Welded state analysis method, welded state analysis device, welding system and computer-readable program
By acquiring and analyzing the three-dimensional melt pool shape, virtual welding drop shape and melt pool pressure distribution, the problem of difficult to control the melt pool state during the back welding without backs in the prior art is solved, and high-precision welding control and defect prediction are achieved.
Patent Information
- Application Number
- JP2023165115
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2023-09-27
- Publication Date
- 2025-04-08
AI Technical Summary
The existing automated welding technology is difficult to accurately control the state of the melt pool during back welding without backing, especially when backing materials are not used, the lack of effective analysis of the pressure and force of the melt pool is made difficult to achieve high-precision control.
By obtaining the shape of the three-dimensional melt pool, the shape of the virtual welding drop, and the pressure distribution or force caused by the welding phenomenon, these data are analyzed to determine the state of the melt pool, and predict the occurrence of welding defects or changes in bead shape according to different welding conditions.
Accurate analysis and prediction of the melt pool state is achieved, and the control accuracy of the welding process is improved. Especially in the case of no backing welding, welding defects can be predicted and avoided more accurately.
Smart Images

Figure 2025055744000001_ABST
Abstract
Description
[Technical field]
[0001] The present invention relates to a technique for analyzing a welding condition. [Background technology]
[0002] Conventionally, in welding sites, for example, in cases where the welding state is easily unstable, such as the first layer uranami welding in multi-layer arc welding, it is difficult to automate using welding robots, etc., and it is mainly performed by skilled workers by manual welding or semi-automatic welding. In particular, one-sided uranami welding without a backing material (i.e., backingless uranami welding) does not require the groove reshaping process or the backing material attachment process, and is expected to improve work efficiency, but since there is a possibility of the molten metal burning through to the back side, it is even more difficult to automate than uranami welding using a backing material.
[0003] Patent Documents 1 and 2 propose a method for automating arc welding of butt joints with a backing material attached to the back side. Specifically, in the automatic welding method of Patent Document 1, an image of the molten pool at the weld is continuously captured by a CCD camera, and the image is subjected to brightness addition processing and smoothing differentiation processing to calculate the amount of advance of the molten pool (i.e., the distance between the tip of the molten pool and the center position of the arc in the image). Then, the welding speed is continuously controlled so that the amount of advance of the molten pool falls within a preset range.
[0004] In addition, in the automatic welding method of Patent Document 2, a camera continuously captures images of the molten pool and the arc, and the images are input into a machine learning model to obtain image feature information (i.e., position information of the arc center, wire tip, and molten pool end), and based on the image feature information, correction amounts for the welding torch position and welding speed, etc. are calculated. Then, the welding torch position and welding speed are continuously controlled based on the correction amounts. [Prior art documents] [Patent documents]
[0005] [Patent Document 1] JP 2000-94130 A [Patent Document 2] Patent No. 7021728 Summary of the Invention [Problem to be solved by the invention]
[0006] Incidentally, in the welding methods of Patent Document 1 and Patent Document 2, although an image of the molten pool is acquired, control is performed based only on the two-dimensional shape of the molten pool on the image. In addition, in these welding methods, analysis is not performed on the pressure or force applied to the molten pool by phenomena occurring during welding such as arc (hereinafter also referred to as "welding phenomena"). For this reason, in these welding methods, it is difficult to accurately grasp the state of the molten pool, and even in uranami welding using a backing material, it is not easy to achieve high-precision control. Therefore, Patent Document 1 and Patent Document 2 do not take into consideration application to backingless uranami welding, which requires more precise control than uranami welding using a backing material.
[0007] The present invention has been made in consideration of the above problems, and has an object to obtain the state of a molten pool with high accuracy. [Means for solving the problem]
[0008] A first aspect of the present invention is a welding condition analysis method for analyzing a welding condition, comprising the steps of: a) acquiring a molten pool shape, which is the three-dimensional shape of a molten pool where welding is being performed; b) acquiring a virtual bead shape, which is the three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no indentation pressure due to welding phenomenon is applied to the molten pool; and c) calculating a welding pressure distribution, which is the distribution of indentation pressure on the molten pool due to welding phenomenon, or a welding force, which is the indentation force on the molten pool due to welding phenomenon, based on the difference between the molten pool shape and the virtual bead shape.
[0009] A second aspect of the present invention is a welding condition analysis method of the first aspect, further comprising a step of d) performing steps a), b) and c) for each of a plurality of welding conditions to determine a plurality of welding pressure distributions or a plurality of welding forces corresponding to the plurality of welding conditions, and acquiring correlation information indicating a correlation between the welding conditions and the welding pressure distributions or welding forces.
[0010] A third aspect of the present invention is a welding state analysis method according to the second aspect, further comprising the steps of: determining a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to one welding condition, based on the one welding condition and the correlation information; and predicting whether or not a welding defect will occur in the molten pool under the one welding condition based on a mathematical model of the molten pool utilizing the corresponding welding pressure distribution or the corresponding welding force.
[0011] A fourth aspect of the present invention is a welding state analysis method according to the second aspect (which may be either the second or third aspect), further comprising the steps of: determining a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to one welding condition, based on the one welding condition and the correlation information; and predicting a shape of a bead after the molten pool has solidified under the one welding condition, based on a mathematical model of the molten pool utilizing the corresponding welding pressure distribution or the corresponding welding force.
[0012] A fifth aspect of the present invention is a method for analyzing a welding condition according to any one of the first to fourth aspects, further comprising the steps of: calculating a first energy which is the surface free energy of the molten metal bridging between two base materials in the form of a liquid film; and a second energy which is the surface free energy of the molten metal in the form of a liquid film bridging between the two base materials when the molten metal is separated from the two base materials and held in the form of droplets on the surfaces of the two base materials; and predicting, based on the first energy and the second energy, whether or not bridge fracture will occur, in which the molten metal in the form of a liquid film bridging between the two base materials is separated.
[0013] A sixth aspect of the present invention is a welding condition analysis method of any one of the first to fourth aspects (or any one of the first to fifth aspects), further comprising a step of predicting the presence or absence of insufficient penetration into the back surface of the base material based on the weld height and the heat input per unit length.
[0014] A seventh aspect of the present invention is a welding state analysis device that analyzes a welding state during welding, and includes a molten pool shape acquisition unit that acquires a molten pool shape, which is the three-dimensional shape of a molten pool where welding is being performed, a bead shape acquisition unit that acquires a virtual bead shape, which is the three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no indentation pressure due to welding phenomenon is applied to the molten pool, and a welding calculation unit that calculates a welding pressure distribution, which is the distribution of indentation pressure on the molten pool due to the welding phenomenon, or a welding force, which is the indentation force on the molten pool due to the welding phenomenon, based on the difference between the molten pool shape and the virtual bead shape.
[0015] An eighth aspect of the present invention is a welding condition analysis device of the seventh aspect, further comprising an information acquisition unit that acquires correlation information indicating the correlation between the welding conditions and the welding pressure distribution or the welding force from a combination of a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces calculated by the welding calculation unit for each of the plurality of welding conditions.
[0016] A ninth aspect of the present invention is a welding condition analysis device of aspect 8, further comprising a condition analysis unit that determines a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to one welding condition, based on a one welding condition and the correlation information, and predicts whether or not a welding defect will occur in the molten pool under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force.
[0017] A tenth aspect of the present invention is a welding state analysis device of aspect 8 (which may be aspect 8 or 9), further comprising a state analysis unit that determines a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to one welding condition, based on one welding condition and the correlation information, and predicts the shape of the bead after the molten pool solidifies under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force.
[0018] An eleventh aspect of the present invention is a welding condition analysis device of aspect 7 (which may be any one of aspects 7 to 10), further comprising a condition analysis unit that calculates a first energy which is the surface free energy of the molten metal bridging between two base materials in the form of a liquid film, and a second energy which is the surface free energy of the molten metal bridging between the two base materials in the form of a liquid film and being held in the form of droplets on the surfaces of the two base materials, and predicts whether or not bridge fracture will occur in which the molten metal bridging between the two base materials in the form of a liquid film is separated, based on the first energy and the second energy.
[0019] A twelfth aspect of the present invention is a welding condition analysis device of aspect 7 (which may be any one of aspects 7 to 11), further comprising a condition analysis unit that predicts whether or not there is insufficient penetration into the back surface of the base material based on the weld height and the heat input per unit length.
[0020] A thirteenth aspect of the present invention is a welding system comprising a welding state analysis device of any one of aspects seven to twelve, and an automatic welding device that performs welding under welding conditions determined based on the welding pressure distribution or welding force obtained by the welding state analysis device.
