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摘要:
结构是航空发动机功能、性能及可靠性设计水平的综合体现，一切技术要求、性能指标、强度指标或者结构的安全性和可靠性都应建立在合理的结构布局设计上。提出了航空发动机转子结构布局并对其进行优化设计的观点，同时以典型高推重比涡扇发动机高压转子的结构构型为例，基于试验设计（DOE）的响应面法，应用有限元计算并通过多目标遗传优化算法，分别从抗变形能力、力学环境适应能力以及转子结构效率综合进行相关优化计算，论证了合理的结构布局形式可以大幅度提升转子的力学特性。研究方法对于航空发动机转子系统的初始结构布局设计具有指导意义，可以显著减少结构设计的迭代次数，缩短设计周期。
Abstract:Structure is the comprehensive embodiment of aero-engine function, performance, and reliabi-lity design level, and all technical requirements, performance indicators, strength indicators, or structural safety and reliability should be based on reasonable structure layout design. This paper puts forward the viewpoint of the layout and optimization about the aero-engine rotor structure. Taking the structure configuration of the high-pressure rotor of a typical turbofan engine as an example and based on the response surface method of the design of experiment (DOE), the finite element method is used to calculate through multi-objective genetic optimization algorithm. Relevant optimization calculations are carried out from the aspects of deformation resistance, mechanical environment adaptability and rotor structural efficiency respectively. It is demonstrated that reasonable structure layout can greatly enhance the mechanical properties of rotors. The research method is of great guiding significance for the initial structure layout design of the aero-engine rotor system, which can significantly reduce the number of iterations and shorten the design cycle.
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Key words:
- aero-engine /
- rotor system /
- structure layout /
- configuration design /
- structural efficiency
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图 5 抗变形能力优化参数关联性云图
Figure 5. Contour of parameter correlation about anti-deforming ability optimization
图 7 抗变形能力优化前后对比
Figure 7. Comparison of results before and after anti-deforming ability optimization
图 8 力学环境适应能力优化参数关联性云图
Figure 8. Contour of parameter correlation about mechanical environment adaptability optimization
图 9 力学环境适应能力优化响应面
Figure 9. Response surface of mechanical environment adaptability optimization
图 10 力学环境适应能力优化前后对比
Figure 10. Comparison of results before and after mechanical environment adaptability optimization
图 12 优化前后结构总体变形
Figure 12. Overall structure deformation before and after optimization
表 2 待优化的原始构型参数
Table 2. Original configuration parameters for subsequent optimization
参数 数值 A1/(°) 56.2 A2/(°) 38.5 R1/mm 12.1 R2/mm 112.2 
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表 3 抗变形能力优化相关性矩阵
Table 3. Correlation matrix of anti-deforming ability optimization
参数 R2 R1 A2 A1 TD_Max TM R2 1 0.006 8 -0.01 0.041 418 -0.017 436 -0.155 R1 -0.006 80 1 0.007 8 0.095 346 0.010 111 -0.144 A2 -0.014 19 0.007 8 1 -0.010 88 0.998 7 -0.954 A1 0.041 418 0.095 3 -0.01 1 -0.001 296 3 0.094 6 TD_Max -0.017 43 0.010 1 0.998 -0.001 29 1 -0.953 TM -0.155 04 -0.145 -0.95 0.094 633 -0.953 4 1
