JP4945312B2 - Method and system for analyzing physical quantity of welded body - Google Patents

Description

The present invention relates to an analysis method and an analysis system for a welded body physical quantity that solves a physical quantity of the welded body when multilayer welding is performed by numerical analysis.

  Welding is a joining method in which a welding rod or welding torch serving as a heat source is moved on the weld line of the welded body, and a high-temperature weld metal is attached to the welded body. A weld formed by passing a welding rod on the weld line is called a welding pass. Repeated welding is performed to form layers by several passes at the same height in the groove. Welding is completed by laminating to. In general, the welded portion has multiple passes and multiple layers.

  Residual stress generated in welded structures such as pipes by welding is generated with local and rapid temperature changes due to heat during welding and is one of the main causes of stress corrosion cracking. Therefore, research and development of a welding method for reducing residual stress has been conventionally performed (for example, see Patent Documents 1 to 5). Further, a method for measuring the residual stress has been studied (see, for example, Patent Document 6 and Patent Document 7).

  On the other hand, methods for predicting / evaluating residual stress have also been studied (see, for example, Patent Document 8 and Patent Document 9). Residual stress analysis, which is one of these methods, requires thermal elastic-plastic analysis that simulates unsteady heat input by welding. This is an analysis that closely simulates the welding process. When multi-layer welding is used, analysis over multiple welding paths is required, so a large amount of calculation time is required even for calculations using a large computer. . For this reason, methods for reducing the calculation time are also being studied (see, for example, Patent Document 10 and Patent Document 11). Residual stress analysis consists of heat transfer analysis that solves heat transfer phenomena and elastoplastic analysis that solves changes in physical properties due to thermal history. However, heat transfer analysis and elastoplastic analysis do not necessarily need to be performed simultaneously. Thermal elasto-plastic stress analysis can be performed using the resulting temperature history.

In welding residual stress analysis, the progress rate of the welding rod in actual welding is generally used as the governing equation expressed by the unsteady heat transfer equation in the heat transfer analysis and the balance equation in the elasto-plastic analysis is advanced over time. Move the heat input part to match. By analyzing the time progress of actually moving the heat input part, analysis results represented by the temperature history, residual stress, strain, etc. of the welded body were obtained. In this way, when moving the welding line through the heat input part, in order to analyze changes in temperature, strain, stress, etc. with high accuracy, a dense analysis grid is prepared over the entire moving range of the welding rod. It was necessary and a large amount of calculation was required.
Japanese Patent Laid-Open No. 10-128534 JP-A-9-229248 JP-A-9-1376 Japanese Patent Laid-Open No. 5-154683 JP 2004-122222 A Japanese Patent Laid-Open No. 2001-221697 JP 2000-146716 A JP 2004-181462 A JP 2004-330212 A JP 2004-53366 A JP-A-6-180271 JP 2005-83810 A M. Gu and JAGoldak, “Steady State Formulation for Stress and Distortion of Welds”, ASME PED-Vol. 64, Manufacturing Science and Engineering, 1993, p. 843-854

  In the residual stress analysis, the calculation time can be reduced by replacing the three-dimensional object with the two-dimensional model. However, in the analysis that requires a three-dimensional model capable of reproducing the event more precisely, the calculation time is reduced. Is enormous.

  In elasto-plastic analysis, attention is often focused only on the portion occupying most of the weld line, not on the welding start and end portions. Further, the portion where the change in residual stress and strain becomes large is mainly in the vicinity of the high temperature portion where the temperature change is large, and the high temperature portion around the welding rod excluding the welding start and end portions is considered to be fixed with respect to the position of the welding rod. In addition, the temperature change at any point of interest having the same distance from the weld line and the direction except for the portion close to the welding start portion and the end portion only shifts the temperature peak generation time.

  Focusing on this point, attempts have been made to reduce the calculation time required for this heat transfer analysis by applying a moving coordinate system (see, for example, Patent Document 12), and the moving coordinate system was also applied to elastoplastic analysis. A technique is disclosed (for example, see Non-Patent Document 1). However, methods employing these moving coordinate systems do not assume continuous welding such as multi-pass or multilayer welding. For this reason, the effects of welding in one welding pass, such as strain and residual stress in elasto-plastic analysis, are not carried over to the analysis of subsequent welding passes. Is difficult.