[0021] A fourteenth aspect of the present invention is a welding condition analysis device for analyzing a welding condition, comprising: a storage unit for storing correlation information indicating a correlation between a welding pressure distribution, which is a distribution of a plunge pressure due to a welding phenomenon on a molten pool where welding is being performed, or a welding force, which is a plunge force on the molten pool due to a welding phenomenon, and a welding condition; and a condition analysis unit for determining a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on a welding condition and the correlation information, and predicting whether or not a welding defect occurs in the molten pool under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force. The correlation information is determined based on a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces corresponding to the plurality of welding conditions, respectively. The plurality of welding pressure distributions or the plurality of welding forces are each determined based on a difference between a molten pool shape, which is a three-dimensional shape of the molten pool, and a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that a plunge pressure due to a welding phenomenon is not applied to the molten pool.
[0022] A fifteenth aspect of the present invention is a welding condition analysis device for analyzing a welding condition, comprising: a storage unit for storing correlation information indicating a correlation between a welding pressure distribution, which is a distribution of a plunge pressure due to a welding phenomenon on a molten pool where welding is being performed, or a welding force, which is a plunge force on the molten pool due to a welding phenomenon, and a welding condition; and a condition analysis unit for determining a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on a welding condition and the correlation information, and predicting a shape of a bead after the molten pool has solidified under the one welding condition, based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force. The correlation information is determined based on a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces, respectively corresponding to the plurality of welding conditions. The plurality of welding pressure distributions or the plurality of welding forces are each determined based on a difference between a molten pool shape, which is a three-dimensional shape of the molten pool, and a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that a plunge pressure due to a welding phenomenon is not applied to the molten pool.
[0023] A sixteenth aspect of the present invention is a computer-readable program that causes a computer to perform an analysis of a welding condition during welding, and when the program is executed by a computer, the following steps are performed: a) acquiring a molten pool shape, which is the three-dimensional shape of the molten pool where welding is being performed; b) acquiring a virtual bead shape, which is the three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no indentation pressure due to welding phenomenon is applied to the molten pool; and c) calculating a welding pressure distribution, which is the distribution of indentation pressure on the molten pool due to welding phenomenon, or a welding force, which is the indentation force on the molten pool due to welding phenomenon, based on the difference between the molten pool shape and the virtual bead shape. Effect of the Invention
[0024] In the present invention, the state of the molten pool can be obtained with high accuracy. [Brief description of the drawings]
[0025] [Figure 1] FIG. 1 is a side view showing a welding system. [Diagram 2] FIG. 2 is a front view showing a part of the automatic welding device. [Diagram 3] FIG. 1 is a diagram showing a configuration of a welding state analyzing device. [Figure 4] FIG. 2 is a diagram illustrating a functional configuration of a welding state analyzing device. [Diagram 5] FIG. 11 is a diagram showing a flow of obtaining correlation information. [Figure 6] FIG. [Figure 7] FIG. [Figure 8] FIG. [Figure 9] FIG. 13 is a diagram showing a flow of prediction of welding defects. [Figure 10] FIG. [Figure 11] FIG. 1 is a diagram showing a flow of burn-through prediction. [Figure 12A] FIG. [Figure 12B] FIG. [Figure 13] FIG. 13 is a diagram showing a flow of prediction of bridge fracture. [Figure 14] FIG. 13 is a diagram showing the results of bridge fracture prediction. [Figure 15] FIG. 13 is a diagram showing a flow of prediction of insufficient penetration. [Figure 16] FIG. 13 is a diagram showing the results of penetration insufficiency prediction. [Figure 17] FIG. 13 is a diagram showing a flow of prediction of a bead shape. [Figure 18] FIG. [Figure 19] FIG. 13 is a diagram showing the results of burn-through prediction. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0026] FIG. 1 is a side view showing a configuration of a welding system 1 according to an embodiment of the present invention. The welding system 1 includes an automatic welding device 2 and a welding state analysis device 5. FIG. 2 is a front view showing a part of the automatic welding device 2. In FIG. 1 and FIG. 2, three mutually orthogonal directions are indicated by arrows as an X direction, a Y direction, and a Z direction. In the example shown in FIG. 1 and FIG. 2, the X direction and the Y direction are horizontal directions perpendicular to each other, and the Z direction is a vertical direction, but is not limited to this.
[0027] The automatic welding device 2 is, for example, a welding device with an automatic tracing function that moves a welding position along a groove portion 93 of base materials 91, 92 that are objects to be welded, while performing continuous welding on the groove portion 93. In this embodiment, the automatic welding device 2 performs arc welding on the base materials 91, 92. In FIG. 2, the base materials 91, 92 are shown in cross section. The welding state analysis device 5 obtains the welding state of the groove portion 93 by analysis based on the welding conditions (e.g., welding speed, welding current, etc.) in the automatic welding device 2 and the cross-sectional shape of the groove portion 93, and determines the welding conditions suitable for welding the groove portion 93. In the automatic welding device 2, automatic welding is performed on the groove portion 93 under the welding conditions determined by the welding state analysis device 5.
[0028] In the example shown in FIG. 1, the automatic welding device 2 includes a welding robot 21 and a holding unit 22 that holds base materials 91, 92. The welding robot 21 includes a manipulator 211, a welding torch 212, and a sensor unit 213. The manipulator 211 is a robot arm having a multi-axis multi-joint structure. The welding torch 212 and the sensor unit 213 are attached to the tip of the manipulator 211. The welding torch 212 is a welding part that performs welding on the base materials 91, 92. The sensor unit 213 is a measuring unit that measures the cross-sectional shape of the groove portion 93.
[0029] In the automatic welding device 2, the manipulator 211 is driven to move the welding torch 212 and the sensor unit 213 in a predetermined welding direction (i.e., the direction in which the groove portion 93 extends) along the groove portion 93, and welding is performed on the groove portion 93. In the example shown in FIG. 1 and FIG. 2, the groove portion 93 having a substantially V-shaped cross-sectional shape extends substantially linearly substantially parallel to the Y direction, and welding is performed from the (-Y) side to the (+Y) side of the groove portion 93. In the following description, the (+Y) side is also referred to as the "front side of the welding direction" or the "downstream side of the welding direction," and the (-Y) side is also referred to as the "rear side of the welding direction" or the "upstream side of the welding direction." Note that the groove portion 93 does not necessarily have to be linear, and may extend while curving. In addition, the cross-sectional shape of the groove portion 93 is not limited to a V shape, and may be variously changed. Note that the groove portion 93 may be omitted.
[0030] The sensor unit 213 is disposed on the (+Y) side of the welding torch 212. The sensor unit 213 measures the shape of a cross section (i.e., a cross section in the XZ plane) of the groove portion 93 perpendicular to the welding direction. The sensor unit 213 includes, for example, a light-cutting sensor. The light-cutting sensor irradiates the surfaces of the base materials 91, 92 with a strip-shaped laser light (so-called slit laser) extending in the X direction, and receives the reflected light diffused and reflected by the surface with an imaging element, thereby acquiring the cross-sectional shape of the base materials 91, 92 including the groove portion 93. The sensor unit 213 acquires the cross-sectional shapes of the groove portion 93 and the area near the groove portion 93 as a set of multiple points (i.e., a point sequence) corresponding to the multiple measurement points arranged in the X direction. The multiple measurement points are arranged, for example, at approximately equal intervals in the X direction.
[0031] When welding is performed by automatic welding device 2, sensor unit 213 and welding torch 212 are moved in the Y direction (i.e., the welding direction) by manipulator 211, while sensor unit 213 acquires the cross-sectional shape of groove portion 93. Then, manipulator 211 is driven based on the cross-sectional shape, and the position of welding torch 212 in the X direction and Z direction is adjusted. In automatic welding device 2, while welding of groove portion 93 is being performed by welding torch 212, acquisition of the cross-sectional shape of groove portion 93 by sensor unit 213 and adjustment of the position of welding torch 212 are continuously performed.
[0032] In the automatic welding device 2, for example, backing-less uranami welding is performed on the groove portion 93. Backing-less uranami welding is a welding method in which welding is performed only from one main surface side of the base materials 91, 92 without using a backing material, melting to the other main surface, and a bead is formed on the other main surface as well. In the backing-less uranami welding, the groove forming process on the other main surface side and the backing material attachment process are not required, so that the welding work efficiency is improved. In the welding state analysis device 5, the welding state of the backing-less uranami welding in the automatic welding device 2 is analyzed. In addition, in the welding state analysis device 5, welding conditions suitable for the backing-less uranami welding are also determined.
[0033] 3 is a diagram showing the configuration of the welding condition analyzing device 5. The welding condition analyzing device 5 has a configuration of a general computer system including a CPU 51, a ROM 52, a RAM 53, a fixed disk 54, a display 55, an input unit 56, a reading device 57, a communication unit 58, and a bus 50. The CPU 51 performs various arithmetic processing. The ROM 52 stores basic programs. The RAM 53 stores various information. The fixed disk 54 stores information. The display 55 is a display unit that displays various information such as images. The input unit 56 includes a keyboard 56a and a mouse 56b that receive input from an operator.
