KR100363711B1 - Method of 3 dimention heat distribution for welding - Google Patents

Abstract

The present invention relates to a three-dimensional welding heat distribution analysis method for analyzing the heat distribution of the moving heat source during the welding by using the finite element method to data and display automatically.

The three-dimensional welding heat distribution analysis method according to the present invention includes a first step of inputting initial data such as mesh data and heat transfer data for an analysis model, and determining whether there is heat transfer and heat radiation according to the shape of the analysis model and the mesh data. A second step of calculating the total number of unknowns, which is the temperature at each node by automatically dividing the nodes for each coordinate in the step and a third step of calculating the bandwidth of the analysis model to select and implement only the required area And a fourth step of initializing the heat conduction matrix for the global coordinate system, a fifth step of determining whether the fused metal is heated, and an automatic calculation of each time increment when the fused metal is heated and cooled by the determination. Step 6 and comparing the preset heating value and the automatically calculated time increment value to determine whether or not the heating of the fusion metal In the seventh step, and in splitting the analysis model into finite elements to use the finite element method, an eighth step of determining whether a current element exists in the analysis model, and, if the element exists in the ninth step, A ninth step of defining the nodal coordinates of the element, a tenth step of setting local node temperatures over time in any one element of the defined nodal coordinates, an eleventh step of constructing a local coordinate system thermal conductivity stiffness matrix, and , A twelfth step of constructing a local coordinate system heat capacity matrix, a thirteenth step of constructing a local coordinate system heat transfer matrix, a fourteenth step of constructing a local coordinate system heat flux vector, and a heating time of all elements In step 15 of performing global coordinates of the vector and the thermal conductivity equations derived from the previous steps, a node temperature is defined and solved. The 16th step, the 17th step of determining the temperature increment of the next step by the element that does not exist in the eighth step and the temperature before and after the time increment, and the commercial heat distribution automatically the result derived in a predetermined manner through each step And an eighteenth step of automatically displaying a weld heat distribution of the analysis model on the screen as input data of the program.

According to this configuration, the three-dimensional welding heat distribution analysis method according to the present invention can not only accurately predict the heat distribution generated during welding, but also improves the accuracy of the result. In addition, the three-dimensional welding heat distribution analysis method of the present invention is configured to derive the optimum welding conditions and to make economical and efficient welding conditions to be easily utilized by non-experts in the actual industrial field, improving the technical skills and reduce the number of processes There is an advantage to this.

Description

3D welding heat distribution analysis method {METHOD OF 3 DIMENTION HEAT DISTRIBUTION FOR WELDING}

The present invention relates to a heat distribution analysis method, and more particularly, to a three-dimensional weld heat distribution analysis method to analyze the heat distribution of the moving heat source during the welding in real time according to the change of time to form a data and automatically display it by using the finite element method.

Typically, heat distribution is analyzed by dividing the instantaneous heat source, solving the instantaneous heat source, and analyzing the thermal conductivity. In this case, the method of obtaining the solution by the instantaneous heat source is determined by the planar heat source, the linear heat source and the point heat source. This will be described in detail.

The solution of the thermal conductivity equation is obtained as shown in Equation 1 when the temperature of the minute region a rises as much as Ti (= θ _i -θ _o ).

Here, c means specific heat [㎈ / g · ° C.], ρ means density [g / cm 3], and n means the dimension number of the heat oil (n = 1, 2, 3). In addition, the characteristic of the heat conduction by the instantaneous heat source is shown in FIG. As shown in FIG. 1, after the time t has been administered and the heat source is administered, most of the dose (q) (eg, 96 to 99%) is It exists in the range of. That is, the spread of heat to be. Using the simple graft, in the steel (teel) r is 1cm when t is 0.6 seconds, r is 10cm if t is 1 minute, r is 1m if t is 2 hours. While the maximum temperature is reached in the simple graft, the time does not depend on the intensity of the heat source, but increases in the order of point, line, and plane heat sources at a certain position r, and the time is proportional to the square of the distance r from the heat source and the thermal diffusion rate (k). Inversely proportional to. At this time, the maximum temperature is proportional to the intensity (q) of the heat source and irrelevant to the thermal diffusion rate (k). In this case, the temperature becomes smaller as r is larger. In addition, the cooling rate at the origin is inversely proportional to q ^{2 / n} .