  Therefore, an object of the present invention is to shorten the calculation time required for numerical analysis of physical quantities such as residual stress of a welded body during multi-layer welding.

To solve the problems described above, the physical quantity of the object to be welded body when the multilayer welding in multiple weld pass by moving a plurality of times a heat source along the weld line of the welded body, governing the phenomenon differential equation and integrating In the method of analyzing a physical quantity to be welded that solves an equation described by any of the equations by numerical analysis, using a moving coordinate system that moves in the opposite direction at the same speed as the moving speed of the heat source in the welding path, The numerical analysis of the analysis model in which the welded body is projected and arranged corresponding to each welding path so that the welding line is continuous downstream of the moving coordinate system of the welding line in the previous welding path gastric row, at the same time the analysis of the final welding pass is completed, to get the results of the physical quantity of the total welding end condition, characterized by.

Further, the present invention is that the physical quantity of the object to be welded body when the multilayer welding in multiple weld pass by moving a plurality of times a heat source along the weld line of the welded body, the differential equation and integral equation governing the behavior In the system for analyzing a physical quantity to be welded that solves the equation described by any one of the numerical values, the welding line is moved using a moving coordinate system that moves in the opposite direction at the same speed as the moving speed of the heat source in the welding path. An analysis model that generates and stores an analysis model in which the welding target is projected and arranged corresponding to each welding path so that the welding line is continuous downstream of the moving coordinate system of the welding line in the previous welding pass a model storage device, wherein the physical quantity of the object to be welded body, computer programming solved by numerical analysis equations described by any of the differential equation and integral equation governing the behavior Obtained a program storage device for storing beam, obtains the physical quantity of the object to be welded member using the computer program based on the analysis model, and at the same time the analysis of the final welding pass is completed, the results of the physical quantity of the total welding end condition And an arithmetic unit.

  According to the present invention, it is possible to reduce the calculation time required for numerical analysis of physical quantities such as residual stress of the welded body during multi-layer welding.

  An embodiment of residual stress analysis during multi-layer welding according to the present invention will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected to the same or similar structure, and the overlapping description is abbreviate | omitted.

[First Embodiment]
FIG. 2 is a perspective view showing multi-layer welding to be analyzed in the first embodiment of residual stress analysis during multi-layer welding according to the present invention.

  In welding, a welding rod 22 or a welding torch serving as a heat source is moved along a welding line 25 of the welded body 21, and a high-temperature weld metal 24 is attached to the welded body 21. A welded portion formed by passing the welding rod 22 over the weld line 25 is referred to as a welding pass. In multilayer welding, welding is repeatedly performed, layers are formed by several passes of the same height in the groove, and a plurality of layers are stacked in the groove to complete the welding. In the present embodiment, the multilayer linear welding in which the welded portion of the flat plate-like workpiece is multi-pass / multi-layered is set as the analysis target, and this analysis target is handled by the moving coordinate system, and the elasto-plastic analysis and transmission are performed. Perform thermal analysis.

  Next, an analysis method using a moving coordinate system will be described.

  FIG. 3 is a perspective view schematically showing an analysis model in a fixed coordinate system. FIG. 4 is a perspective view schematically showing an analysis model in the moving coordinate system. FIGS. 3 and 4 both show a state in which linear welding along the welding line 5 is performed on the flat plate-like workpiece 1.

  In the analysis model in the fixed coordinate system as shown in FIG. 3, for example, the same shape as the welded body 1 is used as the analysis region, the welding rod 2 is not modeled, and the heat input portion 7 is modeled as a boundary condition. In the analysis, heat input is modeled by a method of giving the heat input portion 7 as a boundary condition, a method of regarding a region in the welded body as a heating element, or the like.

  In welding residual stress analysis using an analysis model in a fixed coordinate system, the unsteady heat transfer equation in heat transfer analysis and the governing equation expressed by the balance equation in elasto-plastic analysis are progressed over time, so welding in actual welding The heat input part 7 is moved in accordance with the traveling speed 8 of the rod 2. For this reason, when a certain time passes, the welding rod 2 and the heat input part 7 will be in the position of the code | symbol 9 and the code | symbol 10, respectively. In this way, by analyzing the time progress of actually moving the heat input section 7, analysis results represented by the temperature history, residual stress, strain, and the like of the welded body 1 are obtained.