[0034] The reading device 57 reads information from a computer-readable recording medium 511 such as an optical disk, a magnetic disk, a magneto-optical disk, or a memory card. The display 55, the keyboard 56a, the mouse 56b, and the reading device 57 are connected to the bus 50 via an interface I / F. The communication unit 58 transmits and receives signals between the automatic welding apparatus 2 and devices external to the welding system 1. The bus 50 is a signal circuit that connects the CPU 51, the ROM 52, the RAM 53, the fixed disk 54, the display 55, the input unit 56, the reading device 57, and the communication unit 58.
[0035] In the welding condition analyzing device 5, a program 512 recorded in advance on a recording medium 511 is read out via a reading device 57 and stored in a fixed disk 54. The program 512 may be stored in the fixed disk 54 via a network. The CPU 51 functions as a calculation unit that executes calculation processing while using the RAM 53 and the fixed disk 54 in accordance with the program 512. Other components that function as a calculation unit other than the CPU 51 may be employed.
[0036] FIG. 4 is a diagram showing a functional configuration realized by the welding state analysis device 5 executing arithmetic processing and the like according to the program 512. These functional configurations include a memory unit 501, a molten pool shape acquisition unit 502, a bead shape acquisition unit 503, a welding calculation unit 504, an information acquisition unit 505, and a state analysis unit 506. All or part of these functions may be realized by a dedicated electric circuit. Also, these functions may be realized by a plurality of computers. Among the functional configurations shown in FIG. 4, the molten pool shape measurement unit 502, the bead shape acquisition unit 503, the welding calculation unit 504, the information acquisition unit 505, and the state analysis unit 506 are realized by the CPU 51, the ROM 52, the RAM 53, the fixed disk 54, and their peripheral configurations. Also, the memory unit 501 is mainly realized by the RAM 53 and the fixed disk 54.
[0037] The memory unit 501 stores various information used for analyzing the welding state, and a plurality of welding conditions that can be implemented by the automatic welding device 2. The molten pool shape acquisition unit 502 acquires the molten pool shape, which is the three-dimensional shape of the molten pool where welding is being performed (i.e., a pool of molten metal formed when the electrode and base material are melted by arc heat or the like). The bead shape acquisition unit 503 acquires a virtual bead shape. The virtual bead shape is the three-dimensional shape of a bead formed at a position corresponding to the molten pool, assuming that no pressing pressure due to a phenomenon occurring during welding (hereinafter also referred to as "welding phenomenon") is applied to the molten pool.
[0038] The welding calculation unit 504 determines the welding pressure distribution and / or the welding force based on the difference between the above-mentioned molten pool shape and the virtual bead shape. The welding pressure distribution is the distribution of the pressing pressure on the molten pool due to the welding phenomenon. In this embodiment, the welding pressure distribution is the distribution of the pressure applied to the molten pool by the collision of the arc or the droplets in arc welding, and is hereinafter also referred to as the "arc pressure distribution". The welding force is the pressing force on the molten pool due to the welding phenomenon. In this embodiment, the welding force is the force applied to the molten pool by the collision of the arc or the droplets in arc welding, and is hereinafter also referred to as the "arc force". The information acquisition unit 505 acquires correlation information indicating the correlation between the welding conditions and the arc pressure distribution and / or the arc force.
[0039] The state analysis unit 506 analyzes the welding state by using the above-mentioned correlation information and the like. The state analysis unit 506, for example, predicts the occurrence of welding defects in the molten pool. The welding defects include, for example, a phenomenon in which molten metal falls downward from the (-Z) side surface (i.e., the back surface) of the base materials 91, 92 (hereinafter, also referred to as "burn-through"). The welding defects also include, for example, a phenomenon in which a liquid film-like molten metal bridging between the two base materials 91, 92 (i.e., between the side surfaces on the (+X) side and the (-X) side of the groove portion 93) separates (hereinafter, also referred to as "bridge fracture"). The welding defects include, for example, a phenomenon in which penetration into the back surface of the base materials 91, 92 is insufficient (hereinafter, also referred to as "insufficient penetration").
[0040] The state analysis unit 506 also predicts, for example, the shape of the bead after the molten pool has solidified. The shape of the bead includes, for example, the shape of the bead on the (+Z) side of the base materials 91, 92 (i.e., the front bead) and the shape of the bead on the (-Z) side of the base materials 91, 92 (i.e., the back bead). Specifically, for example, the state analysis unit 506 predicts the amount of protrusion of the back bead from the (-Z) side surface of the base materials 91, 92 to the (-Z) side (i.e., the back bead height).
[0041] Next, a description will be given of the operation of the welding condition analyzing device 5. First, a flow of acquiring the above-mentioned correlation information in the welding condition analyzing device 5 will be described below, and then a flow of analyzing the welding condition using the correlation information will be described.
[0042] 5, when correlation information is acquired, first, arc welding is performed on base materials 91, 92 under one welding condition in the automatic welding device 2, and the molten pool shape, which is the three-dimensional shape of the molten pool in the state where arc welding is being performed, is acquired by the molten pool shape acquisition unit 502 of the welding state analysis device 5 (step S11). The acquired molten pool shape is sent from the molten pool shape acquisition unit 502 to the memory unit 501 and stored in the memory unit 501.
[0043] The molten pool shape is acquired by the molten pool shape acquisition unit 502, for example, by a known non-contact measurement. The molten pool shape may be measured, for example, by a light cutting method in which the base materials 91, 92 including the molten pool are scanned with a slit laser or the like. Alternatively, the molten pool shape may be acquired by a triangulation method based on stereo images captured by a stereo camera (i.e., multiple images captured by multiple cameras with different shooting directions).
[0044] The one welding condition described above is input to the welding state analyzing device 5 via the input unit 56 or the like before step S11, and is stored in advance in the storage unit 501. The welding conditions include various parameters that can be set in the automatic welding device 2, such as the welding speed and welding current in the automatic welding device 2. The welding conditions may include, for example, the cross-sectional shape of the groove portion 93 (for example, the groove angle, the gap amount, the root height, etc.).
[0045] Next, the shape of the front bead 94 shown in Fig. 6 is acquired. For convenience of illustration, the base material 91 is omitted in Fig. 6, and the shape of a portion of the front bead 94 formed on the base material 92 (i.e., the (+X) side half of the front bead 94) is shown (similarly in Fig. 7). In Fig. 6, to facilitate understanding of the figure, contour lines based on the upper surface of the base material 92 are drawn by two-dot chain lines on the surfaces of the front bead 94 and the molten pool 95. The shape of the front bead 94 is acquired by, for example, an optical cutting method, and the shape of a cross section 941 of the front bead 94 at one position in the Y direction is acquired.
[0046] 6 is a cross section perpendicular to the Y direction of the (+X) side half of the front bead 94. The cross section 941 is, for example, substantially sector-shaped with a central angle of about 90°. The cross section of the (-X) side half of the front bead 94 is plane-symmetrical to the cross section 941 with respect to an imaginary plane (hereinafter also referred to as the "center plane") that extends perpendicular to the X direction at the center of the front bead 94 in the X direction. In the following description, the cross section 941 and the (-X) side cross section plane-symmetrical to the cross section 941 are collectively referred to as the "reference cross section" of the front bead 94.
[0047] In Figure 6, upstream in the melting direction from molten pool 95 indicated by a thin line (i.e., on the (-Y) side from the (-Y) end of molten pool 95), the cross-sectional shape at each position in the longitudinal direction (i.e., in the Y direction) of front bead 94 is approximately the same as the shape of the reference cross section described above. The molten pool 95 in Figure 6 is recessed on the (-Z) side due to the pressing pressure caused by the welding phenomenon described above. Specifically, the molten pool 95 is recessed on the (-Z) side due to pressure from the arc from welding torch 212 (see Figure 1), pressure from the collision of molten droplets, etc.
[0048] If it is assumed that the pressure is not applied to the molten pool 95, the depression in the molten pool 95 disappears, and a convex portion (hereinafter, also referred to as a "virtual bead 942") having substantially the same cross-sectional shape as the front bead 94 is formed at the position corresponding to the molten pool 95 (i.e., the space on the (+Z) side of the molten pool 95) as shown by the two-dot chain line in Figs. 7 and 8. Fig. 7 is a perspective view similar to Fig. 6, and shows the outline of the virtual bead 942 with a lattice-like two-dot chain line. Fig. 8 shows the cross-sectional shapes of the front bead 94 and the virtual bead 942 at the center plane described above (i.e., the shape of the cross section perpendicular to the X direction). Fig. 8 also shows the configuration behind the cross section (base material 92, etc.).
[0049] As described above, the cross-sectional shape of phantom bead 942 except for the tip portion (i.e., the end portion on the (+Y) side) of phantom bead 942 is the same as the shape of the reference cross section of front bead 94. The tip face (i.e., the end face on the (+Y) side) of the portion of phantom bead 942 having a cross section with the same shape as the reference cross section is a predetermined distance away from the position of welding torch 212 on the (-Y) side. In the following description, the position of the tip face in the Y direction is also referred to as the "reference cross section tip position."
