Study on finite element method of thermal stress of turbine blade under large deformation
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摘要:
以航空发动机涡轮叶片为研究对象,基于有限单元法,采用六面体八节点单元,提出考虑几何非线性影响的热应力计算方法;使用B-bar和混合网格技术提高了复杂网格的求解精度;采用更新拉格朗日格式考虑了大变形条件下的几何非线性问题,使用Newton-Raphson迭代方法进行涡轮叶片热应力数值求解。通过缺口平板、立方体、悬臂梁、圆环算例,与ABAQUS对比,热应力、大变形模型的相对精度达到99%;最后讨论了考虑大变形对热应力的影响,在温度、气动、离心力载荷工况下,考虑大变形后,涡轮叶片变形量减小,热应力降低,相对计算精度提高4.67%。提出的考虑大变形的热应力数值算法,可用于涡轮叶片径向间隙设计和服役寿命评估,为航空发动机零部件精细化设计提供理论和计算工具支撑。
Abstract:Focusing on the finite element method for simulating the large deformation of turbine blade under varied loads, a method for calculating the thermal stress coupled with geometric nonlinearity was proposed based on the eight-node hexahedron element. B-bar and hybrid element technologies were used to improve the precision of results; the updated-Lagrangian (UL) incremental approach was presented for the simulation of large deformation, and the Newton-Raphson iterative method was utilized to numerically calculate the thermal stress of turbine blade. Compared with ABAQUS, the relative accuracy of thermal stress and large deformation models reached 99% through examples of notched plate, cube, cantilever beam, and ring; finally, the influence of considering large deformation on thermal stress was discussed. Under temperature, aerodynamic, and centrifugal load conditions, the radial deformation of turbine blades and thermal stress decreased, and relative calculation accuracy improved by 4.67%. This research is of great benefit to the design of radial clearance and assessment of low cycle fatigue life of turbine blade, and furthermore it can provide theoretical and computational support for exquisite design of aeroengine components.
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Key words:
- turbine blade /
- large deformation /
- thermal stress /
- geometrically nonlinear /
- finite element algorithm
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表 1 传热参数
Table 1. Heat transfer parameters
参数 说明 $ \rho $/(kg/m3) 材料密度 $ {{c}} $/(J/(kg·℃)) 材料比热容 $ t $/s 时间 ($ {k_x},{k_y},{k_{\textit{z}}} $)/(W/(m·℃)) 材料沿x、y、z这3个方向导热系数 $ Q $/(W/kg) 物体内部热源密度 $ {n_x},{n_y},{n_{\textit{z}}} $ 边界外法向方向余弦 $ \overline \phi $/℃ 第1类边界上的给定温度 $ q $/(W/m2) 第2类边界上的给定热流密度 $ h $/(W/m2·℃) 表面传热系数 $ {\phi _{\mathrm{a}}} $/ ℃ 第3类边界条件的外界环境温度 表 2 不同网格悬臂梁挠度
Table 2. Cantilever beam deflection with different grids
网格模型 网格数量 挠度 相对误差/% 四面体 914 0.114677 8.26 六面体 640 0.123786 0.97 混合 3399 0.125131 0.10 表 3 悬臂梁挠度
Table 3. Cantilever beam deflection
泊松比 ABAQUS 无
B-bar相对
误差/%有
B-bar相对
误差/%0.3 0.1254 0.1237 1.31 0.1253 0.09 0.35 0.1252 0.1229 1.83 0.1251 0.10 0.4 0.1249 0.1213 2.91 0.1248 0.12 0.45 0.1245 0.1176 5.56 0.1244 0.13 0.46 0.1245 0.1162 6.66 0.1243 0.09 0.465 0.1244 0.1151 7.44 0.1243 0.12 表 4 缺口平板材料参数和边界条件
