JP2005083810A - Heat transfer analyzing method, recording medium having heat transfer analyzing program recorded thereon, heat transfer analyzer and residual stress analyzing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To reduce a calculation time and a calculation cost in the analysis of heat transfer such as the analysis of residual stress or the like. <P>SOLUTION: A heat source 8, of which the size is smaller than that of a member 1 being a solid, is moved on the surface of the member 1 and the temperature change brought about in the member 1 by the moving heat source 8 is calculated by numerically solving a heat transfer equation, which governs the phenomenon described by a differential equation or an integral equation, by the discretion of a space and time. A moving coordinates system moving at the same speed as the moving heat source 8 or a rotary coordinates system rotated at the same angular speed as the moving heat source is employed. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a heat transfer analysis method when a heat source moves on a solid surface, a recording medium recording a heat transfer analysis program, a heat transfer analysis device, and a residual stress analysis method.

Residual stress generated during welding of welded structures and pipes is caused by a rapid and local temperature change caused by the heat source of welding, but it may cause problems such as stress corrosion cracking. Welding methods for reducing residual stress have been pursued. Examples are shown in Patent Literature 1 (in-furnace equipment welding method), Patent Literature 2 (socket welded pipe joint), Patent Literature 3 (welding method of low residual stress structure), and Patent Literature 4 (stress relaxation method). Yes.
Further, Patent Document 5 (residual stress measurement method and apparatus), Patent Document 6 (residual stress measurement method and apparatus), and the like have been proposed as methods for measuring the residual stress.

  On the other hand, as a method for predicting residual stress, that is, a residual stress analysis method, a thermoelastic-plastic analysis that simulates unsteady heat input to the welded body is required. This is a simulation to be simulated, and even with the current large computer, a large amount of calculation time and calculation cost are required. Therefore, the following prediction methods with a short calculation time have been proposed as alternatives. Patent Document 7 (residual stress prediction method and apparatus), Patent Document 8 (welding residual stress and residual deformation prediction apparatus), Patent Document 9 (residual stress prediction method), Patent Document 10 (residual stress and deformation prediction method) The method is shown.

  The thermal elasto-plastic analysis mainly consists of a heat transfer analysis part that solves the heat transfer phenomenon and an elasto-plastic analysis that takes into account changes in physical properties due to its thermal history, but the heat transfer analysis part is not necessarily solved simultaneously with the elasto-plastic analysis. It is not necessary, and it is also possible to separately perform an elasto-plastic analysis after that using the temperature history as the heat transfer analysis result, that is, the time change of the temperature.

但し、∇はベクトル微分演算子である。
ここで、ρは密度、ｃは比熱、Ｔは温度、ｔは時刻、ｋは熱伝導率、Ｓは単位体積・単位時間当たりの熱発生率である。 Conventional heat transfer analysis of the welded body uses the unsteady heat transfer equation (1) as a basic equation, heat input considering the movement of the welding rod, that is, the heat input part, and heat dissipation on the surface of the welded body. Under the given boundary conditions, etc., unsteady heat transfer analysis was performed to calculate the temperature history of the welded body.

Where ∇ is a vector differential operator.
Here, ρ is density, c is specific heat, T is temperature, t is time, k is thermal conductivity, and S is a heat generation rate per unit volume / unit time.

  With respect to the heat input portion, the spatial temperature distribution is usually extremely local in the vicinity of the welding rod for the purpose of locally melting and fixing the welded body. In addition, since the welding rod as the heat source travels on the weld line, at a fixed point near the weld line of the welded body, the temperature rapidly increases as the heat source approaches, and thereafter the temperature decreases rapidly. . In the heat transfer analysis of the welded body for the residual stress analysis, it is necessary to accurately calculate this temperature history. In particular, the distribution of the highest temperature reached in the welded body is an important factor for the residual stress analysis. Conventionally, in the heat transfer analysis, which is a part of the weld residual stress analysis, an analysis of actually moving the heat source is performed while the expression (1) is advanced over time. An example is Non-Patent Document 1.

  Since this method is an essentially unsteady analysis in which the heat input position moves as described above, it requires an enormous calculation time compared to an analysis that requires a steady calculation. In addition, the spatial distribution of heat input near the heat source is known to have a heat input like a Gaussian distribution with the center position of the welding rod as the highest point. Since the change in the temperature of the welded object is extremely large near the heat source, equation (1) is used to solve the equation numerically by discretizing the space, such as the finite element method, finite volume method, and finite difference method. In order to ensure the accuracy of the numerical solution, it is necessary to make spatial discretization (hereinafter abbreviated as analysis grid, grid, or grid point) close to the heat source.

  In such numerical analysis method, when spatially changing the heat input is spatially discretized, the heat input distribution is approximated by a predetermined function within the discretization interval, so the discretization interval is large, In other words, the coarser the lattice, the greater the error that accompanies it and the lower the maximum temperature calculation accuracy of the weld. For this reason, it is required that the analysis grid of this part be taken densely without affecting the calculation accuracy. However, in the case of moving heat source analysis, the analysis grid has to be made dense over the entire moving range, so the number of analysis grid points in the entire analysis region increases, and even in this respect, much more calculation time is required. .