[0050] At the tip of the virtual bead 942, the shape of the virtual bead 942 is considered to be dome-shaped due to the surface tension of the molten metal. Therefore, a rotating body obtained by rotating the cross section 941 by 180° around a virtual straight line extending in the Z direction on the center plane at the tip position of the reference cross section as a rotation axis is set as the tip of the virtual bead 942. In other words, the arc length of an arbitrary cross section including the rotation axis at the tip of the virtual bead 942 is the same as the arc length of the cross section 941 of the front bead 94 (i.e., the (+X) side half of the reference cross section). In the welding condition analyzing device 5, the three-dimensional shape of the virtual bead 942 described above is acquired as a virtual bead shape by the bead shape acquiring unit 503 (step S12). The virtual bead shape acquired by the bead shape acquiring unit 503 is sent from the bead shape acquiring unit 503 to the storage unit 501 and stored in the storage unit 501.
[0051] In step S12, the virtual bead shape (i.e., the three-dimensional shape of the virtual bead 942) does not necessarily have to be acquired based on the shape of the cross section 941 of the front bead 94. For example, in the vicinity of the end of the molten pool 95 on the (-Y) side, the shape of the cross section of the molten pool 95 perpendicular to the Y direction may be substantially the same as the reference cross section of the front bead 94. In this case, in step S12, the shape of the cross section of the molten pool 95 may be acquired at a portion of the molten pool 95 whose cross section shape is the same as that of the front bead 94, and the virtual bead shape may be acquired in the same manner as described above, using the cross section of the molten pool 95 as the reference cross section. Alternatively, the three-dimensional shape of the front bead 94 may be acquired in a manner substantially similar to the acquisition of the molten pool shape in step S11, and the virtual bead shape may be acquired based on the three-dimensional shape of the front bead 94.
[0052] In the welding state analyzing device 5, steps S11 and S12 may be performed in parallel, or step S12 may be performed before step S11. When steps S11 and S12 are completed, the molten pool shape and virtual bead shape stored in the memory unit 501 are read out by the welding calculation unit 504. The welding calculation unit 504 calculates an arc pressure distribution (i.e., a welding pressure distribution (i.e., a distribution of the pressing pressure on the molten pool 95 due to the welding phenomenon)) which is the distribution of the pressure applied to the molten pool 95 by the arc welding based on the difference between the molten pool shape and the virtual bead shape, and calculates an arc force (i.e., a welding force (i.e., a pressing force on the molten pool 95 due to the welding phenomenon)) which is the pressing force on the molten pool 95 due to the welding phenomenon) based on the arc pressure distribution (step S13).
[0053] Specifically, the kinetic energy imparted to the liquid surface of the molten pool 95 is considered to be equal to the amount of decrease in potential energy caused by the depression of the molten pool 95 from the virtual bead 942. Therefore, the arc pressure p arc can be calculated as shown in Equation 1.
[0054]
number
[0055] p arc is the arc pressure at each position of the molten pool 95. h is the vertical distance between the surface of the molten pool 95 and the upper end of the virtual bead 942 (i.e., the end on the (+Z) side) at each position. ρ is the density of the molten metal forming the molten pool 95. g is the gravitational acceleration. The above-mentioned arc pressure distribution is expressed as the arc pressure p arc This is the distribution of.
[0056] In addition, the arc force applied to the entire molten pool 95 can be considered as the sum of the arc pressures applied to each position of the molten pool 95. Therefore, the arc force F arc can be calculated as shown in Equation 2.
[0057]
number
[0058] F arc is the arc force imparted to the entire molten pool 95. S pool indicates each position of the molten pool 95, and dS is the infinitesimal area at each position.
[0059] In step S13, the welding calculation unit 504 may obtain the arc force without calculating the arc pressure distribution, as shown in Equation 3.
[0060]
number
[0061] When steps S11 to S13 are completed, the welding conditions for arc welding in the automatic welding equipment 2 are changed (steps S14, S15), and the process returns to step S11. Steps S11 to S13 are then performed under the changed welding conditions, and an arc pressure distribution and an arc force corresponding to the changed welding conditions are obtained and sent to storage unit 501. In welding state analysis device 5, steps S11 to S13 are performed for each of a predetermined number of welding conditions prepared in advance, and a plurality of arc pressure distributions and a plurality of arc forces corresponding to the predetermined number of welding conditions are obtained and sent to storage unit 501.
[0062] The information acquiring unit 505 acquires correlation information indicating a correlation between the welding conditions and the arc pressure distribution and the arc force based on the above-mentioned multiple welding conditions stored in the storage unit 501 and multiple arc pressure distributions and multiple arc forces corresponding to the multiple welding conditions respectively (step S16). The correlation information may be acquired by machine learning based on the multiple welding conditions and the multiple arc pressure distributions and multiple arc forces, for example. The correlation information may include, for example, a machine learning model (i.e., a model learned by machine learning) based on regression prediction or the like with the arc force as a response and the welding current as an explanatory variable.
[0063] The correlation information indicates the correlation between the welding conditions and the arc pressure distribution, but does not necessarily indicate the correlation between the welding conditions and the arc force. In this case, the arc force does not have to be calculated in step S13. The correlation information indicates the correlation between the welding conditions and the arc force, but does not necessarily indicate the correlation between the welding conditions and the arc pressure distribution. In this case, the arc pressure distribution does not have to be calculated in step S13.
[0064] Next, as described above, a description will be given of the flow of analysis of the welding state in the welding state analysis device 5. As described above, the state analysis unit 506 of the welding state analysis device 5 can predict the presence or absence of welding defects in backingless uranami welding.
[0065] Specifically, first, a welding condition is determined as a target for predicting whether or not a welding defect occurs. The welding condition may be a welding condition used when the correlation information is created, or may be a welding condition not used when the correlation information is created. Then, based on the welding condition and the correlation information, an arc pressure distribution (hereinafter also referred to as a "corresponding arc pressure distribution") corresponding to the welding condition and / or an arc force (hereinafter also referred to as a "corresponding arc force") corresponding to the welding condition are obtained (FIG. 9: step S21). As described above, the arc pressure distribution and the arc force are the welding pressure distribution and the welding force in arc welding, so the corresponding arc pressure distribution and the corresponding arc force are the corresponding welding pressure distribution and the corresponding welding force in arc welding. Next, based on a mathematical model of the molten pool 95 using the corresponding arc pressure distribution and / or the corresponding arc force obtained in step S21, whether or not a welding defect occurs in the molten pool 95 under the welding condition is predicted (step S22). The one welding condition may be input via the input unit 56 of the welding state analyzing device 5, or may be selected from a plurality of welding conditions pre-stored in the storage unit 501. The above-mentioned mathematical model is a concept including a simulation.
[0066] When the welding defect in step S22 is the above-mentioned "burn-through," as shown in FIG. 10, the vertical forces acting on the molten pool 95 that has penetrated into the back surface (i.e., the (-Z) side surface) of the base materials 91, 92 in the groove portion 93 are mathematically modeled. In FIG. 10, the forces acting on the molten pool 95 are indicated by arrows with reference numerals 811 to 814. Arrow 811 indicates the above-mentioned arc force. Arrow 812 indicates gravity acting on the molten pool 95. Arrow 813 indicates the surface tension acting between the molten pool 95 and the base materials 91, 92 at the (+Z) side of the molten pool 95 (hereinafter also referred to as "front side surface tension"). Arrow 814 indicates the surface tension acting between the molten pool 95 and the base materials 91, 92 at the (-Z) side of the molten pool 95 (hereinafter also referred to as "rear side surface tension").
[0067] In the above mathematical model, the vertical force F acting on the molten pool 95 verticalis the arc force F calculated in step S21 above. arc , and gravity F g , Z-direction component of surface tension on the front side F o , and the Z-direction component of the back surface tension F i Using these, it is expressed as in Equation 4 to Equation 8. In this mathematical model, a downward force is considered to be positive, and an upward force is considered to be negative.
[0068]
number
[0069]
number
[0070]
number
[0071]
number
[0072]
number
[0073] A is the area of the cross section of the molten pool 95 perpendicular to the Y direction (i.e., the weld area). o is the average length of the molten pool 95 in the Y direction on the surface of the molten pool 95 on the (+Z) side. i is the average length in the Y direction of the molten pool 95 on the surface on the (-Z) side of the molten pool 95. These average lengths are the arithmetic mean of the lengths in the Y direction of the molten pool 95 at each position in the X direction. γ is the surface tension coefficient between the molten pool 95 and the base materials 91, 92. θ BT_wet is the contact angle (i.e., the wetting angle) between the molten pool 95 and the base materials 91 and 92. g is the groove angle at the groove portion 93.
