Configuration design of aero-engine gear transmission based on graph theory and NSGA Ⅲ-TOPSIS algorithm
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摘要:
提出了基于图论与快速非支配排序遗传算法-组合赋权逼近理想解算法（NSGA Ⅲ-TOPSIS）的航空发动机齿轮传动构型设计方法，以某六附件的航空发动机机匣齿轮传动系统为例，生成32种附件布局、63种传动链布置下，满足动力传递及模型干涉约束条件的1 832种设计构型。进而基于NSGA Ⅲ优化求解齿轮传动结构参数，以质量、迎风面积及承载性能为设计指标，采用主客观组合赋权TOPSIS评价确定了传动系统的最优构型。对比初始构型，优化的传动链方案减少质量20%、迎风面积降低16%、分流轴齿轮负载下降18%，为新一代航空发动机齿轮传动的高功率密度设计提供构型方法支撑。
Abstract:An aero-engine gear transmission configuration design method based on graph theory and non-dominated sorting genetic algorithm Ⅲ- technique for order preference by similarity to ideal solution (NSGA Ⅲ-TOPSIS) was proposed. Using a six-accessory aero-engine gearbox as an example, 1 832 configurations were generated under 32 accessory layouts and 63 transmission chain arrangements, meeting the power transfer and model interference constraints. Subsequently, NSGA Ⅲ was used to obtain the gear transmission structural parameters, with design criteria including weight, frontal area, and load capacity. The best configuration was selected using the TOPSIS combined subjective and objective weights. Compared with the initial configuration, a 20% reduction in weight, a 16% decrease in frontal area, and an 18% reduction in the load on the split-power gear were achieved from the optimized configuration. This methodology can support the configuration design of the next generation’s high-power density aero-engine gear transmission.
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图 1 航空发动机齿轮传动构型设计方法研究技术路线
Figure 1. Technical route for configuration design of aero-engine gear transmission
图 2 某航空发动机齿轮传动系统初始构型方案结构示意图
Figure 2. Original configuration structural scheme of an aero-engine gear transmission
图 3 齿轮传动链拓扑图及其邻接矩阵
Figure 3. Topology graph and adjacency matrix of gear transmission chain
图 4 航空发动机齿轮传动构型设计性能指标
Figure 4. Configuration design performance indexes of aero-engine gear transmission
图 6 齿轮传动结构单元分类及初始构型迭代优化
Figure 6. Classification of gear transmission structure unit and initial configuration iterative optimization
图 7 高/低速级齿轮传动链拓扑图及其邻接矩阵
Figure 7. Topology graph and adjacency matrix of high-speed and low-speed gear transmission chain
图 9 方案154与方案156的齿轮传动结构单元Pareto解集
Figure 9. Pareto solution set of gear transmission structure unit of scheme 154 and scheme 156
图 10 1 832种构型方案的评价结果及相关性分析
Figure 10. Evaluation results and correlation analysis of 1 832 configuration schemes
图 11 TOPSIS评价分析最优构型方案
Figure 11. The best configuration scheme of TOPSIS evaluation and analysis
图 12 初始构型方案齿轮传动链设计结果
Figure 12. Design result of gear transmission of original configuration scheme
图 13 初始构型与最优构型齿轮传动三维结构对比
Figure 13. Three-dimensional structural comparison of original configuration and the best configuration gear transmission
图 14 评分排序1～10组构型方案评价指标对比
Figure 14. Comparison of evaluation indexes of 1—10 groups of configuration schemes ranked by score
表 1 某航空发动机机匣附件工况要求
Table 1. Conditions of an aero-engine gearbox
附件 转速/（r/min） 功率/kW 外廓尺寸/mm 转向 附件Ⅰ 5475.26 67.0 70.0 逆时针 附件Ⅱ 5475.26 66.0 90.0 逆时针 附件Ⅲ 4583.94 8.5 102.5 逆时针 附件Ⅳ 22905.26 78.0 47.5 逆时针 附件Ⅴ 18921.74 0.5 52.5 逆时针 起动机 10120.93 0.0 80.0 顺时针 
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表 2 各项指标重要性等级及其赋值
Table 2. Importance and value of each index
重要性等级 aij赋值 判断矩阵 同样重要 1 $ {\boldsymbol{A}} = \left[ {\begin{array}{*{20}{c}} 1&3&8&9&9 \\ {1/3}&1&8&9&9 \\ {1/8}&{1/8}&1&5&5 \\ {1/9}&{1/9}&{1/5}&1&2 \\ {1/9}&{1/9}&{1/5}&{1/2}&1 \end{array}} \right]{\text{ }} $ 稍微重要 3 明显重要 5 强烈重要 7 极端重要 9
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表 3 主客观权重及其组合赋权结果
Table 3. Subjective and objective weights and their combination weighting results
主观权重 客观权重 组合权重 0.5097 0.1111 0.0856 0.3304 0.0534 0.0267 0.0944 0.0464 0.0066 0.0369 0.5603 0.0313 0.0285 0.2288 0.0099
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