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表 4 抗变形能力响应面误差验证
Table 4. Error verification of response surface of anti-deforming ability
编号 优化变量 验证点(有限元计算) 响应点(响应面计算) 相对误差/% A1/(°) A2/(°) TD_Max/mm TM/kg TD_Max/mm TM/kg TD_Max TM 1 61.162 40.402 0.019 226 340.94 0.019 409 347.24 0.95 1.8 2 58.68 40.591 0.019 436 336.93 0.019 601 341.92 0.85 1.5 3 52.027 39.633 0.018 195 343.12 0.018 297 351.98 0.56 2.6 4 52.043 41.095 0.020 178 335.41 0.020 183 340.56 0.02 1.5 5 57.758 39.611 0.018 13 350.49 0.018 293 355.54 0.90 1.4
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表 5 抗变形能力优化设计结果
Table 5. Design results of anti-deforming ability optimization
编号 优化变量 验证点(有限元计算) 响应点(响应面计算) 相对误差/% A1/(°) A2/(°) TD_Max/mm TM/kg TD_Max/mm TM/kg TD_Max TM 1 51.278 38.531 0.016 908 345.57 0.016 859 346.91☆ 0.29 0.4 2 57.409 37.955 0.016 546 361.77 0.016 267 350.65 1.69 3.1 3 50.646 37.806 0.016 264 360.55 0.016 174☆ 351.24 0.55 2.6
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表 6 力学环境适应能力优化相关性矩阵
Table 6. Correlation matrix of mechanical environment adaptability optimization
参数 R2 R1 A2 A1 TD_Max TM C_S R2 1 0.024 -0.050 0.000 6 -0.372 73 -0.17 0.050 649 R1 0.024 1 0.003 8 -0.012 -0.128 57 0.175 -0.129 87 A2 -0.05 0.003 1 -0.007 -0.589 61 -0.94 -0.961 04 A1 0.006 -0.01 -0.007 1 -0.463 64 0.042 -0.171 43 TD_Max -0.37 -0.12 -0.589 -0.463 1 0.679 0.703 9 TM -0.17 0.175 -0.949 0.042 8 0.679 22 1 0.927 27 C_S 0.051 -0.13 -0.961 -0.171 0.703 9 0.927 1 注：C_S—临界转速。
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表 7 力学环境适应能力响应面误差验证
Table 7. Error verification of response surface of mechanical environment adaptability
编号 优化变量 验证点(有限元计算) 响应点(响应面计算) 相对误差/% A1/(°) A2/(°) TD_Max/mm TM/kg C_S/(r·min-1) TD_Max/mm TM/kg C_S/(r·min-1) TD_Max TM C_S 1 52.929 36.22 2.144 6 353.95 14 543 2.154 8 350.05 14 769 0.48 1.10 1.55 2 52.953 40.724 2.175 4 342.91 13 536 2.142 2 339.45 13 812 1.53 1.01 2.04 3 59.483 36.251 2.103 8 354.49 14 146 2.123 4 351.71 14 555 0.93 0.78 2.89 4 59.015 40.384 2.185 5 344.37 13 391 2.110 5 341.85 13 672 3.43 0.73 2.10 5 50.621 40.172 2.113 343.94 14 662 2.186 341.87 14 255 3.45 0.60 2.78
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表 8 力学环境适应能力优化设计结果
Table 8. Design results of mechanical environment adaptability optimization
编号 优化变量 验证点(有限元计算) 响应点(响应面计算) 相对误差/% A1/(°) A2/(°) TD_Max/mm TM/kg C_S/(r·min-1) TD_Max/mm TM/kg C_S/(r·min-1) TD_Max TM C_S 1 60.774 42.296 2.135 7 340.04 13 620 2.013 2 338.79 13 342 5.7 0.37 2.04 2 59.369 42.266 2.124 1 339.97 13 662 2.019 8☆ 338.29☆ 13 335 4.91 0.49 2.39 3 56.195 41.615 2.159 7 341.37 14 307 2.080 6 343 14 569☆ 3.66 0.48 1.83
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表 9 参数关联性矩阵
Table 9. Parameter correlation matrix
参数 A1 A2 R1 R2 TD_Max A1 1 0.275 -0.028 6 -0.125 0.214 286 A2 0.275 1 -0.032 1 -0.003 5 0.785 71 R1 -0.028 571 -0.032 143 1 -0.171 4 0.203 57 R2 -0.125 -0.003 571 -0.171 4 1 -0.046 42 TD_Max -0.214 286 0.785 71 0.203 57 -0.046 4 1
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