[0074] H r is the welding height in the groove portion 93 (i.e., the distance in the Z direction from the contact position between the (+Z) side surface of the molten pool 95 and the base materials 91, 92 to the (-Z) side surfaces of the base materials 91, 92), and can be calculated using the above-mentioned formula 8. g is the root height in the groove portion 93 (i.e., the size of the root face in the Z direction). g is the gap amount in the groove portion 93 (i.e., the distance in the X direction between the root face of the base material 91 and the root face of the base material 92 in the groove portion 93). A r is the welded area, A r = α r V r It can be calculated as α / ν. r is the welding efficiency (also called the welding rate), and V r is the consumption of welding material per unit time, and ν is the welding speed. W o is the average width of the molten pool 95 in the X direction on the surface of the (+Z) side of the molten pool 95. W i is the average width in the X direction of the molten pool 95 on the (-Z) side surface of the molten pool 95. These average widths are the arithmetic means of the widths in the X direction of the molten pool 95 at each position in the Y direction.
[0075] The above-mentioned θ BT_wet are fitting coefficients obtained by, for example, a curve fitting method. A and A related to the shape of the molten pool 95 r , L o , L i , W o and W i may be calculated by known theoretical calculations or may be calculated by a pre-constructed machine learning model. In the mathematical model shown in Equation 4, F vertical Although the internal pressure of the molten pool 95 is not included in the calculation of the internal pressure, the internal pressure may be included.
[0076] In the right-hand side of equation 6, -γcosθ BT_wetOf the three terms separated by "+" in the formula in parentheses multiplied by, the first term indicates the force at the side of the molten pool 95, the second term indicates the force at the rear end of the molten pool 95 (i.e., the rear end in the welding direction), and the third term indicates the force at the front end of the molten pool 95 (i.e., the front end in the welding direction). Similarly, in the right-hand side of the formula 7, -γcosθ BT_wet Of the three terms separated by "+" in the formula in parentheses multiplied by, the first term represents the force at the side of the molten pool 95, the second term represents the force at the rear end of the molten pool 95, and the third term represents the force at the front end of the molten pool 95.
[0077] In step S22, the state analysis unit 506 vertical is required, and F vertical When F is equal to or less than 0, it is determined that no burn-through occurs in the backingless uranami welding performed under the above-mentioned one welding condition (FIG. 11: steps S221 and S222). vertical If is greater than 0, it is determined that burn-through will occur in the backingless uranami welding performed under the one welding condition described above (steps S221, S223). The presence or absence of burn-through predicted by state analysis unit 506 (hereinafter also referred to as "first burn-through prediction") is displayed on display 55 together with the one welding condition described above, for example.
[0078] Table 1 shows the results of comparing the results of the first burn-through prediction described above with the presence or absence of actual burn-through. The presence or absence of actual burn-through was confirmed visually after backingless uranami welding was performed on the base materials 91 and 92 in the automatic welding device 2. In experiments 1 to 5 in Table 1, the gap amount W g By changing the range of F from 0mm to 2mm, vertical has been changed.
[0079] The other experimental conditions for Experiments 1 to 5 were the same. Specifically, the material of the base materials 91 and 92 was SM490A, and the groove angle θ g is 90°, and the root height H g A and A related to the shape of the molten pool 95 arer , L o , L i , W o and W i The contact angle θ BT_wet The angle was set to 71°. The weld length in the welding direction was 300 mm. The shielding gas was carbon dioxide (CO 2 ), the shielding gas flow rate was 20 liters per minute, the connection method was DCEP (so-called direct current positive), the tip-to-base metal distance (CTWD) was 20 mm, and the voltage was unified.
[0080] [Table 1]
[0081] As shown in Table 1, in the first burn-through prediction, F vertical In Experiments 1 to 3, where F was 0 or less, no burn-through occurred in backingless uranami welding using the automatic welding device 2. vertical In Experiments 4 to 5, where was greater than 0, burn-through occurred in backingless uranami welding in the automatic welding device 2. Thus, in Experiments 1 to 5, the occurrence of burn-through could be predicted with high accuracy. Note that in predicting the occurrence of burn-through as described above, arc pressure distribution may be used instead of arc force.
[0082] Furthermore, when the welding condition analyzing device 5 determines whether or not the above-mentioned "bridge fracture" has occurred, the condition analyzing unit 506 compares a state in which a liquid film of molten metal (hereinafter also referred to as "liquid film 951") is bridging between two base materials 91, 92 (for example, between the root faces of the base materials 91, 92) as shown in Fig. 12A with a state in which the molten metal is separated and held as droplets 952 on the base material 91 and droplets 953 on the base material 92 as shown in Fig. 12B. Specifically, a first energy SF 1 (9) and the second energy SF 2 (Equation 10) and are calculated and compared (FIG. 13: step S31).
[0083]
number
[0084]
number
[0085] W is the width of the liquid film 951 in the X direction. t is the height (i.e., thickness) of the liquid film 951 in the Z direction. γ L is the liquid surface tension coefficient of the liquid film 951 and the liquid droplets 952 and 953. γ S is the solid surface tension coefficient of the base material 91, 92. γ LS is the solid-liquid interfacial tension coefficient at the interface between the liquid film 951 and the liquid droplets 952, 953 and the base materials 91, 92. W LL is the work of adhesion on the liquid surface. W LS is the work of solid-liquid adhesion. θ B_wet is the contact angle (i.e., wetting angle) between the droplets 952, 953 and the base materials 91, 92.
[0086] The above-mentioned θ B_wet is a fitting coefficient obtained by, for example, a curve fitting method. W and t relating to the shape of the liquid film 951 may be obtained by a known theoretical calculation, or may be obtained by a machine learning model or the like that is constructed in advance.
[0087] Of the two terms separated by "+" on the right side of Equation 9, the first term indicates the surface free energy at the liquid surface of the liquid film 951, and the second term indicates the surface free energy at the solid-liquid interface between the liquid film 951 and the base materials 91, 92. Of the five terms separated by "+" or "-" (excluding those in parentheses) on the right side of Equation 10, the first term indicates the surface free energy at the liquid surface of the droplets 952, 953, the second term indicates the surface free energy at the solid-liquid interface between the droplets 952, 953 and the base materials 91, 92, and the third term indicates the surface free energy reduced by the liquid film becoming droplets and changing from a solid surface to a solid-liquid interface. Furthermore, of the five terms, the fourth term indicates the work required to separate the liquid film 951 into the (+X) side and the (-X) side at the center of the liquid film 951, and the fifth term indicates the work required to adhere the liquid droplets 952, 953 to the base materials 91, 92.
[0088] Ideally, the second energy SF 2 First Energy SF 1 If the SF 2 and Sci-Fi 1 The difference between these values is used to evaluate the bridge fracture. Specifically, as shown in Equation 11, SF 2 From SF 1 Subtracting Young's equation, Young-Dupre's equation, and area conservation equation, D B is calculated as an evaluation value for bridge fracture.
[0089]
number
[0090] Then, the state analysis unit 506 considers the difference between the theoretical value and the experimental result, and calculates the first energy SF 1 and the Second Energy SF 2 The evaluation value D obtained based on B is a given decision threshold T BIf the evaluation value D B is the decision threshold T B If it is less than the predetermined value, it is determined that bridge fracture will occur (steps S32 and S34). The presence or absence of bridge fracture predicted by the state analysis unit 506 (hereinafter, also referred to as "bridge fracture prediction") is displayed on the display 55 together with, for example, the above-mentioned one welding condition.
[0091] FIG. 14 is a graph comparing the results of the bridge fracture prediction described above with the actual occurrence of bridge fracture. The actual occurrence of bridge fracture was confirmed visually after backingless uranami welding was performed on the base materials 91 and 92 in the automatic welding device 2. The horizontal axis in FIG. 14 indicates the number of the experimental case, and the vertical axis indicates the above-mentioned evaluation value D B In FIG. 14, the decision threshold T B is indicated by a dashed line. In the example shown in FIG. B is -0.5.
[0092] In cases 1 to 23, the root height Hg is changed in the range of 0 mm to 1 mm, and the gap amount W g is changed in the range of 0mm to 2mm, and the groove angle θ g By changing the angle between 60° and 90°, the evaluation value D B was changed. The actual measured values were used for W and t, etc., related to the shape of the liquid film 951. The contact angle θ B_wet The other experimental conditions for Cases 1 to 23 were the same as those for Table 1 above.
[0093] In cases 1 to 5, 6 to 13, and 14 to 18, which are surrounded by dashed double-dashed lines, the evaluation value D B is the decision threshold T B The evaluation value D was larger than the evaluation value D, and no bridge fracture occurred. In cases 1 to 5, normal uranami welding was performed, insufficient penetration occurred in cases 6 to 13, and burn-through occurred in cases 14 to 18. On the other hand, in cases 19 to 23, the evaluation value D B is the decision threshold T B The cross-linking strength was less than 100%, and cross-linking fracture occurred.