On the other hand, the solution of the thermal conduction by the instantaneous heat source is the temperature rise, the amount of heat retained (qr) in the area from the origin to the distance r, the time to reach the maximum temperature (t _m ), the maximum reaching temperature (T _m ), the cooling rate at the origin The solution of thermal conductivity is obtained by a simple transplantation by obtaining (CR). Hereinafter, these will be described. The temperature rise is shown in Equation 2.

Here, T _i is the initial temperature rise, θ is the temperature of any point, θ _o means the initial temperature.

Further, the amount of heat retained qr in the region from the origin to the distance r is shown in equation (3).

Where n is the number of dimensions of the heat flow (e.g., planar heat source if n = 1, line heat source if n = 2, point heat source if n = 3), r is the distance from the origin, q is the heat source Intensity, a means the size of the initial temperature rise, respectively.

On the other hand, the time t _m to reach the maximum temperature is shown in equation (4).

In addition, the maximum reaching temperature (T _m ) is shown in equation (5).

In addition, the cooling rate cr of the origin is shown in equation (6).

The heat source distribution by the analytical method used to date uses a simple transplant based on empirical and simplified experiments, which leads to some problems described below. That is, the solution obtained by using the above simple graft can only consider the heat conduction problem of the welded structure, but there is a difficulty in not considering the heat transfer and heat radiation problems generated on the weld surface. In addition, it is difficult to consider the actual movement effect of the welding heat source. In addition, the physical constants of materials (eg, specific heat, density, thermal conductivity), etc., which depend on the temperature change generated during welding cannot be introduced. In addition, due to mathematical limitations, there is a great difficulty in applying to various types of welds, thereby limiting the welds. As described above, the conventional thermal distribution analysis method uses a simple transplant, and thus is limited to only grasping a simple phenomenon, and there is a problem in that the accuracy and prediction of the result are very insufficient.

Accordingly, it is an object of the present invention to provide a three-dimensional welded heat distribution analysis method that uses the finite element method to analyze the heat distribution of a moving heat source in real three-dimensional phase according to the change of time, to make data and display it automatically.

1 is a view showing a simple temperature change by the heat source of the prior art.

Figure 2 is a view showing for explaining a three-dimensional welding heat distribution analysis method according to the present invention.

FIG. 3 is a diagram illustrating in detail a method of constructing a local coordinate system thermal conductivity stiffness matrix of FIG. 2; FIG.

4 is a view illustrating in detail the method of configuring a local coordinate system heat capacity matrix of FIG.

FIG. 5 is a diagram illustrating in detail a method of constructing a local coordinate system heat transfer matrix of FIG. 2; FIG.

Figure 6 is a view showing in detail the method of configuring the heat flux vector of the local coordinate system of Figure 2. Figure 7 is a view showing a welding model to apply the three-dimensional welding heat distribution analysis method according to the present invention. Fig. 9 shows the heat distribution when the data output from the method according to the present invention is applied to a welder in Fig. 9, when the data output from the method according to the present invention is applied to the weld model in Fig. 7. A diagram showing the heat distribution of the.

In order to achieve the above object, the three-dimensional weld heat distribution analysis method of the present invention comprises the first step of inputting the initial data, such as mesh data and heat transfer data for the analysis model, and the presence or absence of heat transfer and heat radiation according to the shape of the analysis model In addition, the second step of calculating the total number of unknowns, which is the temperature at each node by dividing the elements by automatically dividing the nodes for each coordinate in the mesh data, and the analysis model for selecting and implementing only the required area A third step of calculating a bandwidth, a fourth step of initializing a heat conduction matrix for the global coordinate system, a fifth step of determining whether the fused metal is heated, and when the fused metal is heated and cooled by the determination A sixth step of automatically calculating each time increment; and comparing the preset heating value with the automatically calculated time increment value and A seventh step of determining whether the heating of the metal is finished; an eighth step of determining whether a current element exists in the analysis model when the analysis model is divided into finite pieces to use the finite element method; A nineth step of defining the nodal coordinates of the element when the element exists in step 9, a tenth step of setting the local node temperature according to time increment in any one of the defined nodal coordinates, and a local coordinate system An eleventh step of constructing a thermal conductivity stiffness matrix, a twelfth step of constructing the local coordinate system heat capacity matrix, a thirteenth step of constructing the local coordinate system heat transfer matrix, a fourteenth step of constructing the local coordinate system heat flux vector, Determining a heating time of all the elements and performing global coordinates of the stiffness matrix and the load vector; A sixteenth step of defining a nodal temperature by constructing the solved thermal conductivity equation and solving it; and a seventeenth step of determining a temperature increment of a next step by a temperature not before and after time increments and elements not present in the eighth step; And an eighteenth step of automatically displaying the weld heat distribution of the analysis model on the screen by automatically using the result derived in the predetermined manner as input data of a commercial heat distribution program.