  Hereinafter, a conventional example of heat transfer analysis related to welding of a rotationally symmetric body using a welding rod will be described with reference to FIG. FIG. 18 is a schematic diagram of the welded body 1 for illustrating the concept of the conventional heat transfer analysis example. Here, a rotationally symmetric body is assumed as the welded body 1, and circumferential welding of the outer surface is assumed as the welding direction. The analysis region of the heat transfer analysis is the same as the shape of the welded body 1, and the welding rod 6 is not modeled, but only the heat input portion 8 is modeled as a boundary condition of the welded body 1. As a method of heat input to the object to be analyzed, a method of providing boundary conditions for heat input from the wall surface near the heat input part 8 or a small region in the object to be welded adjacent to the wall surface near the heat input part 8 generates heat. It is usually carried out by a method in which heat is input by giving a value to the S term in the formula (1) as a body.

  In the heat transfer analysis of this conventional method, the heat input section 8 is moved in accordance with the traveling speed 9 of the welding rod 6 in actual welding in the analysis of time progression of the equation (1) which is an unsteady heat transfer equation. I will let you. For this reason, when a certain amount of time has elapsed from the state of the welding rod 6, the heat input portion 8 to the welded body 1, and the position of the high temperature portion 4, the welding rod 12, the heat input portion 11 to the welded body 1, the high temperature Take part 10 position. Thus, in the analysis, the time progress analysis for actually moving the heat input section 8 in the analysis region is performed, and for example, the temperature history 14 at a certain point 13 on the surface of the welded body 1 is obtained as shown in FIG. It was.

Since the heat input portion 8 moves along the welding line 5 in this way, the entire moving range of the welding rod 6 can be analyzed in order to accurately analyze the high temperature portion 4 where the spatial temperature change is severe regardless of the position of the welding rod 6. Therefore, a dense analysis grid for resolving the temperature change is required, and a large amount of calculation is required. Further, in order to obtain the temperature history by performing the analysis of moving the heat input position from the welding rod over the entire actual welding range, it is necessary to advance the expression (1) for the time relating to the movement of the welding rod. Even in this sense, a great deal of calculation was necessary.
Japanese Patent Laid-Open No. 10-128534 JP-A-9-229248 Japanese Patent Laid-Open No. 9-1376 Japanese Patent Laid-Open No. 5-154683 JP 2001-221697 Japanese Unexamined Patent Publication No. 2000-146716 JP 2003-121273 A Japanese Patent Laid-Open No. 10-146689 JP-A-6-186141 Japanese Patent Laid-Open No. 6-18271 Motozuki Masato and Toyoda Masao “Effects of Welding Multiple Thermal Cycles on Joint Performance in Architectural Steel Beam-Column Welds”, Proceedings of the Japan Welding Society, 21-1 (2003), 46-53 Arakawa Tadaichi, “Computational Fluid Engineering”, The University of Tokyo Press, 1994.

  In the heat transfer analysis of the above prior art that constitutes a part of the residual stress analysis, the calculation time and calculation cost are enormous. However, particularly when the welded body is large, the temperature distribution of the high-temperature portion 4 around the moving welding rod may be considered fixed with respect to the welding rod position except for the welding start and end portions. In this case, the temperature change at any point of interest where the distance and direction from the weld line are the same, except for the part close to the welding start and end parts, the temperature history, that is, temperature The rise and fall changes in time are equal.

  Also in the elasto-plastic analysis to obtain the residual stress value that is separately performed after the temperature history, which is the heat transfer analysis result, as an input condition, pay attention only to the portion that occupies most of the weld line other than the welding start and end There are many cases to do.

  The present invention has been made to solve the above-described problems of the prior art from such a viewpoint, and in heat transfer analysis such as residual stress analysis, heat transfer analysis that can reduce the calculation time and cost. It is an object to provide a method, a recording medium on which a heat transfer analysis program is recorded, a heat transfer analysis device, and a residual stress analysis method.

  The present invention meets the above-mentioned object, and in the invention described in claim 1, a heat source smaller than the size of the member moves on the surface of the member that is solid, and is caused in the member by the heat source. In a heat transfer analysis method that obtains a temperature change by numerically solving a heat transfer equation governing a phenomenon described by a differential equation or an integral equation by discretizing space and time, it moves at the same speed as the heat source. They are handled by a moving coordinate system or a rotating coordinate system that rotates at the same angular velocity as the heat source.

