Dynamic modeling analysis of multiple excitations in aeroengine accessory systems
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摘要:
针对某航空发动机附件传动齿轮系统，开展了不同工况下的多激励（啮合刚度激励、误差激励以及摩擦激励）动力学建模分析。通过引入位置角和位移投影向量，利用有限元矩阵组装的思想，建立了某型航空发动机附件齿轮传动系统51自由度动力学模型；利用势能解析法完成单双齿交替的啮合刚度激励表征、使用随机函数完成啮合误差激励表征，并且建立了基于弹流润滑模型的摩擦激励表征方法；采用变步长Runge-Kutta法求解得到传动系统的动态响应，分析了多种内外部激励对传动系统动态特性的影响。结果表明：高转速和低刚度相互耦合作用使得齿轮副间发生瞬时过载、齿面脱离和疲劳破坏的风险增大；润滑条件、精度等级以及齿轮结构对系统动力学影响较大；靠近中央传动的齿轮最危险，需关注其振动裕度，为后续中央传动系统动力学研究提供基础。
Abstract:Considering an aero-engine accessory transmission gear system, the multi-excitation (mesh stiffness excitation, error excitation and friction excitation) dynamic modeling analysis under different working conditions was carried out. By introducing the position angle and displacement projection vector, and using the idea of finite element matrix assembly, a 51-degree-of-freedom dynamic model of a certain type of aero-engine accessory gear transmission system was established; using the potential energy analysis method, the meshing stiffness excitation characterization of alternating single and double teeth was completed. The random function was employed to complete the meshing error excitation characterization, and a friction excitation characterization method was established based on the elastohydrodynamic lubrication model; the variable step size Runge-Kutta method was used to solve the dynamic response of the transmission system, and the dynamic characteristics of the transmission system were analyzed by various internal and external excitations. The results showed that the coupling effect of high speed and low stiffness increased the risk of instantaneous overload, tooth surface detachment and fatigue damage between gear pairs; lubrication conditions, precision grades and gear structures had a greater impact on system dynamics; the gear was the most dangerous, and its vibration margin should be paid attention to. This could provide a basis for the follow-up dynamics research of the central transmission system.
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图 2 某型航空发动机附件齿轮系统运动简图
Figure 2. Motion diagram of a certain type of aero-engine accessory gear system
图 3 某型航空发动机附件齿轮系统动力学简图
Figure 3. Dynamic diagram of a certain type of aero-engine accessory gear system
图 10 含误差的齿轮在双啮区的接触示意图
Figure 10. Contact diagram of a gear with errors in the double mesh area
图 12 不同润滑状态下的G1齿轮的振动位移响应
Figure 12. Vibration displacement response of G1 gear under different lubrication conditions
图 13 不同润滑状态下的G1齿轮x向振动加速度响应
Figure 13. x-direction vibration acceleration response of G1 gear under different lubrication conditions
图 14 不同润滑状态下的G1齿轮的y向振动加速度响应
Figure 14. y-direction vibration acceleration response of G1 gear under different lubrication conditions
图 15 不同润滑状态下的G1-G2齿轮副动态啮合力响应
Figure 15. Dynamic meshing force response of G1-G2 gear pair under different lubrication conditions
图 16 不同润滑状态下G1-G2齿轮副的动态摩擦力响应
Figure 16. Dynamic friction response of G1-G2 gear pair under different lubrication conditions
图 17 不同工况下各齿轮振动加速度响应图
Figure 17. Vibration acceleration response diagram of each gear under different working conditions
图 18 不同工况下的G9齿轮动态响应
Figure 18. G9 gear dynamic response under different working conditions
图 19 不同精度下G1、G2齿轮振动加速度响应
Figure 19. Vibration acceleration response of G1 and G2 gears with different accuracy levels
图 22 辐板有孔圆环部分的局部放大图
Figure 22. Partial enlarged view of the perforated circular part of the web
图 23 不同辐板厚度下的系统振动加速度响应
Figure 23. System vibration acceleration response under different web thicknesses
图 24 不同辐板厚度下的时变啮合刚度和振动加速度响应
Figure 24. Time-varying meshing stiffness and vibration acceleration response under different web thicknesses
图 25 不同轮缘厚度下的时变啮合刚度和振动加速度响应
Figure 25. Time-varying meshing stiffness and vibration acceleration response under different flange thicknesses
表 1 附件齿轮传动系统的主要参数
Table 1. Main parameters of accessory gear transmission system
齿轮
序号额定转速/
（r/min）转速比 齿轮
齿数模数/
mm额定啮合
频率/HzG1 8428 1.0063 35 3.5 4916 G2 8676 0.9776 34 3.5 4916 G3 16388 0.5176 18 3.5 4916 G4 7762 1.0926 38 3.5 4916 G5 7972 1.0639 37 3.5 4916 G6 7762 1.0926 37 3 4787 G7 5744 1.4765 50 3 4787 G8 7023 1.2077 42 3.5 4916 G9 7023 1.2077 21 3.5 2458 G10 4337 1.9553 34 3.5 2458 G11 3687 2.3003 40 3.5 2458 G12 3687 2.3003 40 3 2458 G13 5672 1.4952 26 3 2458 G14 4757 1.7827 31 3 2458 G15 12290 0.6901 12 3 2458 G16 3687 2.3003 48 2.5 2949 G17 6807 1.2460 26 2.5 2949 
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表 2 附件齿轮传动系统的固有频率
Table 2. Natural frequencies of accessory gearing sytems
阶次 固有频域/Hz 未考虑摩擦 考虑摩擦 第1阶 0 0 第2阶 6380 6382 第3阶 10463 10463 第4阶 12868 12870 第5阶 15342 15353 第6阶 18110 18122 第7阶 20625 20622 第8阶 24982 24977 第9阶 31046 31072 第10阶 32052 32071 第11阶 33726 33742 第12阶 45876 45838 第13阶 47150 47106 第14阶 57170 57253 第15阶 84393 84170 第16阶 119809 119814 第17阶 130321 130264
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表 3 各工况下的输入和输出功率
Table 3. Input and output power under various working conditions
工况 功率/kW 全加力工况 巡航工况 慢车工况 输入端 333.55 184.18 187.84 液压泵右 94.96 29.22 47.48 液压泵左 94.96 29.22 47.48 直流发电机 66.14 66.14 64.49 交流发电机 61.31 54.14 25.22 燃油增压泵 10.37 2.36 2.36 离心通风器 1.47 0.5 0.29 油气分离器 3.68 1.24 0.72
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表 4 不同精度等级下的齿距和齿形偏差
Table 4. Tooth pitch and tooth profile deviation with different accuracy levels
mm 参数 5级精度 6级精度 7级精度 G1齿距偏差 6.38 9.02 12.7 G1齿形偏差 9.12 12.9 18.2 G2齿距偏差 6.51 9.19 13.1 G2齿形偏差 9.35 13.2 18.7
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