[0094] When the welding state analysis device 5 determines whether or not the above-mentioned "insufficient penetration" occurs, the heat input H per unit length in the groove portion 93 and the above-mentioned welding height H r Based on this, the presence or absence of insufficient penetration is predicted. Specifically, when the heat input H per unit length is large and / or the weld height H r When H / H is small, heat is easily input to the (-Z) side of the base materials 91 and 92. r is a given decision threshold T H If the result is equal to or greater than the above, it is determined that the penetration reaches the (-Z) side surface (i.e., the back surface) of the base materials 91 and 92, and that there is no insufficient penetration (FIG. 15: steps S41 and S42). r T H If it is less than 100%, it is determined that insufficient penetration will occur (steps S41, S43). The presence or absence of insufficient penetration predicted by state analysis unit 506 (hereinafter also referred to as "insufficient penetration prediction") is displayed on display 55 together with the one welding condition described above, for example.
[0095] Fig. 16 is a graph comparing the above-mentioned results of the insufficient penetration prediction with the actual presence or absence of insufficient penetration. The actual presence or absence of insufficient penetration was confirmed visually after backingless uranami welding was performed on base materials 91 and 92 in an automatic welding device 2. The horizontal axis in Fig. 16 indicates the case number as in Fig. 14, and the vertical axis indicates the above-mentioned H / H r Among the plots in FIG. 16, the plots indicated by hollow circles indicate the case where a solid wire was used as the welding wire, and the plots indicated by solid circles indicate the case where a metal-cored wire was used as the welding wire. In FIG. 16, the determination threshold T H In the example shown in FIG. 16, 15 is shown by a thin solid line, and the judgment threshold T H (In the example shown in FIG. 16, 18) is indicated by a dashed line. The experimental conditions for cases 1 to 23 are the same as those for the above-mentioned FIG.
[0096] In cases 1 to 5, 14 to 18, and 19 to 23, respectively, surrounded by dashed double-dashed lines, H / H r is the decision threshold T H As mentioned above, normal uranami welding was performed in cases 1 to 5, burn-through occurred in cases 14 to 18, and bridge fracture occurred in cases 19 to 23. On the other hand, in cases 6 to 13, H / H welding was performed. r is the decision threshold T H The welding depth was less than 100 mm, resulting in insufficient penetration.
[0097] As described above, the state analysis unit 506 of the welding state analysis device 5 can also predict the shape of a bead in backingless uranami welding. Specifically, first, based on one welding condition and the above correlation information, a corresponding arc pressure distribution corresponding to the one welding condition and / or a corresponding arc force corresponding to the one welding condition is obtained (FIG. 17: step S51). Next, based on a mathematical model of the molten pool 95 using the corresponding arc pressure distribution and / or the corresponding arc force obtained in step S51, a shape of a bead after the molten pool 95 is solidified under the one welding condition is predicted (step S52). The one welding condition may be input via the input unit 56 of the welding state analysis device 5, or may be selected from a plurality of welding conditions stored in advance in the storage unit 501.
[0098] When the shape of the bead in step S52 is the above-mentioned "back bead height", the vertical force acting on the molten pool 95 that has penetrated to the back surface (i.e., the surface on the (-Z) side) of the base materials 91, 92 in the groove portion 93 is mathematically modeled as shown in FIG. 18. In the mathematical model shown in FIG. 18, the vertical force F acting on the molten pool 95 described above is vertical As a result, only the curvature of the portion 954 (i.e., the back wave 954) of the molten pool 95 that protrudes downward from the (-Z) side surface of the base materials 91, 92 changes, and it is considered that the macroscopic curvature radius Ri of the back wave 954 eventually reaches a certain value and the forces in the vertical direction are balanced. Equation 12 is the equation for this balance, with the left side being the downward force in FIG. 18 and the right side being the upward force in FIG. 18. αi is a conversion coefficient when the cross-sectional shape of the back wave 954 shown in FIG. 18 is regarded as a circular arc, and is obtained by fitting.
[0099]
number
[0100] 18 is calculated using Equation 12 as shown in Equation 13, thereby obtaining the back bead height. The back bead height h predicted in the state analysis unit 506 (hereinafter, also referred to as the "predicted back bead height h") is displayed on the display 55 together with, for example, one of the welding conditions described above.
[0101]
number
[0102] Table 2 shows the results of comparing the predicted back bead height h described above with the actual back bead height. The actual back bead height was measured by performing backingless back bead welding on the base materials 91 and 92 in the automatic welding device 2 and measuring the back bead height. Experiments 1 to 3 in Table 2 correspond to Experiments 1 to 3 in Table 1 described above, and the gap amount W of the groove portion 93 of the base materials 91 and 92 was g was changed in the range of 0mm to 2mm.
[0103] [Table 2]
[0104] As shown in Table 2, in Experiments 1 to 3, the predicted back bead heights h were 0.76 mm, 0.22 mm, and 0.15 mm, and the actual back bead heights were 0.75 mm, 0.37 mm, and 0.23 mm. Thus, in Experiments 1 to 3, the back bead heights could be predicted with high accuracy. In addition, in the prediction of the back bead height described above, the arc pressure distribution may be used instead of the arc force.
[0105] The state analysis unit 506 can also predict the occurrence of "burn-through", which is one type of welding defect, by using the predicted back bead height h. Specifically, when the predicted back bead height h is greater than or equal to a predetermined judgment threshold T h If the predicted back bead height h is equal to or less than the threshold T h If the difference is larger than 1, it is determined that burn-through will occur. The presence or absence of burn-through predicted by the state analysis unit 506 (hereinafter also referred to as "second burn-through prediction") is displayed on the display 55 together with the one welding condition described above, for example.
[0106] Fig. 19 is a graph comparing the results of the second burn-through prediction described above with the presence or absence of actual burn-through. The presence or absence of actual burn-through was confirmed visually after backingless uranami welding was performed on base materials 91, 92 in an automatic welding device 2. The horizontal axis in Fig. 19 indicates the case number as in Figs. 14 and 16, and the vertical axis indicates the predicted back bead height h described above. In Fig. 19, the judgment threshold T h is indicated by a dashed line. In the example shown in FIG. h is 1. The experimental conditions for cases 1 to 23 are the same as those for the above-mentioned FIG. 14 and FIG.
[0107] In cases 1 to 5, 6 to 13, and 19 to 23, which are surrounded by dashed double-dashed lines, the predicted back bead height h is greater than or equal to the judgment threshold T h As described above, normal back bead welding was performed in cases 1 to 5, insufficient penetration occurred in cases 6 to 13, and bridge fracture occurred in cases 19 to 23. On the other hand, in cases 14 to 18, the predicted back bead height h was greater than the judgment threshold T h In addition, in Fig. 19, the predicted back bead height h in case 18 was greater than 10, which is the upper limit of the graph.
[0108] In the welding system 1, for example, an operator inputs one welding condition into the welding state analyzer 5 and checks the first burn-through prediction, the second burn-through prediction, the bridge fracture prediction, the penetration deficiency prediction, and the predicted back bead height h displayed on the display 55. Then, the operator judges whether the input welding condition is acceptable or not based on one or more of these prediction results. For example, the operator judges as acceptable a welding condition under which no burn-through occurs in the first burn-through prediction and the second burn-through prediction, no bridge fracture occurs in the bridge fracture prediction, no penetration deficiency occurs in the penetration deficiency prediction, and the predicted back bead height h is within a desired range. Then, backingless back bead welding is performed in the automatic welding device 2 under the welding condition judged as acceptable by the operator.
[0109] Alternatively, in the welding system 1, for example, the automatic welding device 2 may generate cross-sectional shape information (e.g., groove angle θ g and root height H g The cross-sectional shape information is acquired by the sensor unit 213 and sent to the welding state analysis device 5. In the welding state analysis device 5, while changing welding conditions other than the cross-sectional shape information (for example, the welding speed and welding current in the automatic welding device 2, etc.), a first burn-through prediction, a second burn-through prediction, a bridge fracture prediction, and a penetration shortage prediction are performed for each of the plurality of welding conditions, and a predicted back bead height h is obtained. Then, based on one or more of these prediction results, the welding state analysis device 5 judges whether each of the plurality of welding conditions is acceptable or not. In the welding system 1, one welding condition judged to be acceptable by the welding state analysis device 5 is sent to the automatic welding device 2, and the automatic welding device 2 performs backingless back bead welding under the one welding condition.
[0110] As described above, the above-mentioned welding state analysis method for analyzing the welding state includes a step of acquiring a molten pool shape that is a three-dimensional shape of the molten pool 95 where welding is being performed (step S11), a step of acquiring a virtual bead shape that is a three-dimensional shape of a bead (i.e., front bead 94) at a position corresponding to the molten pool 95 when it is assumed that no plunge pressure due to the welding phenomenon is applied to the molten pool 95 (step S12), and a step of determining a welding pressure distribution (arc pressure distribution in the above example) that is a distribution of the plunge pressure on the molten pool 95 due to the welding phenomenon or a welding force (arc force in the above example) that is a plunge force on the molten pool 95 due to the welding phenomenon based on the difference between the molten pool shape and the virtual bead shape (step S13). This makes it possible to accurately acquire the state of the molten pool 95 (particularly, the welding pressure distribution and / or the welding force applied to the molten pool 95).
