Gear Fatigue Damage Prediction with Coupling Effect of Environmental Randomness and Load Sequence

doi:10.3969/j.issn.1004-132X.2026.01.012

Abstract

Abstract:

To accurately assess the fatigue damage of wind turbine gears under operational conditions， a prediction framework that integrated environmental randomness and load temporal characteristics was proposed. A nonlinear damage correction model was utilized to calculate and analyze the influences of different wind speeds on the fatigue damage of gears. The results indicate that the bending fatigue damage of gears in the low wind speed range is dominated by high-frequency low-amplitude cyclic stresses， while the contact fatigue of gears in the high wind speed range is significantly exacerbated by extreme loads accumulation. The rated wind speed range is identified as the main risk interval for gear fatigue damages. Based on the damage analysis results， a quantitative speed control strategy was proposed to extend the service life of the gearbox， providing a basis for the reliability design of the gearbox and the control of the wind turbine hub speed.

Key words: random wind speed, gear stress, fatigue damage, wind turbine gear

摘要：

为准确评估风电齿轮在服役工况下的疲劳损伤，提出一种融合环境随机性与载荷时序性的预测框架，利用非线性损伤修正模型计算并分析了不同风速对齿轮疲劳损伤的影响规律。结果表明，低风速段的齿轮弯曲疲劳损伤由高频低幅循环应力主导，极端载荷累积显著加剧高风速段的齿轮接触疲劳，额定风速区间是造成齿轮疲劳损伤的主要风险区间。基于损伤分析结果提出了定量转速控制策略以延长齿轮箱服役寿命，为齿轮箱可靠性设计及风机轮毂转速控制提供了依据。

关键词: 随机风速, 齿轮应力, 疲劳损伤, 风电齿轮

WANG Rong, LI Junjie, ZHENG Wenge, WANG Jia, HE Mingrong. Gear Fatigue Damage Prediction with Coupling Effect of Environmental Randomness and Load Sequence[J]. China Mechanical Engineering, 2026, 37(1): 105-113.

王荣, 李俊杰, 郑文革, 王嘉, 贺明荣. 环境随机性与载荷时序性耦合作用下齿轮疲劳损伤的预测[J]. 中国机械工程, 2026, 37(1): 105-113.

Figures/Tables 19

Tab.1 5 MW wind turbine parameters

项目	参数
额定功率/MW	4.55
切入风速/（m·s $- 1$ ）	4
切出风速/（m·s $- 1$ ）	25
额定风速/（m·s $- 1$ ）	10
额定叶轮转速/（r·min $- 1$ ）	16.2
轮毂中心高度/m	80
叶轮直径/m	118

Tab.1 5 MW wind turbine parameters

项目	参数
额定功率/MW	4.55
切入风速/（m·s $- 1$ ）	4
切出风速/（m·s $- 1$ ）	25
额定风速/（m·s $- 1$ ）	10
额定叶轮转速/（r·min $- 1$ ）	16.2
轮毂中心高度/m	80
叶轮直径/m	118

Fig.1 Wind turbine global coupling model

Fig.2 Gearbox topology structure diagram

Tab.2 Gear parameters

项目	输入级	中间级	输出级
法向模数/mm	21.00	12.20	11.00
法向压力角/（°）	25.00	25.00	25.00
螺旋角/（°）	4.50	11.35	11.85
中心距/mm	685.00	685.00	453.00
齿宽/mm	380.00	184.50	170.00
太阳轮齿数		30	23
行星轮齿数	19	83	58
齿圈齿数	84		139

Tab.3 Material parameters of gear

	太阳轮	内齿圈
材料	18CrNiMo7-6	42CrMo4
许用接触应力［σ_H］/MPa	1500	1000
许用弯曲应力［σ_F］/MPa	500	370
弹性模量E/GPa	206
泊松比ν	0.30

Fig.3 Result of contact spots simulation and test under rated working condition

Tab.4 Design load case

项目	风模型	仿真时长/s
正常发电工况 DLC1.2	正常湍流风	600
控制系统故障工况 DLC2.4	正常湍流风	600
正常停机工况 DLC4.1	正常风廓线	180
空转工况 DLC6.4	正常湍流风	600

Fig.4 Wind turbine hub coordinate system

Fig.5 Wind speed distribution（vmean=10m/s）

Fig.6 Torque in the X-direction at the hub center under different working conditions

Fig.7 Dynamic meshing force of the sun gear under DLC1.2 operating conditions（10 m/s）

Tab.5 Output stage sun gear stress calculation parameters

弯曲系数	数值	接触系数	数值
K_A	1.00	K_A	1.00
K_V	1.03	K_V	1.03
K_Fβ	1.00	K_Hβ	1.00
K_Fα	1.04	K_Hα	1.04
Y_F	1.31	Z_H	2.28
Y_S	2.18	Z_E	190.27
Y_β	0.90	Z_ε	0.81
Y_B	1.21	Z_β	1.01
Y_DT	1.00

Fig.8 Statistics of stress cycle counts

Fig.9 Short-term gear stress distribution under steady-state conditions

Fig.10 Short-term gear stress distribution under non-steady-state conditions

Fig.11 Distribution of gear contact stress and bending stress under service conditions（one year）

Fig.12 Stress distribution of the solar gear under different wind speeds in DLC1.2 working conditions

Fig.13 Short-term contact damage with different wind speeds under normal power generation conditions

Fig.14 Long-term wind speed probability distribution（one year）

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