Other objects and features of the present invention other than the above object will become apparent from the description of the embodiments with reference to the accompanying drawings.

With reference to Figures 2 to 9 will be described a preferred embodiment of the present invention.

Technical principles applied to the three-dimensional welding heat distribution analysis method according to the present invention are as described below. First, the effect of heat source movement is considered for clear analysis of welding and other heat source distributions. Second, in order to improve the degree of interpretation, iso-parametric 8, which uses the natural coordinate system with the same interpolation function for element coordinates and displacements, can be used to find the required values at arbitrary integral points as well as nodes and elements. Node finite element is introduced. Third, in the case of welding, since the temperature changes with time, the physical constant of the material (that is, the specific heat (c), density (ρ), thermal conductivity (α), etc.) is changed because this is considered. Fourth, the temperature increment was calculated over time, and it was considered to automatically determine and output the heat affected zone (HAZ) for the element.

In addition, the formulation process of the theory introduced in the present invention will be described in order to obtain the weld heat distribution by a numerical method. When the material of the metal is isotropic (Isotropic), the governing equation (Governing Equation) of the abnormal thermal conductivity problem of the continuum is expressed as shown in Equation 7.

Q is the amount of heat input per unit time [㎈ / sec].

In addition, when Equation 7 is described as a three-dimensional abnormal heat conduction equation, Equation 8 is expressed as Equation 8.

Here, a means thermal conductivity [㎈ / cm · sec · ° C] in the x, y, and z directions.

The thermal boundary condition of the surface of an object is represented by Equation 9 using Fourier's Law.

Where q is heat flow [㎈ / sec · cm 2], n is the outer normal direction of the object surface, and α is the heat transfer coefficient. When there is heat transfer at this boundary, q satisfies Equation 10.

Here, α _c means the heat transfer coefficient [㎈ / cm 2 · sec · ° C.], and T _c means the external temperature [° C.].

In order to formulate the heat transfer of the solid by the finite element method, the analytical model can be divided into finite elements and the temperature distribution in one element can be expressed as in Equation (11).

Here, T is the temperature of the element, [N] is the shape function matrix connecting the node temperature and the temperature in the element, {Φ} means the node temperature vector of the element over time (t).

On the other hand, if the shape function [N] to the equation (8) as a weighting function (Weighting) applied to the equation (12).

Equation 12 is developed using the Green-Gauss theorem as shown in Equation 13.

Here, s means the boundary of the element.

When the three-dimensional abnormal thermal conductivity is matrixed, it can be expressed as Equation 14.

Here, [K] means a heat conduction matrix, [C] means a heat capacity matrix, and {F} means a heat flux vector.

The thermal conductivity matrix is shown in equation (15).

At this time, the heat capacity matrix is shown in equation (16).

At this time, the heat flux vector {F} is shown in equation (17).

When the equation (14) is calculated by substituting equations (15) to (17), two unknown amounts of {Φ} and {∂Φ / ∂t} exist, but the time increment is called t and the temperature before the increment , The temperature after the increment And the temperature in the middle In this case, it is expressed as in Equation (18).

(19) is constructed from (18).

Accordingly, Equation 14 can be finally obtained as in Equation 20.

Here, Δt means time increment, Φ ^A means nodal temperature after increment, and Φ ^B means nodal temperature before increment. Knowing the value of {Φ ^B } for time t in Equation 20, the solution of the system of equations {Φ ^A } can be obtained. In other words, {Φ ^B } _{t = 0} may be substituted as an initial condition. This procedure attempts to formulate a weld heat distribution.

Accordingly, the three-dimensional welding heat distribution analysis method of the present invention is configured based on the above-described technical principles and equations.

2A and 2B, there is shown a flow chart for explaining the three-dimensional weld heat distribution analysis method of the present invention.