[0111] As described above, the welding condition analysis method preferably further includes a step of performing steps S11, S12, and S13 for each of a plurality of welding conditions to determine a plurality of welding pressure distributions or a plurality of welding forces corresponding to the plurality of welding conditions (steps S11 to S15), and acquiring correlation information showing a correlation between the welding conditions and the welding pressure distributions or welding forces (step S16). By utilizing the correlation information, the welding pressure distribution or welding force corresponding to one welding condition can be acquired without actually performing welding.
[0112] As described above, it is preferable that the welding condition analysis method further includes a step (step S21) of determining a corresponding welding pressure distribution (in the above example, a corresponding arc pressure distribution) which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force (in the above example, a corresponding arc force) which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information, and a step (step S22) of predicting the presence or absence of welding defects in the molten pool 95 under the one welding condition, based on a mathematical model of the molten pool 95 using the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the presence or absence of welding defects (e.g., burn-through) under one welding condition, without actually performing welding.
[0113] As described above, it is preferable that the welding condition analysis method further includes a step (step S51) of determining a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information, and a step (step S52) of predicting a shape of a bead after molten pool 95 is solidified under the one welding condition, based on a mathematical model of molten pool 95 using the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the shape of a bead formed under one welding condition (e.g., back bead height) without actually performing welding.
[0114] The above-mentioned welding condition analysis method preferably further includes a step (step S31) of calculating a first energy which is the surface free energy of the molten metal bridging between the two base materials 91, 92 in the form of a liquid film, and a second energy which is the surface free energy in a state in which the molten metal bridging between the two base materials 91, 92 in the form of a liquid film is separated and held in the form of droplets on the surfaces of the two base materials 91, 92, and a step (steps S32 to S34) of predicting the occurrence of bridge fracture in which the molten metal bridging between the two base materials 91, 92 in the form of a liquid film is separated, based on the first energy and the second energy. This makes it possible to predict the occurrence of bridge fracture without actually performing welding.
[0115] The above-mentioned welding condition analysis method preferably further includes a step (steps S41 to S43) of predicting the presence or absence of insufficient penetration into the back surface (the (-Z) side surface in the above example) of the base materials 91, 92 based on the weld height and the heat input per unit length. This makes it possible to predict the presence or absence of insufficient penetration without actually performing welding.
[0116] The above-mentioned welding state analysis device 5 for analyzing the welding state includes a weld pool shape acquisition unit 502, a bead shape acquisition unit 503, and a welding calculation unit 504. The weld pool shape acquisition unit 502 acquires a weld pool shape that is a three-dimensional shape of the weld pool 95 where welding is being performed. The bead shape acquisition unit 503 acquires a virtual bead shape that is a three-dimensional shape of a bead (i.e., a front bead 94) at a position corresponding to the weld pool 95 when it is assumed that no pressing pressure due to the welding phenomenon is applied to the weld pool 95. The welding calculation unit 504 obtains a welding pressure distribution that is a distribution of pressing pressure on the weld pool 95 due to the welding phenomenon, or a welding force that is a pressing force on the weld pool 95 due to the welding phenomenon, based on the difference between the weld pool shape and the virtual bead shape. This makes it possible to accurately acquire the state of the weld pool 95 (particularly, the welding pressure distribution and / or the welding force applied to the weld pool 95) as described above.
[0117] As described above, it is preferable that the welding condition analyzing device 5 further includes an information acquiring unit 505. The information acquiring unit 505 preferably acquires correlation information indicating a correlation between a welding condition and a welding pressure distribution or a welding force from a combination of a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces calculated for each of the plurality of welding conditions by the welding calculation unit 504. By utilizing the correlation information, the welding condition analyzing device 5 can acquire a welding pressure distribution or a welding force corresponding to one welding condition without actually performing welding.
[0118] As described above, the welding condition analysis device 5 preferably further includes a condition analysis unit 506. The condition analysis unit 506 preferably obtains a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information. The condition analysis unit 506 preferably predicts the presence or absence of welding defects in the molten pool 95 under the one welding condition, based on a mathematical model of the molten pool 95 using the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the presence or absence of welding defects (e.g., burn-through) under the one welding condition without actually performing welding.
[0119] As described above, the state analyzing unit 506 predicts the shape of the bead after the molten pool 95 has solidified under a certain welding condition, preferably based on a mathematical model of the molten pool 95 that utilizes the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the shape of the bead (e.g., back bead height) formed under a certain welding condition without actually performing welding.
[0120] As described above, the state analyzing unit 506 preferably calculates a first energy which is the surface free energy of the molten metal bridging between the two base materials 91, 92 in the form of a liquid film, and a second energy which is the surface free energy in a state in which the molten metal bridging between the two base materials 91, 92 in the form of a liquid film is separated and held in the form of droplets on the surfaces of the two base materials 91, 92. The state analyzing unit 506 preferably predicts the occurrence of bridge rupture, in which the molten metal bridging between the two base materials 91, 92 in the form of a liquid film is separated, based on the first energy and the second energy. This makes it possible to predict the occurrence of bridge rupture without actually performing welding.
[0121] As described above, the state analyzing unit 506 preferably predicts the presence or absence of insufficient penetration into the rear surfaces of the base materials 91, 92 based on the welding height and the amount of heat input per unit length. This makes it possible to predict the presence or absence of insufficient penetration without actually performing welding.
[0122] The welding system 1 includes the above-mentioned welding state analysis device 5 and an automatic welding device 2 that performs welding under welding conditions determined based on the welding pressure distribution or welding force obtained by the welding state analysis device 5. As described above, the welding state analysis device 5 can predict the state of the molten pool 95 under certain welding conditions without actually performing welding, so there is no need to perform trial and error involving actual welding to determine the welding conditions. Therefore, the welding state analysis device 5 is particularly suitable for automatic welding in the automatic welding device 2, which requires a lot of trial and error, rather than manual welding, in which trial and error is relatively easy.
[0123] As described above, the program 512 is a computer-readable program that causes a computer to execute an analysis of the welding state. The program 512 is executed by a computer to perform the following steps: acquiring a weld pool shape that is a three-dimensional shape of the weld pool 95 in which welding is being performed (step S11); acquiring a virtual bead shape that is a three-dimensional shape of a bead (i.e., a front bead 94) at a position corresponding to the weld pool 95 when it is assumed that no plunge pressure due to the welding phenomenon is applied to the weld pool 95 (step S12); and calculating a welding pressure distribution that is a distribution of the plunge pressure on the weld pool 95 due to the welding phenomenon, or a welding force that is a plunge force on the weld pool 95 due to the welding phenomenon, based on the difference between the weld pool shape and the virtual bead shape (step S13). As a result, the state of the weld pool 95 (particularly, the welding pressure distribution and / or the welding force applied to the weld pool 95) can be acquired with high accuracy, as described above.
[0124] In the welding state analyzing device 5, it is not necessary to acquire correlation information indicating the correlation between the welding conditions and the welding pressure distribution or the welding force, and for example, the correlation information prepared in advance may be stored in the storage unit 501. As described above, the correlation information is obtained based on a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces corresponding to the plurality of welding conditions. In addition, the plurality of welding pressure distributions or the plurality of welding forces are each obtained based on the difference between a molten pool shape, which is a three-dimensional shape of the molten pool, and a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no plunge pressure due to a welding phenomenon is applied to the molten pool.
[0125] In this case, the state analysis unit 506 obtains a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information. Then, the state analysis unit 506 predicts the presence or absence of a welding defect in the molten pool 95 under the one welding condition, based on a mathematical model of the molten pool 95 using the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the presence or absence of a welding defect (e.g., burn-through) under the one welding condition without actually performing welding. Furthermore, the state analysis unit 506 predicts the shape of a bead after the molten pool 95 has solidified under the one welding condition, based on the mathematical model of the molten pool 95 using the corresponding welding pressure distribution or the corresponding welding force. This makes it possible to predict the shape of a bead (e.g., back bead height) formed under the one welding condition, without actually performing welding. In addition, when the correlation information is prepared in advance in this manner, the molten pool shape acquisition unit 502, the bead shape acquisition unit 503, the welding calculation unit 504 and the information acquisition unit 505 may be omitted in the welding state analysis device 5.
[0126] The above-described welding condition analysis method, welding condition analysis device 5, welding system 1, and program 512 can be modified in various ways.
[0127] For example, in the welding condition analyzing device 5, the welding defects the occurrence of which is predicted by the condition analyzing unit 506 are not limited to the above-mentioned examples (burn-through, bridge fracture, and insufficient penetration) and may be changed in various ways. For example, the welding condition analyzing device 5 can also predict the occurrence of welding defects such as dripping of molten metal during overhead position welding by applying a mathematical model for predicting the first burn-through.
[0128] The welding condition analyzing device 5 does not necessarily have to predict the occurrence of welding defects and predict the shape of the bead. In this case, the condition analyzing unit 506 may be omitted. Moreover, the welding condition analyzing device 5 does not necessarily have to acquire the above-mentioned correlation information. In this case, the information acquiring unit 505 may be omitted.
