Workable mode optimization design method for dual-rotor system with inter-shaft bearing
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摘要:
为解决航空发动机双转子系统无法避开临界转速的问题，建立带中介轴承的双转子系统模型，考虑不平衡敏感度、阻尼器效果和中介轴承载荷影响，构建低压激励模态可容度评价函数和高压激励模态可容度评价函数，确定双转子“可容模态”优化设计目标函数和约束条件，建立了带中介轴承双转子系统的“可容模态”优化设计方法。研究发现，采用“可容模态”优化设计方法，与传统的“临界转速裕度”准则设计相比，带中介轴承的双转子系统轮盘最大振幅减小39.83%，轴系总质量减轻2.32%，支承外传力减小64.98%，表明所建立的带中介轴承双转子系统的“可容模态”优化设计方法是有效的。
Abstract:In order to solve the problem that the dual-rotor system of aero-engine cannot avoid the critical speed, a model of dual-rotor system with inter-shaft bearing was established. Considering the influence of unbalance sensitivity, damper effect and the load effect of inter-shaft bearing, the tolerability evaluation functions of low-pressure and high-pressure rotor excited modes were constructed, the tolerability objective function and the constraint condition for optimization design on workable mode of dual-rotor were confirmed, and the optimization design method for the workable mode of dual-rotor system with inter-shaft bearing was established. It was found that compared with the traditional critical speed margin design criterion, the maximum amplitude of the disk of the dual-rotor system with inter-shaft bearing was reduced by 39.83%, the total mass of the shafting was reduced by 2.32%, and the external force of the fulcrum was reduced by 64.98% by using the optimization design method for the workable mode, indicating that the optimization design method for the workable mode of dual-rotor system with inter-shaft bearing was effective.
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Key words:
- aero-engine /
- inter-shaft bearing /
- dual-rotor system /
- workable mode /
- dynamic optimization design
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图 4 双转子系统“可容模态”优化设计流程
Figure 4. Workable mode optimization design process of dual-rotor system
图 6 “临界转速裕度”准则下双转子系统模型
Figure 6. Dual-rotor system model under critical speed margin criterion
图 8 “临界转速裕度”准则下双转子系统振动响应
Figure 8. Vibration response of dual-rotor system under critical speed margin criterion
图 9 “可容模态”优化设计下双转子系统振动响应
Figure 9. Vibration response of dual-rotor system under workable mode optimization design
表 1 轴段参数
Table 1. Shaft parameters
转子 轴段 l/mm r/mm R/mm 低压转子 1-2 50.80 7.00 15.24 2-3 50.80 7.00 15.24 3-4 50.80 7.00 15.24 4-5 88.90 7.00 15.24 5-6 76.20 7.00 15.24 6-7 76.20 7.00 15.24 7-8 50.80 7.00 15.24 8-9 50.80 7.00 15.24 9 0 0 0 高压转子 10-11 50.80 19.05 25.40 11-12 76.20 19.05 25.40 12-13 76.20 19.05 25.40 13-14 50.80 19.05 25.40 
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表 2 叶盘参数
Table 2. Disk parameters
转子 节点 m/kg Ip/10−4
（kg·m2）Id/10−4
（kg·m2）低压转子 1 4.90 271.20 135.60 8 4.20 203.40 101.70 高压转子 11 3.33 146.90 73.40 13 2.277 97.2 48.6
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表 3 支承参数
Table 3. Fulcrum parameters
转子 节点 s/107 （N/m） 低压转子 2 2.63 3 2.63 7,14 0.876 9 1.75 高压转子 10 1.75
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表 4 双转子系统临界转速
Table 4. Critical speed of dual-rotor system