Initial data for the analysis model is input. (S1) First, mesh data is input. In this process, the node numbering data is input to reduce the thickness of the model, the number of nodes and node coordinates, the number of elements, the overlapping nodes, the number of nonexistent elements, and the bandwidth. Subsequently, heat transfer data is input. In this process, data on the limit temperature of the heat affected zone (HAZ), initial time increments during cooling and heating, and the surface with heat transfer are input. Next, the total number of unknowns is calculated. S2) It calculates the total number of unknowns from the variable number numbering of the nodes and the total number of variables. In this case, the unknown means the temperature at each node of the analysis model. Through this, it is determined whether there is heat transfer and heat radiation according to the shape of the analytical model, and automatically divides the node for each coordinate and divides the elements. Next, the bandwidth is calculated. (S3) Since the stiffness matrix has a symmetric matrix structure By selecting only the required area of the entire matrix, the computation time and computation space are reduced, which increases the efficiency of computation. That is, by selecting only the required area, the unknown value is reduced, thereby reducing the bandwidth. When the input value, the unknown total number, and the bandwidth for each data are calculated as described above, the thermal conductivity matrix of the global coordinate system is initialized (S4). In order to ensure the accuracy, the stiffness matrix and the heat load matrix of the global coordinate system are initialized to "0". After the heat conduction matrix is initialized, it is determined whether the fused metal is heated. Time increment calculations will be performed. That is, the elements that have been welded according to time increments undergo a temperature lowering process, while the elements on which the welding is performed undergo a temperature raising process. When the fusion metal is not heated (No; during cooling), the time increment is automatically calculated by determining the room temperature or the set temperature. When the fused metal is heated (Yes; at the time of heating), the time increment is automatically calculated by determining the maximum temperature. (S6) After the automatic calculation of each time increment, it is determined whether the heating of the metal is finished. It is determined whether the heating of the metal is finished by comparing the heating value set in the process with the time increment value during heating. Judging from the end of the heating is moved to the next step, and if the heating is not finished, the fused metal is separated and then moved to the next step. Next, the non-existent element is judged (S8). When the analysis model is divided into finite pieces, it is determined whether the current element is an element of the analysis model. At this time, if there is an element present, it moves to S9, and if it does not exist, it moves to S17. When the analysis model is divided into finite pieces, the current element exists as an element of the analysis model. In case of an element, define the nodal coordinates of the element (S9) This defines the nodal coordinates of the element with reference to the input data. Then set the temperature of the local node after time increment (S10). The temperature according to each time is set while increasing the time in one element of. After setting the temperature, the thermal conductivity stiffness matrix [K] of the local coordinate system is configured. (S11) Referring to FIG. First, the integral point coordinates of the Gaussian integral and the weight function are set. (S111) Next, a temperature gradient interpolation matrix [B] is configured. The composition of the trix uses the SHAPE FUNCTION, which is a set of coordinate functions that represents the relationship between a variable and its value at the node. Then, the thermal conductivity α is selected in consideration of the temperature dependency. (S113) After performing the steps S111 to S113, the thermal conductivity stiffness matrix [K] is configured in step S114. At this time, the thermal conductivity stiffness matrix [K] can be simply expressed as the following equation. When the heat conduction stiffness matrix [K] is constructed as described above, the heat capacity matrix [C] of the local coordinate system is configured. (S12) Referring to FIG. The integral point coordinates and the weight function are set (S121). Then, a temperature interpolation matrix [N] is constructed using the model function described in S11 (S122). The specific gravity value ρ and the specific heat value c are selected. After performing S121 to S123, the heat capacity matrix [C] is configured in S124. The heat capacity matrix [C] by performing each process may be represented by the following equation. Next, the heat transfer matrix [T] of the local coordinate system is configured. (S13) Referring to FIG. 5, a method of constructing a heat transfer matrix in the local coordinate system is described first. (S131) Next, in S11, The interpolation matrix [N] is constructed using the model function described above (S132). Next, the thermal conductivity α is selected in consideration of the temperature dependency. After performing S131 to S133, the thermal conductive matrix [T] is configured in S134. Thermal conduction matrix [T] by performing each process can be represented by the following equation. At this time, the thermal conductivity matrix [T] is formed on the basis of the heat transfer plane, that is, two dimensions. The heat flux vector {F} of the local coordinate system is configured. (S14) Referring to FIG. 6, a method of constructing the heat flux vector {F} of the local coordinate system is calculated. First, the coagulated metal thermal density Q is calculated (S141). Subsequently, the integral point coordinates and the weight function of the Gaussian integral are set. (S142) Next, as described in S11, the temperature interpolation matrix [N] is configured using the model function. (S143) S141 After performing S143 to S143, the thermal load vector {F} is configured in S144. The thermal load vector described above is represented by the following equation. Local coordinates are globalized. (S15) The heating time of all elements is judged, and global coordinates of the stiffness matrix and the load vector are performed in the overall system. After constructing the thermal conductivity equation, the nodal temperature obtained is solved. (S16) This process defines the temperature of the node over time. The temperature increment of the next step is determined by the temperature before and after the time increment. (S17) The temperature increment is calculated according to the time, and automatically determined whether or not the heat affected zone (HAZ) for the element is output.