  That is, the relationship between the welding rod 2 serving as a heat source and the welding line 5 is a movement in a certain direction of the welding rod 2 between the welding start point and the end point on the welding line. This relationship is the same even when welding is performed in multiple layers or multiple passes, and the above-described traveling motion is repeated the number of times of the welding passes.

  On the other hand, in the analysis model in the moving coordinate system as shown in FIG. 4, the moving motion of the welding rod 2 serving as the heat source is handled in the moving coordinate system that moves together with the heat source. Considering a moving coordinate system that moves together with the heat source, the heat input portion 7 is apparently stopped, and the welded body 1 moves in the direction 3 opposite to the welding direction along the welding direction.

  FIG. 1 is a perspective view of an analysis model in the present embodiment. FIG. 5 is a flowchart showing an analysis procedure in the present embodiment.

  The residual stress analysis according to the present embodiment is performed when a plurality of welding passes are welded along the weld line 105 of the workpiece 101.

  In the residual stress analysis, first, discretization of the object to be analyzed, analysis conditions, physical property values of the object to be analyzed and the weld metal are set and input, or a file in which these are described in advance is read (step S1).

  In discretization of the object to be analyzed, the welded body 1 is modeled so that the welding end point in one pass and the start point of the next welding pass are numerically continuous. That is, modeling is performed so that the objects to be welded 1 and the objects to be welded 1 in which the welding pass has been completed one or more times are projected side by side and are treated as numerically continuous. Further, it is assumed that the welding rod 102 serving as a heat source corresponding to each welding path and the projected welding rods 202 and 302 on which the welding rod 102 is projected are also arranged side by side. This modeling reproduces the procedure in which weld metal is gradually laminated in an analysis using a moving coordinate system that moves with the heat source, and therefore reflects all the effects of welding from the first welding pass to the end of welding. Analysis can be performed.

  Specifically, the projection welded body 201 is modeled so as to be continuous with the welded body 101 in the first welding pass. The projected welded body 201 is a projection of the welded body 1 in the second welding pass in which the welding pass is completed once. Similarly, projections of welded bodies 101 in which the welding pass has been completed one or more times are arranged side by side, and are modeled so as to continue to the projected welded body 301 on which the welded body 1 is projected in the final welding pass. To do. By this modeling, the weld line 105 of the welded body 101 appears as a straight line continuous to the weld line 205 in the second weld pass and the weld line 305 in the final weld pass.

  In elasto-plastic analysis, constraint conditions, welding start temperature, ambient temperature, and the like can be cited as analysis conditions. Further, in the elasto-plastic analysis, the density, elastic constant, stress-strain relationship, etc. of the welded body and the weld metal are listed as physical property values.

  In the heat transfer analysis, the amount of heat input, the heat input position, the heat input distribution of each welding pass, and their changes over time, the moving speed or moving angular speed of the heat input part, the temperature at the start of welding, the ambient temperature, and the heat related to heat release to the atmosphere. The transmission rate can be cited as an analysis condition. In heat transfer analysis, the physical properties include the density, thermal conductivity, specific heat, and the like of the welded body and the weld metal.

  Next, all the welding pass heat input parts modeled in step S1 are modeled (step S2).

  The heat sources corresponding to the respective welding passes, that is, the respective heat input portions are arranged as follows according to the welding order. The heat source corresponding to each welding pass is along the welding lines 105, 205, 305 to the heat input part 107 of the first welding pass, the heat input part 207 of the second welding pass, and the heat input part 307 of the final welding pass. Be placed. Note that modeling is not performed for the welding rod 102 and the projection welding rods 202 and 302 in the first welding pass, the second welding pass, and the final welding pass.

  In FIG. 1, reference numerals 106, 206, and 306 represent welded weld lines in the first welding pass, the second welding pass, and the third welding pass, respectively. Reference numerals 104, 204, and 304 denote welding rods 102, 202, and 102 to be welded body 101 in the first welding pass, and projection welded bodies 201 and 301 in the second and final welding passes, respectively. 302 represents the relative velocity. In this analysis model, by using a movement coordinate system with the welding rod as a reference, the movement of the welding rod 2 in the direction opposite to the actual movement of the welding rod 2 is performed at each position of the welded body 1.