  According to the present invention, since the heat input part is fixed in the analysis region, in order to ensure the accuracy of the numerical solution, it is only necessary to make the spatial discretization of this part finer, and the number of grid points can be reduced, compared to the conventional method. It is possible to obtain the temperature history of the welded body with the same degree of accuracy as the conventional method with less calculation time and calculation cost. In addition, if boundary conditions such as the actual moving speed of the heat input part and the amount of heat input do not change over time, numerical analysis of unsteady heat transfer with movement of the welding rod can be reduced to steady analysis. Therefore, the temperature history of the heat transfer analysis target solid can be obtained with even less calculation time and calculation cost.

  Embodiments of a heat transfer analysis method according to the present invention will be described below with reference to the drawings. Here, parts that are the same as or similar to those in the prior art are denoted by common reference numerals, and redundant description is omitted.

  First, a first embodiment will be described with reference to FIG. FIG. 1 is a schematic view of an object to be welded for illustrating the concept of the present embodiment relating to the welding of a rotationally symmetric body using a welding rod. The point that a rotationally symmetric body is assumed as the welded body 1, the analysis area is the same as the shape of the welded body 1, and the welding rod 6 is not modeled in the heat transfer analysis, and only the heat input portion 8 is covered. The point to be modeled as the boundary condition of the welded body 1, the method of heat input to the object to be analyzed is the method of inputting heat from the wall surface near the heat input part 8 or the small in the welded object adjacent to the heat input part 8 The method of setting the region as a heating element is the same as that in FIG. 18 of the conventional example.

However, as an analysis region, it is possible to omit a distant place that is so small that the temperature rise due to the heat input portion 8 can be ignored. In the analysis according to the present embodiment, equation (2) is used instead of equation (1) of the conventional example.

  This is an equation known as a thermal energy transport equation in the field of thermohydrodynamics, in which case u uses the value of the velocity vector at each position in the region. This equation results in equation (1) when u is a zero vector.

  The analysis method of the present embodiment handles the analysis region by a coordinate system that moves together with the heat input unit 8, and u is a relative velocity vector at each position in the welded body 1. Such a definition of u at each position in the analysis region, that is, in each position of the member, is that there is no deformation of the member after a minute time, that is, the member moves and rotates as a lump, and this embodiment targets a solid. There is no contradiction even in the case of.

  In the example of FIG. 1, since the circumferential symmetry welding of the rotationally symmetric body is performed, the coordinate system is a rotational coordinate system, and the relative velocity vector rotates in the direction opposite to the actual rotation 9 of the welding rod at each position of the welded body 1. For example, the direction velocity vector is a direction as indicated by an arrow 7 on the workpiece 1. When the actual moving speed of the heat input part is constant, u becomes a constant vector in time at a point fixed in the analysis region.

  Equation (2) is a rotational coordinate that moves with the heat input part, which is a moving heat source, although it is solved numerically by advancing time by a method of discretizing space and time such as a finite element method, a finite volume method, and a finite difference method. Due to the analysis by the system, the heat input portion is relatively fixed on the analysis region. For this reason, when boundary conditions, such as the actual moving speed of the heat input part 8 and the heat quantity of heat input, do not change in time, it can be reduced to a stationary problem, and the time progression of the equation (2) is essentially non-existent. Since it is no longer stationary, it may be considered as a means of iterative solution simply for obtaining a convergent solution.

  In this case, the temperature distribution of the steady solution can be obtained by aborting the calculation when it can be considered that the temperature distribution as the solution has disappeared with time. In the field of scientific and technical calculation, this method of obtaining a steady solution by making time progress of a non-stationary equation including a time differential term in numerical analysis is called a time progression method or a time marching method. However, when a steady solution is obtained using a numerical analysis method other than the time progression method, the steady solution is directly obtained by solving equation (3), which is a stationary equation in which the time derivative term is deleted from equation (2). Also good.

  As described above, when the boundary conditions such as the actual moving speed of the heat input section 8 and the heat quantity of the heat input do not change with time, and the steady analysis is performed, the heat of the welded area in the analysis area is not yet obtained. In order to avoid wrapping around the weld, it is desirable that the analysis region is not connected in the circumferential direction as shown in FIG.

  Here, the example of the implementation procedure of the heat transfer analysis by this Embodiment using (2) Formula is demonstrated. In this example, it is assumed that the finite volume method is used as a numerical calculation method, the movement of the heat input part is a constant speed in the linear direction, the physical property value is a constant value independent of temperature, and an analysis for obtaining a steady solution by an explicit method. Suppose that When a structured grid model in a Cartesian coordinate system is targeted, a finite volume cell (hereinafter referred to as a calculation cell or simply a cell) divided by grid lines is a rectangular parallelepiped. First, the following formula (2) is transformed into a discrete equation that can be numerically calculated.

  The analysis target in the present embodiment is a solid, and the distribution of u defined so that the member moves and rotates as a lump as a relative velocity vector with respect to the movement of the heat input portion satisfies the law of conservation of mass. The continuous equation (4) is established.

（４）式を用いて変形すると、（２）式は（５）式のように書き直すことができる。

When the equation (4) is transformed, the equation (2) can be rewritten as the equation (5).

