Experiment on traveling wave resonance dynamic response characteristics of aviation high speed thin-walled spiral bevel gear
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摘要:
针对航空高速薄辐板弧齿锥齿轮在工作中由于行波共振导致轮齿断裂故障频发，其行波共振动力学响应特性不清晰的问题，建立了一种基于显式算法的航空薄辐板弧齿锥齿轮瞬态接触动力学分析模型。考虑齿轮转速、扭矩以及时变啮合刚度的影响，计算齿轮动频值进而对行波共振点进行精准预测，研究了行波共振下齿轮轴向振动位移和动应力的动态响应特性以及振动位移场和应力场的分布规律。研究结果表明：在三节径前行波共振工况下，从动锥齿轮轴向振动位移场在周向呈现谷峰交替的三峰三谷扇形分布快速迁移的特征，行波迁移方向与齿轮转动方向相同、迁移速度远高于齿轮的旋转速度；振动应力场在周向表现为三峰的花瓣状分布形式，在齿根槽位置和齿面啮合位置存在应力集中现象；振动位移和应力响应均表现为高次谐波振动密集分布的特征。试验测量从动锥齿轮三节径前行波共振转速与仿真计算预测的行波共振转速的相对误差为1.1%，试验测量的应力值与仿真提取分析的应力值两者量级相当，验证了行波共振点预测的准确性及瞬态接触动力学分析模型的有效性。
Abstract:In view of the problem that the traveling wave resonance (TWR) of the aviation high speed thin-walled spiral bevel gear causes frequent tooth fracture faults during operation, and the dynamic response characteristics of the TWR are not clear, a transient contact dynamics analysis model of the aviation thin-walled spiral bevel gear based on the explicit algorithm was established. Considering the influence of gear speed, torque and time-varying meshing stiffness, the dynamic frequency value of the gear was calculated and the TWR point was accurately predicted. The dynamic response characteristics of the axial vibration displacement and dynamic stress of the gear under the TWR as well as the distribution law of the vibration displacement field and the stress field were studied. The results showed that the axial vibration displacement field of the driven bevel gear presented a three-peak and three-valley distribution form with alternating valleys and peaks in the circumferential direction under the condition of forward traveling wave (FTW) resonance with the third nodal diameter. The traveling wave migration direction was the same as the rotation direction of the gear, and the migration speed was much higher than the rotation speed of the gear, which was characterized by the rapid migration of the sector distribution displacement field. The vibration stress field showed a petal-shaped distribution of three peaks in the circumferential direction, and there was a stress concentration phenomenon at the root groove position and the tooth surface meshing position. The vibration displacement and stress response were characterized by the dense distribution of high-order harmonic vibration. The relative error between the FTW resonant speed with the third nodal diameter of the driven bevel gear measured by the experiment and predicted by the simulation calculation was 1.1%, and the stress value measured by the experiment was consistent with the stress value extracted by the simulation, which verified the accuracy of the prediction of the TWR point and the validity of the transient contact dynamics analysis model.
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图 5 从动锥齿轮行波共振分析坎贝尔图
Figure 5. Traveling wave resonance analysis of driven bevel gear Campbell diagram
图 6 锥齿轮啮合模型耦合约束、接触对及载荷加载
Figure 6. Bevel gear meshing model coupling constraints,contact pairs and load loading
图 8 三节径前行波共振工况不同时刻轴向振动位移云图
Figure 8. Axial vibration displacement nephogram under forward traveling wave resonance with the third nodal diameter at different times
图 9 三节径前行波共振工况不同时刻轴向位移展开图
Figure 9. Axial displacement expansion diagram under forward traveling wave resonance with the third nodal diameter at different times
图 10 三节径前行波共振轴向位移时频域图
Figure 10. Time-frequency domain diagram of axial vibration displacement under forward traveling wave resonance with the third nodal diameter
图 11 三节径前行波共振应力分布云图
Figure 11. Distribution nephogram of vibration stress under forward traveling wave resonance with the third nodal diameter
图 12 三节径行波共振应力时频域图
Figure 12. Time-frequency domain diagram of vibration stress under forward traveling wave resonance with the third nodal diameter
图 17 仿真与试验应力对比结果
Figure 17. Results of stress comparison between simulation and experiment
表 1 材料参数
Table 1. Material parameters
温度/℃ 密度/（kg/m3） 弹性模量/GPa 泊松比 20 7860 2.15 0.38 200 7860 2.10 0.41 
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表 2 从动锥齿轮固有频率试验与仿真结果对比
Table 2. Comparison of natural frequency experiment and simulation results of driven bevel gear
振型 固有频率/Hz 相对
误差/%仿真结果 试验结果 三节径 8119.9 7964 1.96 四节径 13554 13420 1.00
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