  Next, the conditions at the start of welding are set as initial conditions (step S3). The initial temperature is the welding start temperature.

  Thereafter, elastoplastic analysis and heat transfer analysis are performed under the welding conditions of each welding pass (step S4). The calculation is performed sequentially under the welding conditions for each pass.

  In the welded body 101, calculation of welding by the first welding pass is performed, and the residual stress by the first welding pass is calculated in the downstream portion. This state serves as an input for analysis of the projection welded body 201, and the heat input portion 207 of the projection welded body 201 performs welding analysis of the second welding pass in addition to the welding end state of the first welding pass. . Therefore, in the downstream portion of the welded body 201, in addition to the history of the first welding pass, the residual stress in the state where the analysis of the second welding pass is completed is calculated. By repeating the same, on the downstream side of the projection welded body 301 that models the final welding pass, after the heat input by all the welding passes is applied, that is, the residual stress in the state of completion of all the weldings is obtained.

  By the above modeling, the object to be analyzed in the final welding pass finishes welding, and at the same time, the object to be analyzed 1 finishes the elasto-plastic analysis and the heat transfer analysis through calculation by all the welding passes. By treating all the welding passes as numerically continuous, the calculation history by welding is inherited as the elasto-plastic analysis conditions and heat transfer analysis conditions of the subsequent welding passes.

  Finally, the calculation result is output (step S5), and the analysis is terminated.

  Although the elastoplastic analysis and the heat transfer analysis may be performed simultaneously, the heat transfer analysis may be performed first, and then the elastoplastic analysis may be performed using the temperature history obtained by the heat transfer analysis.

  FIG. 6 is a block diagram of the analysis system in the present embodiment.

  This analysis system includes an analysis program storage device 13, a calculation result storage device 14, an analysis condition / physical property / analysis model storage device 15, a CPU (arithmetic unit) 16, a memory 17, an input device 18, and a display device 19. The analysis program storage device 13 stores a computer program for realizing the above analysis method. For example, analysis conditions, physical property values, and an analysis model input from the input device 18 are stored in the analysis condition / physical property / analysis model storage device 15. The analysis model may be automatically generated by inputting, into the analysis condition / physical property / analysis model storage device 15, the shape of the welded body 1, the movement of the welding rod 2 in each welding pass, and the like.

  When an analyst inputs an analysis execution command to the arithmetic device 16 via the input device 18, the arithmetic device 16 sends an elasto-plastic analysis program from the elasto-plastic analysis recording device 13 to analyze conditions, physical properties, and an analysis model. Reading from the physical property / analysis model recording device 15 and starting calculation of elasto-plastic analysis and heat transfer analysis. After the analysis is completed, the analysis result is recorded in the calculation result recording device 14 and the process ends. The analysis device may notify the analyst that the analysis has been completed.

  Note that a parallel calculation method may be used in which the entire region of the welded object 101 and the projection welded objects 201 and 301 to be analyzed is divided and the calculation is performed simultaneously and independently by different CPUs. In this case, a distributed memory type parallel computer such as a shared memory type parallel computer having a plurality of CPUs 16 or a PC cluster parallel computer in which a plurality of the above-described analysis systems are coupled to each other via a network can be used.

  When the welding line is modeled so that the heat input moves in a fixed coordinate system, it is necessary to analyze the changes in temperature, strain, stress, etc. with high accuracy over the entire moving range of the welding rod. It is necessary to prepare a dense analysis grid, which requires a large amount of calculation. On the other hand, when an analysis model of a moving coordinate system is used as in the present embodiment, a high temperature state during welding is shown in the vicinity of the heat input part, but the welding rod passes sufficiently on the downstream side of the heat input part. It represents a state in which the temperature has been lowered over time, and residual stress and strain after welding can be obtained. Therefore, by analyzing only the portion where the welding rod on the downstream side of the heat input portion passes and becomes low temperature after a sufficient time has passed, a highly accurate analysis result can be obtained in a short time.

  Thus, by using the analysis method of the present embodiment, the calculation time required for residual stress analysis during multi-layer welding can be shortened.

[Second Embodiment]
FIG. 7 is a perspective view of an analysis model in the second embodiment of the residual stress analysis at the time of multilayer welding according to the present invention.