（５）式を、体積および時間に関して積分すると（６）式が得られる。

When equation (5) is integrated with respect to volume and time, equation (6) is obtained.

但し、仮定よりデカルト座標系での構造格子モデルを対象としているため、計算セルの微小体積ｄＶは（７）式で表現できる。

However, since the structure grid model in the Cartesian coordinate system is targeted, it is possible to express the minute volume dV of the calculation cell by the equation (7).

  Here, if the integration range of equation (6) is taken as the finite volume cell region 601 shown in FIG. 4 (viewed from the Z direction) and FIG. 5 (viewed from the −Y direction) and the time step Δt, ( The expression (6) can be expressed as an expression (8) which is an expression discretized at the point P.

但し下添え字のＰ，Ｅ，Ｗ，Ｎ，Ｓ，Ｔ，Ｂ，ｅ，ｗ，ｎ，ｓ，ｔ，ｂは図４と図５中に示したそれぞれの位置での値であることを示し、Δｘ，Δｙ，Δｚ，（δｘ），（δｙ），（δｚ）は同図中に示した区間の長さを表す。

However, the subscripts P, E, W, N, S, T, B, e, w, n, s, t, and b are values at the respective positions shown in FIGS. .DELTA.x, .DELTA.y, .DELTA.z, (.delta.x), (.delta.y), (.delta.z) represent the length of the section shown in FIG.

としている。 Further, the relative velocity vector u for the movement of the heat input part is

It is said.

但し、（８’）式における右辺のＴは全て既知数のＴⁿとして扱う。 When the actual moving speed of the heat input part is constant, the value of the relative velocity vector is a temporal constant in the analysis and does not need to be updated as time progresses. T ⁿ represents a known number of temperature values at the current time, and T ^{n + 1} represents an unknown number of temperature values at the next time. Δt is a time step. For explicit, the temperature T appearing in equation (8) left second and subsequent item with a known number of T ^n, and T ^{n + 1} unknowns case of implicit. In the explicit method, equation (8) can be rewritten into equation (8 ′), which is an equation for obtaining an unknown temperature value at the next time at point P.

However, (8 ') are all treated as the right-hand side of the T number of known T ⁿ in formula.

  The discrete equation transformed as shown in the equation (8) or (8 ′) is processed in time by, for example, a method described in a book (for example, Non-Patent Document 2) explaining the following general finite volume method. Can be solved.

Next, the heat transfer analysis procedure according to the present embodiment will be described with reference to FIG.
First, discretization of the analysis region, analysis conditions, thermophysical values of the object to be analyzed and the welded meat are determined, or a file describing these in advance is read and stored (step S1). Analysis conditions include heat input, heat input position, heat input distribution, and their temporal changes, moving speed or moving angular speed of the heat input part, initial temperature of the welded body, natural convection heat transfer coefficient related to heat dissipation to the atmosphere, The ambient temperature, time increment, maximum analysis time t _max , convergence judgment value ε, and physical properties are the density, thermal conductivity, specific heat, etc. of the welded body.

  Next, an initial value is determined (step S2). For example, a time variable is set to an initial time value at the start of analysis, and a temperature variable in each calculation cell is set to an initial temperature value.

Next, the relative velocity vector at the position of each calculation cell with respect to the moving heat input part is calculated and stored (step S3). This is a value determined by the moving speed or angular velocity conditions of the heat input section. In the case of circumferential welding on the cylindrical surface, the relative velocity vector in each calculation cell also depends on the coordinate value of the calculation cell.
From here, it enters into repeated calculation for time progress.

First, the time t is added to the variable t representing the time, and the time t is advanced by Δt by 1 hour (t ← t + Δt) (step S4).
Next, boundary conditions are given (step S5). Since each calculation cell in the analysis region has a relative velocity vector, considering the relative velocity field, the unwelded part is regarded as upstream from the heat input part, and the welded side is regarded as downstream from the heat input part. This term will be used hereinafter.

  At the upstream boundary (611 in FIG. 2), the temperature value is fixed to the initial temperature value. However, if the weld wall has an upstream boundary (29 in FIG. 11), heat input to this portion is performed by giving the actual molten metal temperature value as the boundary temperature of the weld wall upstream boundary. You can also.

At the downstream boundary (612 in FIG. 2), the temperature value in the adjacent upstream calculation cell is given, thereby giving the condition that the temperature gradient is zero in the flow direction.
The heat input wall surface means a heat input surface when heat input is performed from the wall surface in the analysis. A given value of the distribution of the heat input heat flux value on the heat input wall surface is obtained based on the heat input amount and the heat input distribution given in advance and the time change thereof. The heat input wall boundary condition is applied to the temperature value at the wall position so that the heat flux value calculated by the temperature gradient in the vertical direction on the wall surface is equal to the value given as the boundary condition in the calculation cell adjacent to the heat input wall surface. give.