Table 4. Material parameters and boundary conditions of notched plate
名称 数值 材料参数 参考温度/℃ 0 导热系数/(W/(mm/℃)) 16 弹性模量/GPa 100 泊松比 0.4 线膨胀系数/10−5 1.36 边界条件 给定温度(圆弧面)/℃ 20 固支位移(圆弧面)/ mm 0 给定热流密度(对称面)/(W/mm2) 50 表面传热系数(其余面)/(W/mm2·℃) 4 环境温度(其余面)/℃ 100 表 6 缺口平板特征点合位移
Table 6. Notched plate total displacement of chosen points
特征点 本文/mm ABAQUS/mm 相对误差/% 1 0 0 2 0 0 3 0 0 4 0.001308 0.001302 0.46 5 0.001308 0.001302 0.47 6 0.002548 0.002539 0.38 7 0.002548 0.002538 0.39 8 0.001662 0.001656 0.33 9 0.001512 0.001506 0.39 10 0.00153 0.001524 0.42 11 0.003982 0.003968 0.34 表 5 缺口平板特征点温度
Table 5. Notched plate temperature of chosen points
特征点 本文/℃ ABAQUS/℃ 相对误差/% 1 20 20 0 2 20 20 0 3 20 20 0 4 65.6658 65.3337 0.51 5 65.6451 65.3259 0.49 6 80.3969 80.12 0.35 7 80.3767 80.1138 0.33 8 79.4191 79.2016 0.27 9 75.0735 74.7932 0.37 10 74.0517 73.7278 0.44 11 92.7371 92.3735 0.39 表 7 缺口平板特征点von Mises应力
Table 7. Notched plate von Mises stress of chosen points
特征点 本文/MPa ABAQUS/MPa 相对误差/% 1 66.7524 66.5184 0.35 2 95.0655 94.6352 0.45 3 95.0753 94.6301 0.47 4 16.56 16.5222 0.23 5 16.5627 16.5191 0.26 6 3.14614 3.15748 0.36 7 3.14128 3.14837 0.23 8 10.5039 10.4971 0.06 9 11.255 11.2304 0.22 10 9.3826 9.37852 0.04 11 1.13527 1.13303 0.20 表 8 立方体特征点温度
Table 8. Cube temperature of chosen points
特征点 本文/℃ ABAQUS/℃ 相对误差/% 1 100 100 0 2 100 100 0 3 100 100 0 4 100 100 0 5 100 100 0 6 59.109 59.522 0.69 7 59.1089 59.522 0.69 8 44.8767 45.2803 0.89 9 44.8766 45.2803 0.89 10 50.5658 51.0097 0.87 表 9 立方体特征点von Mises应力
Table 9. Cube von Mises stress of chosen points
特征点 本文/MPa ABAQUS/MPa 相对误差/% 1 325.944 326.111 0.05 2 353.258 353.152 0.03 3 325.949 326.111 0.05 4 353.255 353.152 0.03 5 325.939 326.111 0.05 6 62.0222 62.1076 0.14 7 62.0176 62.1076 0.14 8 16.7717 16.7197 0.31 9 16.7725 16.7197 0.32 10 11.1343 11.1527 0.16 表 10 悬臂梁材料参数和边界条件
Table 10. Material parameters and boundary conditions of cantilever beam
名称 数值 材料参数 弹性模量/GPa 100 泊松比 0.3 边界条件 固支约束(左端面,z轴向)/mm 0 集中载荷(右端面,z轴向)/105 N 6 表 11 圆环特征点位移
Table 11. Ring displacement of chosen points
特征点 本文/mm ABAQUS/mm 相对误差/% 1 17.441 17.3 0.81 2 14.9961 14.8821 0.76 3 10.6651 10.5635 0.95 4 8.61171 8.5362 0.88 5 6.55719 6.5072 0.76 6 2.2499 2.2143 1.58 7 − 0.0667 − 0.0651 2.41 8 2.24991 2.2143 1.58 9 6.5572 6.5072 0.76 10 8.61172 8.5362 0.88 11 10.6652 10.5635 0.95 12 14.9961 14.8821 0.76 表 12 涡轮叶片材料参数和边界条件
Table 12. Material parameters and boundary conditions of turbine blade
名称 数值 材料参数 参考温度/℃ 0 导热系数/(W/(mm·℃)) 0.0167 弹性模量/GPa 121 泊松比 0.42 密度/(kg/m3) 8849 线膨胀系数/10−5 1.36 边界条件 左端面,
z轴向给定温度/℃ 400 固支位移/ mm 0 压力面 p/MPa 0.7 除左端面的
其余面表面传热系数/
(W/(mm2·℃))0.004 环境温度/℃ 800 离心力 Wx/(rad/s) 1256 -
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