KR20010019771A - Method of Heat Distribution for Welding - Google Patents

Abstract

PURPOSE: An analyzing method for welding heat distribution is provided to precisely estimate heat distribution generated in case of welding in a short time at a low cost, and extract an optimum welding condition to be easily utilized in a site. CONSTITUTION: An analyzing method for welding heat distribution includes the steps of inputting an initial data with relation to a model to analyze, computing a final sum of the model, computing a bandwidth of the model, initializing a thermal conductivity matrix with relation to a whole coordinates system, determining whether a fused metal is to be heated or not, computing an increased heating time period if the fused metal is to be heated, determining whether the heating is to be finished, determining existing components, defining nodal points of the components(S9), setting a local nodal temperature after the increased heating time period(S10), forming a thermal conduction stiffness matrix of the local coordinates system(S11), forming a heat capacity matrix of the system, forming heat transfer matrix of the system(S12), forming heat flux vectors of the system(S14), making the local coordinates to the whole coordinates(S15), forming a heat conductivity equation and explaining the equation(S16), and determining an increased temperature amount for a next step(S17).

Description

Method of Heat Distribution for Welding

The present invention relates to a heat distribution analysis method, and more particularly to a weld heat distribution analysis method for analyzing the heat distribution of the moving heat source using the finite element method.

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

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

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) of administration of the heat source, most of the dose (q) (eg, 96-99%) It exists in the range of. In other words, the diffusion 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 increase in temperature, the amount of heat retained in the region from the origin to the distance r (qr), the time to reach the maximum temperature (t _m ), the maximum reaching temperature (T _m ), the cooling at the origin The thermal conduction is solved by a simple transplant by calculating the velocity (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).

Since the heat source distribution by the analytical method used to date uses a simple transplant based on experience and simplified experiments, some problems described below have been derived. 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, have not been 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 transplantation, and thus is limited to only grasping a simple phenomenon, and a problem of lack of accuracy and prediction of the result is derived. Accordingly, there is an urgent need for a new method to solve the above problem.

Accordingly, an object of the present invention is to provide a welding heat distribution analysis method for analyzing a heat distribution of a moving heat source using the finite element method.

1 is a view showing the temperature change by the instantaneous heat source.

Figure 2 is a view showing for explaining the welding heat distribution analysis method of the present invention.

3 is a view illustrating in detail the method of constructing a local coordinate system thermal conductivity stiffness matrix of 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.

FIG. 6 is a diagram illustrating in detail a method of constructing a heat flux vector of the local coordinate system of FIG. 2; FIG.

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In order to achieve the above object, the weld heat distribution analysis method of the present invention includes a first step of inputting initial data for an analysis model, a second step of calculating the total number of unknowns of the analysis model, and a third step of calculating the bandwidth of the analysis model. 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, a sixth step of calculating a heating time increment when the fused metal is heated, and A seventh step of determining whether heating is finished, an eighth step of determining an existing element, a ninth step of defining a node coordinate of the element, a tenth step of setting a local node temperature after time increment, and a local coordinate system An eleventh step of constructing the 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, and a local A fourteenth step of constructing a coordinate system heat flux vector, a fifteenth step of globalizing a local coordinate, a sixteenth step of solving and solving a thermal conductivity equation, and a seventeenth step of determining a temperature increment of a next step.

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.

The technical principle applied to the welding heat distribution analysis method of this invention is as follows. First, the effect of heat source movement is considered for clear analysis of welding and other heat source distributions. Second, Iso-Parametric 4, which uses the natural coordinate system to find the required values at any integral point as well as at the nodes and elements, using the natural coordinate system as the same interpolation function. Node finite element is introduced. Fifth, in the case of welding, since the temperature changes with time, the physical constant of the material (that is, specific heat, density, thermal conductivity, etc.) changes, so this is considered.

In addition, the formalization 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 two-dimensional abnormal heat conduction equation, Equation 8 is expressed as Equation 8.

Here, z means the thermal conductivity [㎈ / cm * sec * degreeC] of ay, z direction.

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

Here, q means heat flow [Flow / sec · cm 2], and n means the outer normal direction of the surface of the object. 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).

Meanwhile, when the shape function [N] is applied to the equation (8) as the weighting function, it is expressed as shown in 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 two-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).

In the case of solving Equation 14 by substituting Equations 15 to 17, two unknown amounts of {??} and {???? / ?? t} exist, but the time increment is called Δt and the temperature before the increment Φ ^B , When the temperature after the increment is Φ ^A and the temperature in the middle thereof is Φ ^M , it is expressed as in Equation 18.

Equation 19 is constructed from Equation 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 process attempts to formulate a weld heat distribution.

Accordingly, the weld heat distribution analysis method of the present invention is constructed based on the above equations.