  For example, when the object to be welded is placed in the atmosphere, the heat radiating wall surface indicates a wall surface that radiates heat to the atmosphere. In the case of no wind, when the welded body is overheated by welding and a temperature difference from the atmosphere occurs, natural convection is generated in the atmosphere due to heat dissipation, so that heat dissipation is mainly due to natural convection heat transfer. As a method of providing the heat radiating wall boundary condition, the natural convection heat transfer coefficient value given in advance, the heat radiating wall outer heat flux value calculated by the heat radiating wall temperature and the atmospheric temperature are perpendicular to the wall surface in the calculation cell adjacent to the heat radiating wall. This is performed by giving a temperature value at the wall surface position so as to be equal to the heat flux value inside the heat radiating wall surface calculated by the temperature gradient in the direction.

Next, using the discrete equation (8 ′), a temperature value T ^{n + 1} at the next time in each calculation cell is obtained and stored in a storage location different from T ⁿ (step S6).
Next, in each calculation cell, the update amount ΔT of the temperature value is obtained, and the temperature value is updated (ΔT ← T ^{n + 1} −T ⁿ , T ⁿ ← T ⁿ + ΔT) (step S7).

When the maximum value of all the calculation cells of the temperature value update amount ΔT is smaller than the convergence determination value ε given in advance, or when the time t reaches the maximum analysis time, this iterative calculation is terminated, and the next step Proceed to If these conditions are not satisfied, the process is repeated from the start of the repeated calculation so far (step S4) (step S8). This is the end of the repeated calculation for time progression.
Next, the temperature value in each calculation cell is stored in the hard disk, and the process ends (step S9).

  As the temperature distribution of the steady numerical solution obtained by this analysis, for example, on the surface of the welded body 1, a temperature distribution as shown in a development view shown in FIG. 6 is obtained. The isotherm 15 shows the temperature distribution on this surface, and the temperature rises as it approaches the heat input section 8. Further, the temperature changes smoothly in the region.

  The procedure for obtaining the temperature history at the point of interest 13 (FIG. 18) on the workpiece 1 shown in the description of the prior art from the steady solution temperature distribution of FIG. 6 which is a numerical solution by the analysis method in the present embodiment. This will be described below.

  The temperature cut line 16 shown in FIG. 6 is parallel to the weld line, that is, the welded weld line 3 or the unwelded weld line 5, and the direction and distance from the weld line is the distance between the point of interest 13 and the weld line. be equivalent to.

  A graph of the one-dimensional temperature distribution on the temperature cut line 16 is the temperature-position relationship 17 shown in FIG. The horizontal axis indicates the position on the temperature cut line 16 and has a length dimension. In the analysis in the rotating coordinate system of the present embodiment that moves at the same angular velocity as the heat input section 8, the welded body 1 rotates in the direction of the temperature cut line 16 in the direction opposite to the actual rotation 9 of the welding rod. Since it moves with the direction velocity vector 7, by dividing the position on the temperature cut-out line, which is the horizontal axis of the graph shown in FIG. 7, by the relative velocity at the point of interest 13 position, as shown in FIG. A temperature history at the attention point 13 can be obtained.

  Although the description here relates to the temperature history at the point of interest on the surface of the welded body 1 as an example, the temperature history can be obtained by the same method at any internal point of the welded body 1. is there. That is, the temperature history of the entire region of the welded body 1 can be obtained by the analysis of the present embodiment. Then, it becomes possible to calculate the residual stress using the temperature distribution in the entire member and its change over time, that is, the temperature history, as input conditions for the elastic-plastic analysis performed after the heat transfer analysis.

  In particular, when the analysis target is a rotationally symmetric body as shown in FIG. 1, the elastic-plastic stress analysis is a two-dimensional analysis in an axially symmetric section perpendicular to the weld line, and attention is paid only to the stress distribution acting in this section. There are many things. Such an axially symmetric two-dimensional elasto-plastic analysis is often used in the prediction of crack growth when circumferential stress corrosion cracking occurs on the surface of a circular pipe. For example, when a rotationally symmetric body as shown in FIG. 1 is to be analyzed, if the heat transfer analysis according to this embodiment is performed in three dimensions, the temperature history at any internal point can be obtained as described above. Therefore, even when the elasto-plastic analysis is two-dimensional, it can be used as an input condition for the temperature history.

  Therefore, in the vicinity of the heat input part, the temperature change, which is the distribution and solution of the heat input itself, is intense, and in order to ensure the accuracy of analysis, it is necessary to make the analysis grid of this part dense, but the heat transfer of this embodiment According to the analysis method, since the position of the heat input part is fixed in the analysis area, it is only necessary to concentrate the grid on this part in order to ensure analysis accuracy, and the heat input part moves in the analysis area. Compared with the conventional method, the number of grid points can be reduced, and the calculation time and calculation cost can be reduced.

  Furthermore, if the boundary conditions such as the actual moving speed of the heat input part and the heat quantity of the heat input do not change with time, the heat transfer analysis accompanying the movement of the heat input part can be reduced to a steady-state analysis. Compared with the analysis, the calculation time and calculation cost can be further reduced.

