is obtained by the position detector 4 and the electrode position detecting circuit 8.
Is read (step 54). The current position data P is compared with the position data P 'read in the previous scan, and if they have the same value, the moving-side electrode 6 comes into contact with the jig and stops, as shown in FIG. (Step 55Y), the rotation of the servo motor 3 is stopped (Step 57), and the routine proceeds to Step 58. Conversely, if the current position data P and the position data P 'read in the previous scan are not the same, steps 54 to 55 are repeated (step 56). In step 58, the total detection / moving side detection switching circuit 21 switches to the moving side detection mode (step 58).
N) Since the reference position writing / wear amount detection switching circuit 16 is in the wear amount detection mode (step 63).
N), the current position data P and the moving-side electrode reference position P2
From the equation, the moving-side electrode wear amount Lm is determined by Lm = P−P2, and the fixed-side electrode wear amount Ls is further calculated as
And stored in the fixed-side electrode wear amount memory 15. The method of correcting the positions of the movable electrode 6 and the fixed electrode 7 using the wear amount is described above.
Since it is the same as that of the reference example, the description will not be repeated. As described above, in the embodiment of the present invention ,
First, the position of the movable electrode 6 when the movable electrode 6 and the fixed electrode 7 are brought into contact with each other before and after the electrodes are worn without the jig is detected, and the difference between the positions is calculated. To determine the total wear of the electrodes. Next, with the jig disposed between the electrodes, before and after the electrodes are worn, the position of the moving-side electrode 6 when the moving-side electrode 6 is brought into contact with the jig is detected, and the difference between the positions is determined. The amount of wear of the moving-side electrode 6 is obtained by the calculation. Further, the wear amount of the fixed electrode is obtained from the total wear amount of the electrodes and the wear amount of the movable electrode 6. According to this method, since the operation of the robot body and the electrodes in order to determine the amount of wear of the movable electrode 6 is required, the aforementioned
It takes more time to calculate the amount of wear of the moving-side electrode 6 than in the method of the reference example described above . However, the method of the embodiment of the present invention is described above.
In the process where there are many types of objects to be welded as in the method of the reference example, it is no longer necessary to determine the electrode wear ratio α each time.
In both cases, more accurate wear amount detection is possible. The correction of the electrode position according to the present invention is performed before the first welding after the electrode wear is greatly changed due to electrode replacement or electrode polishing. If it is performed for each score, highly accurate electrode positioning can be performed. As described above, according to the present invention, in a welding gun having a plurality of electrodes to be paired, such as a C-shaped welding gun, an X-shaped welding gun, etc., the amount of wear of the electrodes is reduced by using the electrodes and the jig. It is assumed that it is possible to detect the amount of electrode wear without causing deformation of the work to be welded.
In particular, it is possible to detect the amount of wear with higher accuracy, and to minimize the deformation of the workpiece caused by the displacement of the pressing point due to the wear of the electrode during welding.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing a configuration of an apparatus used for a welding gun electrode wear amount detecting method according to a reference example. FIG. 2 is a flowchart showing in detail a welding gun electrode wear amount detection method according to a reference example . FIG. 3 is a diagram illustrating the operation of a C-type welding gun. FIG. 4 is an explanatory diagram showing a correction state of an electrode position. FIG. 5 is a block diagram illustrating a configuration of an apparatus used in a method for detecting a wear amount of a welding gun electrode according to an embodiment of the present invention. FIG. 6 is a flowchart illustrating in detail a welding gun electrode wear amount detecting method according to the embodiment of the present invention. [Description of Signs] 1 Arm tip 2 C-shaped welding gun (welding gun) 3 Servo motor 6 Moving electrode 7 Fixed side electrode

Continuation of front page (58) Field surveyed (Int.Cl. ⁷ , DB name) B23K 11/24 336

Claims (1)

(57) [Claims] [Claim 1] Transfer as one electrode by a servomotor
Activating the moving electrode and the other electrode forming a pair with the moving electrode.
The workpiece is sandwiched between the fixed electrode as the pole and the pressure is held.
In the welding gun, before the moving side electrode and the fixed side electrode are worn out, these two electrodes are matched with each other, this position is stored as a reference position 1, and then the servo motor is operated to move the moving side electrode and the fixed side electrode.
The electrode is pressed against a fixed jig, and this position is stored as a reference position 2. Thereafter, the difference between the position where the moving side electrode and the fixed side electrode match and the reference position 1 is referred to as the moving side electrode and the fixed side electrode.
Calculate the total amount of wear on the poles , and then operate the servo motor to move
Pressing the electrode on the fixed fixture, and calculates the wear amount of the movable electrode from the difference between this position and the reference position 2, the movable electrode from the total amount of wear of the movable electrode and the fixed electrode By subtracting the amount of wear on the fixed side
A method for detecting a wear amount of a welding gun electrode, wherein a wear amount of the electrode is calculated.