Structural vibration avoidance method of aerospace thin-spoke plate gearing system under “mechanical-inertial-thermal” loads
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摘要:
考虑传动系统各轴转速与功率、壳体变形导致的轴端偏心量、齿轮材料特性和齿面摩擦等因素，构建了“机械-惯性-热”载荷作用下某航空发动机齿轮传动系统动力学数值模型，描述了考虑锥齿轮传动在内的真实啮合状态下系统的模态特征；补充了高速齿轮传动链振动的传递形式，包含了齿轮副之间节径-节径、节径-涡动、节径-扭转，双联或三联轴及其齿轮的节径-涡动、节径-节径等多种耦合形式，还包括上述形式在整个传动链中的传递；开展了薄辐板齿轮传动系统结构避振方法研究，发现通过改进该航空发动机传动系统中齿轮的辐板厚度、轴内径等结构参数，可实现传动系统仅增加质量11%的前提下，传动系统中各齿轮振动应力的最大值降低15%～59%。
Abstract:A numerical model of an aero-engine gear transmission system dynamics under “mechanical-inertial-thermal” loading was constructed by considering the speed and power of each axis of the transmission system, the eccentricity of the shaft end due to the deformation of the casing, the material properties of the gears and the friction of the gear surface. The modal characteristics of the system under the real meshing state, including the bevel gear transmission, were described. The form of transmission of vibration in a high-speed gear chain was supplemented. Various forms of coupling such as pitch-pitch, pitch-vortex, pitch-torsion between gear pairs, pitch-vortex, pitch-pitch and other forms of coupling between duplex or triple shafts and their gears were included. The transfer of the above forms throughout the transmission chain was also included. A study of structural vibration avoidance methods for thin-spoke plate gear drive systems was carried out. It was found that by improving the thickness of the spoke plate of the gears in the transmission system of the aircraft development, the inner diameter of the shaft and other structural parameters, it was possible to achieve a reduction of the maximum value of the vibration stress in the gears of the transmission system by 15% to 59% under the prerequisite that the mass of the transmission system can be increased by only 11%.
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图 2 某航空发动机附件机匣齿轮传动系统的结构示意图
Figure 2. Schematic structure of an aero-engine accessory magazine gearing system
图 3 该航空发动机齿轮传动系统的有限元模型图
Figure 3. Finite element model diagram of gear transmission of this aero-engine
图 4 该航空发动机齿轮传动系统的耦合模态示例
Figure 4. Examples of coupled modes of gear transmission of this aero-engine
图 7 该航空发动机齿轮传动系统的关键模态识别
Figure 7. Critical modal identification of gear transmission of this aero-engine
图 8 该航空发动机齿轮传动系统的危险元件识别
Figure 8. Hazardous component identification of gear transmission of this aero-engine
图 9 该航空发动机齿轮传动系统中齿轮Ⅳ和Ⅹ Ⅰ的避振效果
Figure 9. Vibration avoidance of gears Ⅳ and Ⅹ Ⅰ of gear transmission of this aero-engine
表 1 该航空发动机齿轮传动系统轴的结构参数
Table 1. Structural parameters of shaft of gear transmission of this aero-engine
mm 轴 轴长 轴内径 轴外径 输入轴Ⅰ 290 15 30 转接轴Ⅱ 190 40 50 转接轴Ⅲ 190 40 60 输出轴Ⅳ 220 30 40 输出轴Ⅴ 250 25 40 输出轴Ⅵ 170 20 30 轴Ⅶ 210 20 30 轴Ⅷ 70 15 25 