  Next, a second embodiment of the heat transfer analysis method according to the present invention will be described with reference to FIG. In this example, this analysis method is applied to welding of a straight portion of a flat plate. Also in this example, the position of the heat input portion is fixed in the analysis region as in the first embodiment by analyzing in the coordinate system that moves together with the heat input portion 8 using the expression (2). If the boundary conditions such as the actual moving speed of the heat input part and the heat quantity of the heat input do not change over time, it can be reduced to a steady analysis, and the calculation time and cost can be reduced. . The coordinate system used here is an orthogonal coordinate system. In this case, the relative velocity vector u in the equation (2) is a linear velocity vector 18.

  Next, a third embodiment of the heat transfer analysis method according to the present invention will be described with reference to FIG. Even when the cross-sectional shape in the normal direction of the welding line changes in the traveling direction of the welding rod 6, such as the thickness of the welded body 1 changes as in this example, the portion where the shape changes is entered. If the temperature rise from the heat input part 8 is extremely far from the heat part 8, and the temperature rise from the heat input part 8 is negligibly small, this shape change is ignored in the shape modeling in the analysis, and it is simply thick enough. It is possible to perform an analysis similar to the second embodiment shown in FIG. 8 by approximating it as a flat plate.

  Next, a fourth embodiment of the heat transfer analysis method according to the present invention will be described with reference to FIG. In this example, this analysis method is applied to circumferential welding in a flat plate surface. In this example as well, the position of the heat input portion is fixed in the analysis region as in the first embodiment by analyzing the rotating coordinate system that moves together with the heat input portion 8 using equation (2). In addition, if the boundary conditions such as the actual moving speed of the heat input section and the heat quantity of the heat input do not change over time, it can be reduced to a steady analysis, and the calculation time and cost can be reduced. Become. In this case, the relative velocity vector u in the equation (2) is the velocity vector 7 in the rotation direction.

  Next, a fifth embodiment of the heat transfer analysis method according to the present invention will be described with reference to FIG. FIG. 11 shows an analysis region in which a flat plate is taken as an example and the groove 27 and the welded meat 28 accumulated in the welded portion are taken into consideration. In actual welding, the groove called a groove is often filled by multiple times of welding. Even in such a case, it is possible to apply the heat transfer analysis according to the present embodiment by taking the analysis region as shown in FIG.

  This is because the welded meat 28 is deposited in the vicinity of the heat input portion 8, and the relative position between the position where the welded meat 28 is deposited and the heat input portion is unchanged when the actual heat input portion moves at a constant speed. That is, when this system is handled in a coordinate system that moves together with the heat input portion 8, the boundary between the unwelded weld line 5 and the welded weld 28 is fixed in the analysis region.

  In the conventional example, as in Non-Patent Document 1, it is necessary to take into account the adhesion of the molten metal by sequentially adding a finite element corresponding to the molten metal as time advances in the analysis. An element is added only when the amount of movement of the part reaches the length of the element. In other words, in the conventional method, the adhesion of molten metal is discrete in time and different from the actual phenomenon, so the length of the element is extremely short, that is, there is a problem in analysis accuracy unless the calculation grid is taken very finely . Since the analysis method of the present embodiment does not have discreteness in this sense, it can be desired to perform highly accurate analysis.

As described in the explanation of the flow chart (FIG. 3), it is also possible to input heat to this portion by giving the actual molten metal temperature value as the boundary temperature of the weld wall upstream boundary 29. .
Each embodiment described above can be combined with a parallel calculation method as a further speed-up method of this analysis. In a method of discretizing a space as a target in the present invention and solving an equation numerically, an area division method is often used as a program parallelization method. By applying such a parallel calculation method, the entire area of the welded object to be analyzed is divided into the number of CPUs, and the calculation can be speeded up by performing the calculation independently in each CPU.

  Next, FIG. 12 shows a first modification of the above-described first embodiment. In this example, when analyzing the temperature distribution and temperature change of a structure during friction stir welding, the above method is applied as a method for performing heat transfer analysis of the structure, and the result of the heat transfer analysis is processed. This is an example of obtaining the temperature history of the welded body.

  This is because frictional heat is generated by rotating the bonded body 101 around the central axis in a state where the friction rod 106 having a cylindrical shape is pressed against the bonded body 101, and the bonded body 101 is not bonded by the frictional heat. The gap between the wires 105 is welded. In the heat transfer analysis at that time, the rotating friction rod 106 is not modeled, and only the phenomenon of heat input to the bonded body 101 is considered. This is realized by changing the heat input in the heat input section 8 in the first embodiment into heat generated by friction in the heat input section 108, and has the same action as in the first embodiment.

  In FIG. 12, reference numeral 102 denotes a relative rotation direction of the joined body 101 with respect to the heat source, reference numeral 103 denotes a joined joint line, reference numeral 104 denotes a high temperature portion, reference numeral 107 denotes a relative rotational speed of the joined body 101 with respect to the friction rod, Each is shown.

