﻿ 铝板焊接过程中温度场的有限元模拟 Finite Element Simulation of Temperature Field during Aluminum Plate Welding

Modeling and Simulation
Vol. 11  No. 05 ( 2022 ), Article ID: 56375 , 11 pages
10.12677/MOS.2022.115128

Finite Element Simulation of Temperature Field during Aluminum Plate Welding

Qiang Shen, Yanye Li

College of Applied Science, Taiyuan University of Science and Technology, Taiyuan Shanxi

Received: Aug. 29th, 2022; accepted: Sep. 20th, 2022; published: Sep. 28th, 2022

ABSTRACT

Aluminum structure is widely used in many fields such as vehicles and aviation. Welding technology plays an important role in the application of aluminum products. Accurately predicting the distribution and variation of temperature field of aluminum products in the welding process has important guiding significance for welding theory and engineering practice. Based on COMSOL software, this paper simulates the welding process of 300 mm * 150 mm * 8 mm type I groove aluminum plate welding parts, mainly discusses the distribution and variation of temperature field under Gauss heat source, double ellipsoid heat source and combined heat source model. It is found that with the improvement of heat source model, the temperature field of weld zone increases gradually. In the double ellipsoid heat source model, with the increase of shape parameters, the temperature in the study area will gradually decrease. In the combined heat source model, with the increase of welding parameters, the temperature field in the weld zone gradually decreases. The conclusions drawn in this paper have certain guiding significance to the improvement of welding process.

Keywords:Aluminum Plate Welding, Finite Element Simulation, Welding Parameters, Temperature Field

1. 引言

2. 焊接温度场的控制方程

$T=T\left(x,y,z,t\right)$ (2-1)

$\rho c\frac{\partial T}{\partial t}=a{\nabla }^{2}T+W$ (2-2)

1、已知物体表面的任意位置的瞬时温度

${T}_{s}={T}_{s}\left(x,y,z,t\right)$ (2-3)

Ts是关于坐标和时间的函数。

2、已知物体表面任意位置的热流密度

$-\lambda {\left(\frac{\partial T}{\partial t}\right)}_{s}={q}_{s}$ (2-4)

3、已知物体边界上任意位置的对流放热情况

$-\lambda {\left(\frac{\partial T}{\partial t}\right)}_{s}=\beta \left({T}_{s}-{T}_{e}\right)$ (2-5)

$\frac{\partial T}{\partial n}=0$ (2-6)

3. 焊接温度场的有限元建模

3.1. 热源模型选择

3.1.1. 高斯分布热源模型

$q\left(r\right)=q\left(o\right){\text{e}}^{-\epsilon {r}^{2}}$ (3-1)

$q={\int }_{F}q\left(r\right)\text{d}F={\int }_{0}^{\infty }q\left(o\right){\text{e}}^{-\epsilon {r}^{2}}2\pi r\text{d}r=\frac{\pi }{3}{\stackrel{¯}{r}}^{2}q\left(o\right)$ (3-2)

$q\left(o\right)=\frac{3q}{\pi {\stackrel{¯}{r}}^{2}}$ (3-3)

$r={\left[{\left(x-{v}_{0}t\right)}^{2}+{y}^{2}\right]}^{\frac{1}{2}}$ (3-4)

$q=\eta UI$ (3-5)

$q\left(r\right)=\frac{k\eta UI}{\pi }{\text{e}}^{-\epsilon \left[{\left(x-{v}_{0}t\right)}^{2}+{y}^{2}\right]}$ (3-6)

3.1.2. 双椭球热源模型

$q\left(x,y,\zeta \right)=q\left(o\right){\text{e}}^{-A{x}^{2}}{\text{e}}^{-B{y}^{2}}{\text{e}}^{-c{\zeta }^{2}}$ (3-7)

$q\left(x,\zeta ,t\right)=\frac{6\sqrt{3}Q}{abc\pi \sqrt{\pi }}{\text{e}}^{-\frac{3{x}^{2}}{{a}^{2}}}\cdot {\text{e}}^{-\frac{3{y}^{2}}{{b}^{2}}}\cdot {\text{e}}^{-\frac{3{\zeta }^{2}}{{c}^{2}}}$ (3-8)

