Crack Fault Characteristic Analysis of a Wind Turbine Gearbox with Flash Temperature Considered
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摘要: 为了研究齿面闪温对风电齿轮箱裂纹故障时系统动力学响应的影响，利用Blok闪温理论分析齿轮啮合时的齿面温度，应用热变形公式计算齿廓形变，进而通过Hertz接触理论获得计及齿面闪温影响的轮齿刚度。考虑齿面闪温、阻尼、时变啮合刚度、综合啮合误差和齿侧间隙，建立含有高速级齿轮齿根裂纹的齿轮箱扭转动力学模型。通过时域图、频谱图、相图和Poincaré截面分析不同裂纹长度下系统振动特性随齿面闪温变化的规律，并比较裂纹故障仿真与实验的时频域结果。结果表明：齿面闪温使时域图上裂纹产生的冲击幅值增大、频域图中故障边频结构更为复杂、相图曲线向外扩展以及Poincaré截面离散点增多，且变化均随裂纹长度的增加越为明显。研究结论可为齿轮裂纹故障状态的诊断与监测提供依据。Abstract: In order to study the influence of the flash temperature on the crack fault characteristic of a wind turbine gearbox, the temperature and profile deformation of the tooth are calculated using the Blok flash temperature theory and thermal deformation formula, respectively, and the tooth stiffness considering the flash temperature is obtained using the Hertz contact theory. For the gearbox with crack fault occurred on the tooth root of the high-speed gear, the torsional dynamic model is established considering flash temperature, damping, meshing stiffness, transmission error and backlash. The variation laws of the vibration characteristics with flash temperature are investigated under different crack conditions through time domain, frequency spectrum, phase diagram and Poincaré section, and the numerical results in the time-frequency domain are compared with those of the test without considering the flash temperature. The results show that the flash temperature makes the impact amplitude from the crack in the time domain increase, the fault side frequency be more complex, the phase diagram expand and the number of discrete points in Poincaré section increase, and the changes are more obvious with increasing the crack length. The research provides the basis for diagnosing and monitoring the gear crack fault state.
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图 2 齿轮传动系统纯扭转动力学模型
Figure 2. Pure torsional dynamic model of the gear transmission system
图 4 齿面闪温随啮合点变化的趋势
Figure 4. Change trend of tooth flash temperature with the meshing point
图 6 高速级齿轮在不同裂纹状态下的啮合刚度
Figure 6. Meshing stiffness of high-speed gears under different crack states
图 7 不考虑齿面闪温时的动力学响应
Figure 7. Dynamic responses without the tooth flash temperature considered
图 9 考虑齿面闪温时的动力学响应
Figure 9. Dynamic responses with the tooth flash temperature considered
表 1 高速级主动轮裂纹故障参数
Table 1. Parameters of crack faults of the high-speed driving gear
裂纹情况 裂纹长度/mm 裂纹角度/（°） 10%裂纹 q1=0.3 70 20%裂纹 q1=0.6 70 50%裂纹 q1=1.5 70 70%裂纹 q1=1.5, q2=0.6 70 
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表 2 齿轮箱各齿轮参数
Table 2. Parameters of gears in the gearbox
参数 高速级定轴 中速级定轴 低速级行星传动 1 2 3 4 s p r 齿数 29 100 36 90 28 36 100 模数/mm 1.5 1.5 1.5 1.5 1 1 1 基圆半径/mm 20.4 70.5 25.3 63.4 13 17 47 齿轮质量/g 125 1224.5 224 1111 41 34.6 − 转动惯量/(kg·m2) 0.05 6 0.14 4 0.007 0.01 − 齿宽/mm 30 30 20 20 20 20 20 压力角/（°） 20 20 20 20 20 20 20 热传导系数/[J·(m·s·℃)−1] 46.47 46.47 46.47 46.47 46.47 46.47 46.47 材料密度/（kg·m−3） 7850 7850 7850 7850 7850 7850 7850 弹性模量/GPa 210 210 210 210 210 210 210 比热容/[J·(kg·℃)−1] 481.5 481.5 481.5 481.5 481.5 481.5 481.5 泊松比$ \nu $ 0.3 0.3 0.3 0.3 0.3 0.3 0.3 线膨胀系数/10−5 1.16 1.16 1.16 1.16 1.16 1.16 1.16 齿轮轴半径/mm 5 10 5 15 5 5 5 轴温/℃ 20 20 20 20 20 20 20 基圆面温度/℃ 100 100 100 100 100 100 100
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