  Next, FIG. 13 shows a second modification of the first embodiment described above. In this example, the above-mentioned method is applied as a method for performing heat transfer analysis of a workpiece and a tool when analyzing the temperature distribution and temperature change of the workpiece and the tool during cutting of a structure. It is an example which acquires the temperature history of a to-be-cut body and a tool by processing the result of heat transfer analysis.

  The workpiece 301 is cut by a tool 305 to generate chips 303. The chip 303 releases part of the deformation energy when subjected to plastic deformation by the tool as heat. At this time, if the coordinate system for performing the heat transfer analysis is moved together with the tool 305, the heat release portion is fixed on the analysis region, which is the same as the analysis in the first embodiment. The heat transfer analysis at that time is realized by changing the heat input in the heat input section 8 in the first embodiment into heat generated by plastic deformation in the heat input section 304. Although heat is generated due to friction between the workpiece 301 and the tool 305, heat transfer analysis can be performed in addition to the heat generation. If the heat transfer analysis method of this embodiment is applied in this way, the same action as in the first embodiment is obtained. In FIG. 13, reference numeral 302 indicates a relative moving speed of the workpiece 301 with respect to the tool 305.

  Next, FIG. 14 shows a third modification of the first embodiment described above. In this example, when analyzing the temperature distribution and temperature change of the workpiece during laser peening performed to improve the stress of the structure, the above-mentioned method is applied as a method for performing heat transfer analysis of the workpiece. In this example, the temperature history of the workpiece is obtained by processing the result of the heat transfer analysis.

  Laser peening is to change the stress state by irradiating the workpiece 401 with laser light 403 to cause thermoplastic deformation in the high temperature portion 404. Here, circumferential processing is assumed. At this time, the heat transfer analysis is realized by changing the heat input in the first embodiment to the heat from the laser beam 403 in the heat input section 404, and has the same action as in the first embodiment.

  In FIG. 14, reference numeral 402 denotes a relative rotation direction of the workpiece with respect to the laser irradiation position, reference numeral 405 denotes a laser irradiation portion, reference numeral 406 denotes a laser light emitting device, reference numeral 407 denotes a relative rotation speed of the workpiece with respect to the irradiation position, Reference numeral 408 indicates a heat input portion.

  Next, FIG. 15 shows a fourth modification of the first embodiment described above. In this example, in analyzing the temperature distribution and temperature change of the structure when the structure is cut by the burner, the above-mentioned method is applied as a method for performing the heat transfer analysis of the object to be cut. It is an example which obtains the temperature history of a to-be-cut body by processing.

  The object to be cut 501 is cut by a flame 509 of combustion gas radiated from the burner 506, and here, cutting in the circumferential direction is assumed. At this time, the heat transfer analysis is realized by changing the heat input in the first embodiment to the heat from the flame 509 in the heat input unit 508, and has the same action as the first embodiment.

In FIG. 15, reference numeral 502 denotes a relative rotation direction of the object to be cut with respect to the burner, reference numeral 503 denotes a cut weld line, reference numeral 504 denotes a high-temperature portion, reference numeral 505 denotes an uncut cutting line, and reference numeral 507 denotes a cutting object relative to the burner. The relative rotational speeds are shown respectively.
Each modification (FIGS. 12 to 15) of the first embodiment described above can also be applied in combination with the second to fifth embodiments.

  The first embodiment described above can be applied to a rotationally symmetric structure in which the annular structure has symmetry with respect to the central axis. It is also possible to perform the residual stress analysis when the heat transfer analysis according to the first embodiment is performed in three dimensions and the elasto-plastic analysis is performed as a two-dimensional analysis in the axial object cross section.

  Next, an embodiment of a heat transfer analysis device for executing the heat transfer analysis method according to the present invention will be described. First, FIG. 16 shows the configuration of the first embodiment of the heat transfer analysis apparatus according to the present invention. This apparatus includes a heat transfer analysis program recording device 19, a calculation result recording device 20, an analysis condition / physical property / lattice model recording device 21, an arithmetic device 22, a memory 23, an input device 24, and a display device 25.

  The analyst issues an analysis execution instruction to the arithmetic device 22 via the input device 24. The arithmetic device 22 reads the heat transfer analysis program into the heat transfer analysis program recording device 19, and sets the analysis conditions, physical properties, and lattice model. The calculation is started after reading from the analysis condition / physical property / lattice model recording device 21. When the analysis is completed, the analysis result is recorded in the calculation result recording recording apparatus 20 and the process ends. The display device 25 may notify the analyst that the analysis is completed.

  The heat transfer analysis program stored in the heat transfer analysis program recording device 19 is the one to which the parallel calculation method is applied. When performing parallel calculation using this program, a plurality of arithmetic devices 22 are used. A shared memory type parallel computer is used, or a distributed memory type parallel computer such as a PC cluster parallel computer in which the heat transfer analysis apparatus is connected by a plurality of networks.