  In the present embodiment, a part of the side surface of the cylinder is the welded body 101, and an analysis is performed in the case where multilayer outer circumferential welding is performed on the outer surface of the welded body 101. Since the welded body 101 is a part of a rotationally symmetric body, the welding rod 102 rotates in a fixed coordinate system in which the welded body 101 is fixed. Therefore, in this embodiment, a rotating coordinate system that moves with the heat input unit is used as the coordinate system. The movement of the welded body 101 is in the direction opposite to the actual rotation of the welding rod 102.

  Even in such a welded body 101, the residual stress analysis can be performed in the same manner as in the first embodiment by using the rotating coordinate system, and the calculation time required for the residual stress analysis during multi-layer welding is shortened. can do.

[Third Embodiment]
FIG. 8 is a perspective view of an analysis model in the third embodiment of the residual stress analysis at the time of multilayer welding according to the present invention.

  In the present embodiment, the welded body 101 has a sector shape, and an analysis is performed in the case of performing multilayer circumferential welding in the circumferential direction of the upper surface of the welded body 101. Since the welding is in the circumferential direction, the welding rod 102 rotates in a fixed coordinate system in which the workpiece 101 is fixed. Therefore, in this embodiment, a rotating coordinate system that moves with the heat input unit is used as the coordinate system. The movement of the welded body 101 is in the direction opposite to the actual rotation of the welding rod 102.

  Even in such a welded body 101, the residual stress analysis can be performed in the same manner as in the first embodiment by using the rotating coordinate system, and the calculation time required for the residual stress analysis during multi-layer welding is shortened. can do.

[Fourth Embodiment]
FIG. 9 is a perspective view of an object to be welded in the fourth embodiment of residual stress analysis during multi-layer welding according to the present invention.

  The welded body 1 of the present embodiment is a cylindrical rotationally symmetric body. Residual stress analysis is performed when the welding rod 2 is moved along the circumferential welding line 5 on the outer surface of the welded body 1 to perform multilayer circumferential welding. In FIG. 9, reference numeral 6 represents a welded weld line, reference numeral 11 represents a relative rotational direction of the welded body 1 with respect to the welding rod, and reference numeral 12 represents a relative rotational speed of the welded body 1 with respect to the welding rod 2.

  FIG. 10 is a perspective view of the analysis model in the present embodiment.

  Also in the present embodiment, as in the second embodiment, the welding end point 1 of each welding pass and the welding welding end point in one pass and the starting point of the next welding pass are numerically continuous. Project. At this time, in the second and subsequent welding passes, the projected workpiece 1001 may spatially overlap the previous welding pass, but this is allowed. That is, the welded body 1001 in each welding path is a numerically continuous projection, but each welding path is treated as a numerically different coordinate in calculation.

  10, reference numeral 102 denotes a welding rod in the first welding pass, and reference numeral 202 denotes a welding rod in the second welding pass. Reference numeral 107 denotes a heat input portion in the first welding pass, and reference numeral 202 denotes a heat input portion in the second welding pass. Reference numeral 1005 denotes a projected unwelded weld line, and reference numeral 1006 denotes a projected welded line. The circumferential length of the body 1 to be welded is determined from the time until the welding rod 102 passes through the weld and the next welding rod 202 appears and the welding speed.

  According to the analysis method of the present embodiment, even if the object 1 to be welded is projected continuously in correspondence with a plurality of welding passes, even if it is more than the circumferential length of the actual structure. It can be modeled so that the residual stress can be calculated in one analysis. Therefore, the calculation time required for the residual stress analysis at the time of multilayer welding can be shortened.

[Fifth Embodiment]
FIG. 11 is a perspective view of an object to be welded in a fifth embodiment of residual stress analysis during multilayer welding according to the present invention.

  The welded body 1 of the present embodiment is a disk-shaped rotationally symmetric body. Residual stress analysis is performed when the welding rod 2 is moved along the circumferential welding line 5 on the upper surface of the welded body 1 to perform multilayer circumferential welding.

  FIG. 12 is a perspective view of the analysis model in the present embodiment.

  Also in this embodiment, as in the third embodiment, the welding end point of each weld pass 1 in the welding pass and the starting point of the next welding pass are numerically continuous. Project. At this time, in the second and subsequent welding passes, as in the fourth embodiment, the projected welded object 1001 may spatially overlap the previous welding pass, but this is allowed. That is, the welded body 1001 in each welding path is a numerically continuous projection, but each welding path is treated as a numerically different coordinate in calculation.