激励转子 模态阶数 Ωl /（r/min） Ωh /（r/min） 低压转子 1 11946 17919 2 16827 25241 高压转子 1 7612 11418 2 10443 15664 3 14424 21635
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表 5 遗传算法关键参数
Table 5. Key parameters of genetic algorithm
参数 数值 遗传代数 80 种群数量 5 种群个体 50 迁移率 0.2 代沟 0.9 交叉概率 0.7 变异概率 0.1
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表 6 轴段参数优化结果
Table 6. Optimization results of shaft parameters
转子 轴段 l/mm r/mm R/mm 低压转子 1-2 45.97 6.72 15.63 2-3 59.39 7.57 15.96 3-4 40.64 6.58 14.76 4-5 106.68 7.25 13.88 5-6 78.71 5.90 16.44 6-7 82.28 6.37 13.88 7-8 56.94 7.12 15.79 8-9 48.39 6.90 15.13 9 0 0 0 高压转子 10-11 40.89 20.57 24.71 11-12 65.83 20.88 26.88 12-13 74.99 18.72 22.93 13-14 58.56 19.90 27.18
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表 7 叶盘参数优化结果
Table 7. Optimization results of disk parameters
转子 节点 m/kg Ip/10−4
（kg·m2）Id/10−4
（kg·m2）低压转子 1 4.62 255.96 127.98 8 4.04 195.46 97.73 高压转子 11 3.66 161.56 80.72 13 2.31 98.67 49.33
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表 8 支承参数优化结果
Table 8. Optimization results of fulcrum parameters
转子 节点 s/107 （N/m） 低压转子 2 0.466 3 7.23 7,14 5.21 9 0.906 高压转子 10 0.05
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表 9 双转子系统可容度评价函数对比
Table 9. Comparison of dual-rotor system tolerability evaluation function
激励转子 模态 评价函数 优化前 优化后 低压转子 1 0.72 0.98 2 0.89 0.85 3 0.79 0.92 高压转子 1 0.77 0.99 2 0.81 0.87 3 0.82 0.91
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表 10 “临界转速裕度”准则下轴段参数设计结果
Table 10. Shaft parameters design results under critical speed margin criterion
转子 轴段 l/mm r/mm R/mm 低压转子 1-2 42.20 7.48 13.98 2-3 43.60 7.48 13.98 3-4 41.16 7.48 14.00 4-5 71.91 7.48 14.01 5-6 69.94 7.48 14.23 6-7 61.71 7.48 14.27 7-8 48.04 7.48 14.27 8-9 42.73 7.48 13.87 9 0 0 0 高压转子 10-11 45.70 17.36 23.25 11-12 63.50 17.36 23.28 12-13 61.65 17.36 23.38 13-14 41.20 17.36 23.45
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表 11 “临界转速裕度”准则下叶盘参数设计结果
Table 11. Disk parameters design results under critical speed margin criterion
转子 节点 m/kg Ip/10−4
（kg·m2）Id/10−4
（kg·m2）低压转子 1 5.39 298.32 149.16 8 4.12 199.33 99.97 高压转子 11 3.43 151.31 75.65 13 2.21 94.28 47.14
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表 12 “临界转速裕度”准则下支承参数设计结果
Table 12. Fulcrum parameters design results under critical speed margin criterion
转子 节点 s/107 （N/m） 低压转子 2 0.776 3 0.204 7,14 0.177 9 0.0759 高压转子 10 2.77
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表 13 “临界转速裕度”准则下双转子系统临界转速
Table 13. Critical speed of dual-rotor system under critical speed margin criterion
激励转子 模态 Ωl /
（r/min）Ωh /
（r/min）低压转子 1 3809 5714 2 11670 17505 3 13301 19951 高压转子 1 2460 3689 2 7419 11128 3 8478 12717
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表 14 双转子系统附加阻尼
Table 14. Added damping of dual-rotor system
转子 节点 c/（N·s/m） 低压转子 2 2000 3 300 7,14 300 9 1000 高压转子 10 2 000
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表 15 优化结果对比
Table 15. Comparison of optimization results
项目 “临界转速裕度”
准则设计“可容模态”
优化设计变化量/
%轮盘最大振幅/μm 89.63 64.10 −39.83 轴系总质量/kg 18.06 17.65 −2.32 支承最大
外传力/N70.33 24.63 −64.98
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