  As a residual stress analysis method, in calculating the magnitude and distribution of residual stress generated during welding of welded structures and pipes, as a method for conducting heat transfer analysis of the welded body that forms part of the method The heat transfer analysis method can also be applied. By processing the result of this heat transfer analysis, it is possible to obtain the temperature history of the welded body, perform elasto-plastic analysis using it as input conditions, and calculate the magnitude and distribution of the residual stress.

  Next, the configuration of the second embodiment of the heat transfer analysis apparatus according to the present invention is shown in FIG. This apparatus comprises a residual stress analysis program recording device 26, a calculation result recording recording device 20, an analysis condition / physical property / lattice model recording device 21, an arithmetic device 22, a memory 23, an input device 24, and a display device 25.

  The analyst issues an analysis execution command to the arithmetic device 22 via the input device 24. The arithmetic device 22 reads the residual stress analysis program into the residual stress analysis program recording device 26 and analyzes the analysis conditions, physical properties, and lattice model. Calculation is started after reading from the condition / physical property / grid model recording device 21. When the analysis is completed, the analysis result is recorded in the calculation result recording recording apparatus 20 and the process ends. The display device 25 may notify the analyst that the analysis is completed.

  Note that a heat transfer analysis program constituting a part of the residual stress analysis program stored in the residual stress analysis program recording device 26 applies the above-mentioned parallel calculation method, and performs parallel calculation using this program. In this case, a shared memory type parallel computer having a plurality of arithmetic units 22 is used, or a distributed memory type parallel computer such as a PC cluster parallel computer in which the heat transfer analysis device is connected by a plurality of networks.

The typical perspective view for demonstrating the concept of 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view explaining how to take the analysis field in the case of performing the steady analysis in the first embodiment of the heat transfer analysis method according to the present invention. The flowchart in 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The figure which shows the example of definitions, such as a calculation cell and a lattice point, in the case of performing the analysis in 1st Embodiment of the heat-transfer analysis method concerning this invention by a finite volume method, Comprising: The figure seen from the Z direction. It is a figure which shows the example of definitions, such as a calculation cell and a lattice point, when performing the analysis in 1st Embodiment of the heat-transfer analysis method based on this invention by a finite volume method, Comprising: The figure seen from -Y direction. The figure which shows the example of the steady solution temperature distribution in 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The graph which shows the example of the one-dimensional temperature distribution on the temperature cut-out line in 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of 2nd Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of 3rd Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of 4th Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of 5th Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of the 1st modification of 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The typical top view for demonstrating the concept of the 2nd modification of 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of the 3rd modification of 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The typical perspective view for demonstrating the concept of the 4th modification of 1st Embodiment of the heat-transfer analysis method which concerns on this invention. The block diagram which shows 1st Embodiment of the heat-transfer analysis apparatus which concerns on this invention. The block diagram which shows 2nd Embodiment of the heat-transfer analysis apparatus which concerns on this invention. The typical perspective view for demonstrating the concept of the conventional heat-transfer analysis method. The graph which shows the example of the temperature history in a certain point on a to-be-welded body.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... To-be-welded body (member), 2 ... Relative rotation direction with respect to welding rod of to-be-welded body, 3 ... Welded welding line, 4 ... High temperature part, 5 ... Unwelded welding line, 6 ... Welding rod, 7 ... Welding rod 8 ... Heat input part (heat source), 13 ... Interesting point, 16 ... Temperature cut line, 19 ... Heat transfer analysis program recording device, 20 ... Calculation result recording recording device, 21 ... Analysis Condition / physical property / lattice model recording device, 22 ... arithmetic unit, 23 ... memory, 24 ... input device, 25 ... display device, 26 ... residual stress analysis program recording device.

Claims (7)

  A heat source smaller than the size of the member moves on the surface of the member that is solid, and the temperature change caused in the member by the heat source is changed to a heat transfer equation that governs the phenomenon described by the differential equation or the integral equation. In the heat transfer analysis method obtained by discretizing and numerically solving space and time, it is handled by a moving coordinate system that moves at the same speed as the heat source or a rotating coordinate system that rotates at the same angular velocity as the heat source. Heat transfer analysis method.   The heat transfer analysis method according to claim 1, wherein a parallel calculation method is applied.   The heat transfer analysis method according to claim 1 or 2, wherein the heat source is one of welding, friction, deformation, laser light, and flame.   The heat transfer analysis method according to claim 1, wherein the member has a rotationally symmetric shape.   A heat transfer analysis program for realizing the method according to claim 1.   A recording device that records a heat transfer analysis program for realizing the method according to any one of claims 1 to 4, an arithmetic device that executes the program, a recording device that records a calculation result of the program execution, A heat transfer analysis device. A residual stress analysis method, comprising: obtaining a residual stress based on a temperature history of the member obtained by the method according to claim 1.

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