[0129] The welding condition analyzing device 5 may determine the arc pressure distribution and / or the arc force applied to the molten pool 95 in arc welding other than backingless uranami welding. Alternatively, for welding other than arc welding (e.g., laser-arc hybrid welding, laser welding, etc.), the welding pressure distribution, which is the distribution of the plunge pressure on the molten pool 95 due to the welding phenomenon, and / or the welding force, which is the plunge force on the molten pool 95 due to the welding phenomenon, may be determined by the welding condition analyzing device 5.
[0130] In the automatic welding device 2, arc welding other than backingless uranami welding may be performed.
[0131] In the automatic welding device 2, a movement mechanism for moving the holding part 22 relative to the welding robot 21 may be provided.
[0132] The welding condition analyzer 5 does not necessarily have to be included in the welding system 1, and may be used independently of the automatic welding device 2, for example.
[0133] The configurations in the above-described embodiment and each of the modified examples may be combined as appropriate as long as they are not mutually inconsistent. [Explanation of symbols]
[0134] 1 Welding system 2 Automatic welding equipment 5. Welding condition analysis device 91,92 Base material 94 Front bead 95 Molten Pool 502 Molten pool shape acquisition section 503 Bead shape acquisition unit 504 Welding Calculation Unit 505 Information Acquisition Department 506 Status Analysis Unit 512 Program 942 Virtual Bead S11~S16, S21~S22, S31~S34, S41~S43, S51~S52, S221~S223 Steps
Claims
1. A welding condition analysis method for analyzing a welding condition, comprising: a) acquiring a three-dimensional shape of a molten pool in which welding is being performed; b) acquiring a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no plunge pressure due to a welding phenomenon is applied to the molten pool; c) determining a welding pressure distribution, which is a distribution of a pressing pressure on the molten pool due to a welding phenomenon, or a welding force, which is a pressing force on the molten pool due to a welding phenomenon, based on a difference between the molten pool shape and the virtual bead shape; A welding condition analysis method comprising:
2. The welding state analysis method according to claim 1, d) performing steps a), b), and c) for each of a plurality of welding conditions to determine a plurality of welding pressure distributions or a plurality of welding forces corresponding to the plurality of welding conditions, respectively, and acquiring correlation information indicating a correlation between the welding conditions and the welding pressure distributions or the welding forces.
3. The welding state analysis method according to claim 2, determining a corresponding welding pressure distribution that is a welding pressure distribution corresponding to the one welding condition or a corresponding welding force that is a welding force corresponding to the one welding condition based on the one welding condition and the correlation information; a step of predicting whether or not a welding defect will occur in the molten pool under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force; The welding condition analysis method further comprises:
4. The welding state analysis method according to claim 2, determining a corresponding welding pressure distribution that is a welding pressure distribution corresponding to the one welding condition or a corresponding welding force that is a welding force corresponding to the one welding condition based on the one welding condition and the correlation information; predicting a shape of a bead after the molten pool is solidified under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force; The welding condition analysis method further comprises:
5. 5. A welding condition analysis method according to claim 1, further comprising the steps of: Calculating a first energy, which is the surface free energy of the molten metal bridging between two base materials in the form of a liquid film, and a second energy, which is the surface free energy of the molten metal in the form of a liquid film bridging between the two base materials when the molten metal is separated from the liquid film and held in the form of droplets on the surfaces of the two base materials; a step of predicting whether or not a bridge fracture occurs, in which the molten metal in a liquid film state bridging between the two base materials is separated, based on the first energy and the second energy; The welding condition analysis method further comprises:
6. 5. A welding condition analysis method according to claim 1, further comprising the steps of: The welding condition analysis method further includes a step of predicting whether or not there is insufficient penetration into the back surface of the base material based on the weld height and the heat input per unit length.
7. A welding condition analysis device for analyzing a welding condition, a molten pool shape acquisition unit that acquires a molten pool shape, which is a three-dimensional shape of the molten pool where welding is being performed; a bead shape acquisition unit that acquires a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no pressing pressure due to a welding phenomenon is applied to the molten pool; a welding calculation unit that calculates a welding pressure distribution, which is a distribution of a pressing pressure on the molten pool due to a welding phenomenon, or a welding force, which is a pressing force on the molten pool due to a welding phenomenon, based on a difference between the molten pool shape and the virtual bead shape; A welding condition analysis device comprising:
8. The welding condition analysis device according to claim 7, The welding condition analysis device further includes an information acquisition unit that acquires correlation information indicating a correlation between a welding condition and a welding pressure distribution or a welding force from a combination of a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces calculated by the welding calculation unit for each of the plurality of welding conditions.
9. The welding condition analysis device according to claim 8, The welding condition analysis device further includes a condition analysis unit that calculates a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information, and predicts whether or not a welding defect will occur in the molten pool under the one welding condition based on a mathematical model of the molten pool that utilizes the corresponding welding pressure distribution or the corresponding welding force.
10. The welding condition analysis device according to claim 8, The welding condition analysis device further includes a condition analysis unit that calculates a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to one welding condition, or a corresponding welding force, which is a welding force corresponding to one welding condition, based on one welding condition and the correlation information, and predicts a shape of a bead after the molten pool has solidified under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force.
11. The welding condition analysis device according to claim 7, The welding condition analysis device further includes a condition analysis unit that calculates a first energy, which is the surface free energy of the molten metal bridging between two base materials in the form of a liquid film, and a second energy, which is the surface free energy of the molten metal bridging between the two base materials in the form of a liquid film and being held in the form of droplets on the surfaces of the two base materials, and predicts whether or not bridge fracture will occur in which the molten metal bridging between the two base materials in the form of a liquid film will separate, based on the first energy and the second energy.
12. The welding condition analysis device according to claim 7, The welding condition analyzing device further includes a condition analyzing unit that predicts whether or not there is insufficient penetration into the back surface of the base material based on the weld height and the heat input per unit length.
13. 1. A welding system comprising: A welding condition analyzing device according to any one of claims 7 to 12, an automatic welding device that performs welding under welding conditions determined based on the welding pressure distribution or welding force obtained by the welding state analysis device; A welding system comprising:
14. A welding condition analysis device for analyzing a welding condition, a storage unit that stores correlation information indicating a correlation between a welding pressure distribution, which is a distribution of a plunge pressure due to a welding phenomenon on a molten pool where welding is being performed, or a welding force, which is a plunge force on the molten pool due to a welding phenomenon, and a welding condition; a state analysis unit which determines a corresponding welding pressure distribution, which is a welding pressure distribution corresponding to the one welding condition, or a corresponding welding force, which is a welding force corresponding to the one welding condition, based on the one welding condition and the correlation information, and predicts whether or not a welding defect will occur in the molten pool under the one welding condition, based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force; Equipped with the correlation information is obtained based on a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces respectively corresponding to the plurality of welding conditions; A welding condition analysis device in which the multiple welding pressure distributions or the multiple welding forces are each determined based on the difference between a molten pool shape, which is the three-dimensional shape of the molten pool, and a virtual bead shape, which is the three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no pressing pressure due to a welding phenomenon is applied to the molten pool.
15. A welding condition analysis device for analyzing a welding condition, a storage unit that stores correlation information indicating a correlation between a welding pressure distribution, which is a distribution of a plunge pressure due to a welding phenomenon on a molten pool where welding is being performed, or a welding force, which is a plunge force on the molten pool due to a welding phenomenon, and a welding condition; a state analysis unit that calculates a corresponding welding pressure distribution that is a welding pressure distribution corresponding to the one welding condition or a corresponding welding force that is a welding force corresponding to the one welding condition based on the one welding condition and the correlation information, and predicts a shape of a bead after the molten pool has solidified under the one welding condition based on a mathematical model of the molten pool using the corresponding welding pressure distribution or the corresponding welding force; Equipped with the correlation information is obtained based on a plurality of welding conditions and a plurality of welding pressure distributions or a plurality of welding forces respectively corresponding to the plurality of welding conditions; A welding condition analysis device in which the multiple welding pressure distributions or the multiple welding forces are each determined based on the difference between a molten pool shape, which is the three-dimensional shape of the molten pool, and a virtual bead shape, which is the three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no pressing pressure due to a welding phenomenon is applied to the molten pool.
16. A computer-readable program for causing a computer to execute an analysis of a welding state, When the program is executed by a computer, a) acquiring a three-dimensional shape of a molten pool in which welding is being performed; b) acquiring a virtual bead shape, which is a three-dimensional shape of a bead at a position corresponding to the molten pool when it is assumed that no plunge pressure due to a welding phenomenon is applied to the molten pool; c) determining a welding pressure distribution, which is a distribution of a pressing pressure on the molten pool due to a welding phenomenon, or a welding force, which is a pressing force on the molten pool due to a welding phenomenon, based on a difference between the molten pool shape and the virtual bead shape; A computer readable program for carrying out the steps of the present invention.
Citation Information
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