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表 2 连续运转工况的额定转速与功率
Table 2. Rated speed and power under continuous operation
轴 额定转速/（r/min） 齿轮 输入轴Ⅰ 22000 Ⅰ Ⅲ 转接轴Ⅲ 15098 Ⅴ Ⅸ 输出轴Ⅳ 16947 Ⅶ 输出轴Ⅵ 12249 Ⅹ Ⅰ 输出轴Ⅶ 9643 Ⅹ Ⅲ
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表 3 连续运转工况时的直齿轮副受力情况
Table 3. Forces on spur gears under continuous operation
直齿轮副 传递扭矩/
（N·m）啮合力/
N啮合
偏角/（°）轴向力/
NⅤ-Ⅵ 214 3970 0.12 8.32 Ⅶ-Ⅷ 109 2831 0.13 6.42 Ⅸ-Ⅹ 115 1736 0.09 2.73 Ⅹ Ⅰ-Ⅹ Ⅱ 147 2502 0.10 4.37 Ⅹ Ⅲ-Ⅹ Ⅳ 43 1012 0.05 0.88
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参数 常温数值 温度系数 Em/GPa 200 −0.187 ρn/（kg/m3） 7860 −0.26 μl 0.3 8×10−5 α/10−6 （1/℃） 12.4 0
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表 5 连续运转工况下系统转频与啮频
Table 5. Rotation and engagement frequency of the system under continuous operation
Hz 轴 编号 转频 一倍啮频 二倍啮频 三倍啮频 输入轴Ⅰ 锥Ⅰ 367 15033 30067 45100 锥Ⅲ 12833 25667 38500 转接轴Ⅱ 锥Ⅱ 242 15033 30066 45099 转接轴Ⅲ 锥Ⅳ 252 12833 25667 38500 直Ⅴ 13840 27680 41520 直Ⅸ 10820 21640 32461 输出轴Ⅳ 直Ⅵ 282 13840 27680 41520 直Ⅶ 18924 37848 56772 输出轴Ⅴ 直Ⅷ 541 18924 37848 56772 输出轴Ⅵ 直Ⅹ 204 10820 21640 32460 直Ⅹ Ⅰ 7554 15107 22661 输出轴Ⅶ 直Ⅹ Ⅱ 161 7554 15107 22661 直Ⅹ Ⅲ 3054 6107 9161 输出轴Ⅷ 直Ⅹ Ⅳ 90 3054 6108 9161
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表 6 传动系统的危险模态信息
Table 6. Hazardous modal information for driveline systems
模态振型 频率/Hz 危险
齿轮辐板振动
应力/MPa一-三节径耦合 2108 Ⅱ 198 一-一节径耦合 2285 Ⅴ 127 一-一节径耦合 2700 Ⅵ 138 二-三节径耦合 2810 Ⅳ 132 二-三节径耦合 3120 Ⅳ 120 涡动-涡动耦合 3680 Ⅷ 103 节径节圆-涡动耦合 3912 Ⅹ Ⅰ 103 二-三节径耦合 4212 Ⅲ 113 二-四节径耦合 5610 Ⅰ 122 二-四节径耦合 6778 Ⅳ 110 四节径-涡动耦合 7100 Ⅶ 135 节径节圆-涡动耦合 7940 Ⅶ 103 二节径-节径节圆耦合 8410 Ⅹ Ⅱ 103
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表 7 该航空发动机传动系统中各级齿轮避振改进前后的结构参数对比
Table 7. Comparison of structural parameters before and after the improvement of vibration avoidance of gears at all levels in gear transmission of this aero-engine
mm 结构参数 齿轮编号 Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ Ⅶ Ⅷ Ⅹ Ⅰ Ⅹ Ⅱ 改进前 辐板厚度 21.6 10 10 10 5 5 5 5 5 5 轴内径 15 40 15 40 40 30 30 25 20 20 改进后 辐板厚度 24 17 11 8.5 6 6 5 5.5 6.5 5.5 轴内径 15 35 15 35 35 25 25 25 20 18
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表 8 该航空发动机传动系统中各级齿轮避振改进前后的动力学特性对比
Table 8. Comparison of the dynamic characteristics before and after the improvement of vibration avoidance of the gears at all levels of gear transmission of this aero-engine
参数 齿轮编号 Ⅰ Ⅱ Ⅲ Ⅳ Ⅹ Ⅰ 一节径 二节径 三节径 四节径 二节径 三节径 四节径 节圆-节圆耦合 改进前 频率/Hz 2101 5610 2108 5600 4212 2810 3120 6778 3912 应力/MPa 162 122 198 112 113 132 120 110 103 改进后 频率/Hz 2678 5871 2787 5723 4465 2756 2998 6534 4121 应力/MPa 76 57 81 62 78 84 76 89 74 参数 齿轮编号 Ⅴ Ⅵ Ⅶ Ⅷ Ⅹ Ⅱ 受Ⅵ影响 一节径 四节径 节径-节圆耦合 涡动 节圆-节圆耦合 改进前 频率/Hz 2285 2622 2280 2700 7100 7940 2530 3680 8410 应力/MPa 127 107 106 138 135 103 102 103 103 改进后 频率/Hz 2421 2812 2364 2812 7121 7956 2621 3753 8536 应力/MPa 79 71 76 81 89 87 73 81 78
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