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

Enter initial data for the analysis model. (First Step) 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 about the limit temperature of the heat affected zone (HAZ), the initial time increment at the time of cooling and heating, and the surface with heat transfer are input. Calculate the total number of unknowns. (Step 2) Determine the presence of heat transfer and heat radiation according to the shape of the analysis model. Subsequently, the nodes are divided by automatically dividing the nodes for each coordinate. The unknown total number is calculated from the variable number numbering and the variable total data of the node. In this case, the unknown means the temperature at each node of the model. Calculate your bandwidth. (Step 3) Since the rigid matrix has a symmetric matrix structure, the computation time and computation space are reduced by selecting only the necessary area of the entire matrix, thereby increasing the computational efficiency. That is, by selecting only the required area, the unknown value is reduced, thereby reducing the bandwidth. Initialize the thermal conductivity matrix of the global coordinate system. (Step 4) Set "0" to initialize the stiffness matrix and the heat load matrix of the global coordinate system. Determine whether the fused metal is heated. (Step 5) According to the time increment, the welded element undergoes the temperature lowering process, while the welded element undergoes the temperature increase process. When the fusion metal is not heated, the time increment is calculated by determining the room temperature or the set temperature. If the fused metal is heated, calculate the time increment. The sixth step is to determine the maximum temperature and calculate the time increment. It is determined whether the heating of the metal is finished. (Step 7) It is determined whether the heating of the metal is finished by comparing the heating value set in the temperature rising process with the time increment value during heating. Determine which element does not exist. (Step 8) When the analysis model is divided into finite elements to use the finite element method, it is determined whether the current element is an element of the analysis model. Defines the node coordinates of the element. (Step 9) In the case of an existing element, the node coordinates of the element are defined by referring to the input data. Set temperature of local node after time increment. (Step 10) The temperature for each time is set while incrementing the time in any one element. The thermal conductivity stiffness matrix [K] of the local coordinate system is constructed. An eleventh step will be described with reference to FIG. 3 to construct a thermally conductive stiffness matrix in a local coordinate system. In step 111, the integral point coordinates of the Gaussian integral and the weight function are set. Subsequently, in step 112, a temperature gradient interpolation matrix B is formed. Next, the thermal conductivity α is selected. After performing steps 111 to 113, a heat conductive stiffness matrix [K] is formed in step 114. The heat capacity matrix [C] of the local coordinate system is constructed. 12, a method of constructing a heat capacity matrix in a local coordinate system will be described. In operation 121, the coordinates of the integral point of the Gaussian integral and the weight function are set. Subsequently, a temperature interpolation matrix [N] is formed in step 122. Next, specific gravity value (rho) specific heat value (c) is selected. After performing steps 121 through 123, the heat capacity matrix C may be configured in step 124. It constructs the heat transfer matrix [T] of the local coordinate system. A thirteenth step will be described with reference to FIG. 5 to construct a heat transfer matrix in a local coordinate system. In operation 131, the heat transfer surfaces are distinguished. Subsequently, in step 132, a temperature interpolation matrix N is formed. Next, the thermal conductivity α is selected. After performing steps 131 to 133, a heat conduction matrix T is formed in step 134. The heat flux vector {F} of the local coordinate system is constructed. Referring to FIG. 6, a method of constructing the heat flux vector {F} in the local coordinate system will be described. In step 141, the coagulated metal thermal density (Q) is calculated. Subsequently, in step 142, the coordinates of the integral point of the Gaussian integral and the weight function are set. Next, in step 143, the temperature interpolation matrix [N] is configured. After performing steps 141 to 143, a heat flux vector {F} is configured in step 144. Local coordinates are globalized. (Step 15) The heating time of all elements is determined, and global coordinates of the stiffness matrix and the load vector are performed in the overall system. After constructing the thermal conductivity equation, we define the nodal temperature obtained by solving it. This step 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. (Step 17) The temperature increment is calculated according to time, and it is determined whether or not the heat affected zone (HAZ) for the element is output.

On the other hand, when applied to a general program such as a grapher (Traphp), Tekplot, etc. by using the data output by the welding heat distribution analysis method of the present invention as described above, welding to the welding model as shown in FIG. Accurately determine the time heat distribution. For example, FIG. 8 shows the heat distribution when the data output by the heat distribution analysis method of the present invention from the weld model is applied to the grapher. In addition, the heat distribution when the data output by the heat distribution analysis method of the present invention from the weld model is applied to the techplot is shown in FIG. 9. Accordingly, the weld heat distribution analysis method of the present invention is configured to accurately output the heat distribution during welding.

As described above, the welding heat distribution analysis method of the present invention has the advantage that the heat distribution generated during welding can be accurately predicted and the accuracy of the result is very high. This gives us a comparative advantage in time and cost over traditional experimental methods. In addition, the welding heat distribution analysis method of the present invention is configured to derive the optimal welding conditions to data economical and efficient welding conditions to be easily utilized by non-experts in the actual industrial field, which can improve the technical skills and reduce the number of processes There is an advantage.

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 for the analysis model; A second step of calculating an unknown total number of the analysis model; Calculating a bandwidth of the analysis model; 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 calculating a heating time increment when the fused metal is heated; A seventh step of determining whether the heating of the fused metal is finished; An eighth step of judging an element present; A ninth step of defining the nodal coordinates of the element, A tenth step of setting the local node temperature after time increment; 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; A fifteenth step of globalizing the local coordinates; The sixteenth step of constructing and solving the thermal conductivity equation, And a seventeenth step of determining a temperature increment of the next step. The method of claim 1, The eleventh step, 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, 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, Separating heat transfer surfaces, 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, Calculating the coagulated 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.