  According to the analysis method of the present embodiment, even if the object 1 to be welded is projected continuously in correspondence with a plurality of welding passes, even if it is more than the circumferential length of the actual structure. It can be modeled so that the residual stress can be calculated in one analysis. Therefore, the calculation time required for the residual stress analysis at the time of multilayer welding can be shortened.

[Other embodiments]
The above description is merely an example, and the present invention is not limited to the above-described embodiments, and can be implemented in various forms. Moreover, it can also implement combining the characteristic of each embodiment.

It is a perspective view of an analysis model in a 1st embodiment of residual stress analysis at the time of multilayer welding concerning the present invention. It is a perspective view which shows the multilayer welding of the analysis object in 1st Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view which shows typically the analysis model in a fixed coordinate system. It is a perspective view which shows typically the analysis model in a movement coordinate system. It is a flowchart which shows the analysis procedure in 1st Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a block diagram of an analysis system in a 1st embodiment of residual stress analysis at the time of multilayer welding concerning the present invention. It is a perspective view of the analysis model in 2nd Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view of the analysis model in 3rd Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view of the to-be-welded body in 4th Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view of the analysis model in 4th Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view of the to-be-welded body in 5th Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention. It is a perspective view of the analysis model in 5th Embodiment of the residual stress analysis at the time of the multilayer welding which concerns on this invention.

Explanation of symbols

1, 2, 101, 1001 ... welded object, 2, 22, 102 ... welding rod, 5, 25, 105, 205, 305 ... weld line, 6 ... welded weld line, 7, 107, 207, 307 ... Heat input part, 8 ... Progression speed, 24 ... Weld metal, 201, 301 ... Projected body, 202, 302 ... Projected rod, 13 ... Analysis program storage device, 14 ... Calculation result storage device, 15 ... Analysis condition Physical property / analysis model storage device, 16 ... CPU, 17 ... memory, 18 ... input device, 19 ... display device

Claims (5)

The physical quantity of the object to be welded when the heat source is moved a plurality of times along the weld line of the object to be welded and multilayer welding is performed with a plurality of welding passes is described by either a differential equation or an integral equation governing the phenomenon. In the method of analyzing the physical quantity of the welded body that solves the equation by numerical analysis,
Using a moving coordinate system that moves in the opposite direction at the same speed as the moving speed of the heat source in the welding pass, the weld line is continuous downstream of the moving coordinate system of the weld line in the previous welding pass. There line the numerical analysis for the analysis models arranged by projecting the welded body to respond to each of the weld pass so, at the same time the analysis of the final welding pass is completed, the results of the physical quantity of the total welding end condition Getting ,
A method for analyzing a physical quantity of an object to be welded characterized by the following.   The said physical quantity contains stress, distortion, and temperature distribution, The to-be-welded body physical quantity analysis method of Claim 1 characterized by the above-mentioned.   The method for analyzing physical quantities to be welded according to claim 1 or 2, wherein the heat source rotates and the moving coordinate system is a rotating coordinate system.   When the projected welded object spatially overlaps with the welded object in another welding pass, the projected welded object is handled as being located at a numerically different coordinate. The method for analyzing physical quantities of a welded body according to claim 3. The physical quantity of the object to be welded when the heat source is moved a plurality of times along the weld line of the object to be welded and multilayer welding is performed with a plurality of welding passes is described by either a differential equation or an integral equation governing the phenomenon. In the physical quantity analysis system for the welded body that solves the equation by numerical analysis,
Using a moving coordinate system that moves in the opposite direction at the same speed as the moving speed of the heat source in the welding pass, the weld line is continuous downstream of the moving coordinate system of the weld line in the previous welding pass. An analysis model storage device for generating and storing an analysis model in which the welded objects are projected and arranged corresponding to each welding path,
A program storage device storing computer program to solve the physical quantity of the object to be welded body, the numerical analysis of the described equations by either differential equation and integral equation governing the phenomenon,
Determine the physical quantity of the object to be welded member using the computer program based on the analysis model, and at the same time the analysis of the final welding pass is completed, the resulting Ru computing device results of the physical quantity of the total welding end condition,
A system for analyzing a physical quantity of an object to be welded, comprising:

Images