$q\left(x,\zeta ,t\right)=\frac{6\sqrt{3}Q}{abc\pi \sqrt{\pi }}{\text{e}}^{-\frac{3{x}^{2}}{{a}^{2}}}\cdot {\text{e}}^{-\frac{3{y}^{2}}{{b}^{2}}}\cdot {\text{e}}^{-\frac{3{\left[z+v\left(T-t\right)\right]}^{2}}{{c}^{2}}}$ (3-9)

$q\left(x,y,z,t\right)=\frac{6\sqrt{3}{f}_{f}Q}{abc\pi \sqrt{\pi }}{\text{e}}^{-\frac{3{x}^{2}}{{a}^{2}}}\cdot {\text{e}}^{-\frac{3{y}^{2}}{{b}^{2}}}\cdot {\text{e}}^{-\frac{3{\left[z+v\left(T-t\right)\right]}^{2}}{{c}^{2}}}$ (3-10)

3.1.3. 组合热源

${\Phi }_{s}+{\Phi }_{w}=\Phi$ (3-11)

${\Phi }_{s}=\gamma \text{ }\Phi$ (3-12)

${\Phi }_{w}=\left(1-\gamma \right)\Phi$ (3-13)

3.2. 温度场有限元模型

Table 1. Material parameters

4. 不同热源模型下的温度场分布

4.1. 高斯热源模型温度场分析

Figure 1. Temperature variation curve of weld zone

4.2. 双椭球热源模型的温度场分析

Table 2. Shape parameters

4.2.1. 形状参数对温度场的影响

4.2.2. 椭球的扁平程度对温度场的影响

Figure 2. Chang curve of weld zone temperature with time: (a) different values of weld width a; (b) different values of melting depth b; (c) different values of the anterior ellipsometer Cf; (d) different values of the posterior ellipsometry Cr

Table 3. Centrifuge selection

Figure 3. Temperature contour at different eccentricities: (a) temperature contour of group A; (b) temperature contour of group B; (c) temperature contour of group C

Figure 4. Change curve of weld area temperature

4.3. 组合热源模型的温度场分析

Table 4. Welding parameters

Figure 5. Change curve of weld zone temperature with time: (a) different values for V; (b) different values for Rin; (c) different values for Pin

5. 结论

1、对比三种热源模型的温度场，在同等参数设置下，高斯热源的温度值最低，在800℃附近，随着热源模型的该进，温度值逐渐升高；在双椭球热源模型下，温度最大值上升为1000℃，温度上升了200℃；在组合热源模型中，温度为1600℃，温度相比双椭球热源上升了600℃，说明随着热源模型的改进，热源逐渐贴合实际热源时，焊件的温度场逐渐上升，数值模拟逐渐精确。

2、在双椭球热源模型中，研究了熔宽(a)、熔深(b)、椭球前半轴长Cf和椭球后半轴长Cr对温度场的影响。研究发现，随着形状参数的逐渐增大，温度场会逐渐减小；在冷却阶段，温度场的变化不受形状参数的影响。

3、在组合热源模型中，研究了焊接速度(V)、入射光斑半径(Rin)和热输入(Pin)对温度场的影响。结果发现，随着焊接速度的增大，焊缝区域温度场会逐渐降低，同时焊接速度不影响焊件的冷却阶段；随着入射光斑半径的增大，焊缝区域温度场逐渐降低，其变化不影响焊件的冷却阶段；随着热输入功率的逐渐增大，焊缝区域温度场逐渐增大，当热输入功率逐渐增大时，在冷却阶段的温度并不是趋于一致的，即在冷却阶段的同一时间下，会产生明显的温度差。

Finite Element Simulation of Temperature Field during Aluminum Plate Welding[J]. 建模与仿真, 2022, 11(05): 1358-1368. https://doi.org/10.12677/MOS.2022.115128

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