On the other hand, the results derived by the welding heat distribution analysis method of the present invention as described above are automatically processed into post processing (Post-) by using the input data of general-purpose programs such as Grapher and Teplot, which are commercial programs. The interface is interfaced so that the heat distribution can be accurately realized in three dimensions in the welding model as shown in FIG. 7. For example, the heat distribution when the data output from the weld model by the three-dimensional weld heat distribution analysis method of the present invention is applied to the grapher is shown as in FIG. 8. In addition, the heat distribution in the case of applying the data output by the heat distribution analysis method of the present invention from the weld model to the techplot is shown as in FIG. Accordingly, the welding heat distribution analysis method of the present invention is configured to accurately output the heat distribution during welding.

As described above, the three-dimensional welding heat distribution analysis method of the present invention has the advantage that the heat distribution generated during welding can be accurately predicted in three dimensions, and the accuracy of the result is very high. In addition, accurate history of temperature rise and cooling over time can be used as initial data for stresses and deformations in welds. This gives us a much higher comparative advantage in terms of time, cost and accuracy than conventional numerical and experimental methods. In addition, the welding heat distribution analysis method of the present invention is configured to derive the optimum welding conditions to data economical and efficient welding conditions, to derive the desired results automatically by inputting the basic data in the actual industrial site, and to utilize them As a result, the technology can be improved and the number of processes can be reduced.

Those skilled in the art will appreciate that various changes and modifications can be made without departing from the technical spirit of the present invention. Therefore, the technical scope of the present invention should not be limited to the contents described in the detailed description of the specification but should be defined by the claims.

Claims (5)

A first step of inputting initial data such as mesh data and heat transfer data for the analysis model; A second step of determining whether there is heat transfer and heat radiation according to the shape of the analytical model, and automatically dividing a node for each coordinate in the mesh data to divide an element to calculate the total number of unknowns, which is the temperature at each node; Calculating a bandwidth of the analysis model for selecting and implementing only a required area; A fourth step of initializing the thermal conductivity matrix for the global coordinate system, A fifth step of determining whether the fused metal is heated; A sixth step of automatically calculating each time increment when the fused metal is heated and cooled by the determination; A seventh step of determining whether or not the heating of the fusion metal is finished by comparing a preset heating value with the automatically calculated time increment value; An eighth step of judging whether the current element is an element present in the analysis model in dividing the analysis model into finite pieces to use the finite element method; A ninth step of defining node coordinates of the element when the element exists in the eighth step; A tenth step of setting a local node temperature according to time increment in any one element of the node coordinate defined above, An eleventh step of constructing a local coordinate system thermal conductivity stiffness matrix, A twelfth step of constructing the local coordinate system heat capacity matrix; A thirteenth step of constructing the local coordinate system heat transfer matrix; A fourteenth step of constructing the local coordinate system heat flux vector; Determining a heating time of all the elements to perform global coordinates of the stiffness matrix and the load vector; A sixteenth step of constructing a thermal conductivity equation derived from the previous steps and then solving it to define the node temperature; A seventeenth step of determining a temperature increment of the next step by the elements not present in the eighth step and the temperature before and after the time increment; And an eighteenth step of automatically displaying the weld heat distribution of the analysis model on the screen by automatically using the result derived in the predetermined manner as input data of a commercial heat distribution program. Way. The method of claim 1, The eleventh step may include setting integral point coordinates and weighting functions of the Gaussian integral; Constructing a temperature gradient interpolation matrix, Selecting a thermal conductivity, Weld heat distribution analysis method further comprises the step of forming a thermally conductive stiffness matrix. The method of claim 1, The twelfth step may include setting integral point coordinates and weighting functions of the Gaussian integral; Constructing a temperature interpolation matrix, Selecting specific gravity values and specific heat values, Weld heat distribution analysis method further comprising the step of constructing a heat capacity matrix. The method of claim 1, The thirteenth step may include: classifying a heat transfer surface; Constructing a temperature interpolation matrix, Selecting a thermal conductivity, Weld heat distribution analysis method further comprising the step of constructing a heat transfer matrix. The method of claim 1, The fourteenth step is to calculate the solidified metal thermal density, Setting an integral point coordinate and a weighting function of the Gaussian integral; Constructing a temperature interpolation matrix, Weld heat distribution analysis method further comprising the step of constructing a heat flux vector.