Analyzing Vortex Phenomenon of High-speed Gear Shafting System and Its Critical Speed with Gyroscopic Effect Considered
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摘要: 高速齿轮轴系由于不平衡量等因素受陀螺效应会产生较大弯矩存在潜在共振危险，计及转轴及齿轮轮体陀螺效应，分别采用梁单元法和有限元法建立某型共轴高速直升机传动系统高速输入轴系模型，系统研究高速齿轮轴系不同振型的涡动现象，结合临界转速坎贝尔图，对比自由与约束模态和约束模态下不同轴承刚度对临界转速数值影响。结果表明：高速齿轮轴系扭转和伸缩振型在自由及约束模态均不会产生涡动，弯曲、节径等横向振型产生明显涡动现象，且在约束模态下涡动现象减弱；临界转速数值随约束模态轴承刚度增加呈增大趋势。在高速齿轮轴系临界转速准确计算中，轴承刚度及陀螺效应影响不可忽视。Abstract: Due to the unbalance quantity factors ofa high-speed gear shafting system,its gyroscopic effect may generate a large bending moment and cause potentially dangerous resonance. The high-speed input shafting model of a certain type of coaxial high-speed helicopter′s transmission system was established with the beam element method and the finite element method respectively. The vortex phenomenon of the high-speed gear shafting system with different vibration modes was systematically studied. Combined with its critical speed Campbell diagram, the freedom iscompared with the constraint modal under different influences of bearing stiffness on the critical speed value. The results show that the torsion and expansion modes of the high-speed gear shafting system do not produce vortices in free and constrained modes, while the transverse modes such as bendingdiameter and pitch diameter generate significant vortices, which are weakened in the constrained mode. The value of critical speed increases with the increase of the bearing stiffness of constrained modal. The critical speed of the high-speed shafting system can be accurately calculated with the bearing stiffness and the gyroscopic effect considered.
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表 1 各工况下对应轴承刚度
工况 轴承 刚度/108(N·m−1) kxx kyy 地面慢车（0.5n） 1 1.28 5.61 2 1.18 4.89 起飞、着陆（1.0n） 1 1.71 6.53 2 1.27 5.28 悬停 （0.9n） 1 1.71 6.53 2 1.27 5.28 悬停 （1.0n） 1 1.56 5.18 2 1.21 5.00 正常前飞或侧飞（1.0n） 1 1.28 5.63 2 1.18 4.89 高速前飞或侧飞（0.85n） 1 2.19 7.58 2 2.53 6.29 单发飞行（1.0n） 1 1.61 6.3 2 1.22 5.09 
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表 5 各工况下的临界转速
不同工况 阶次 频率/
Hz临界转速/
（r·min−1）安全裕度/
%地面慢车 1 1143 68580 535 起飞/着陆 1 1305 78300 262 悬停（0.9n） 1 1305 78300 302 悬停（1.0n） 1 1252 75120 247 正常前飞或侧飞 1 1143 68580 217 高速前飞或侧飞 1 1473 88380 381 单发飞行 1 1270 76200 252
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