Hierarchical Optimization of Meshing and Lubrication for Planetary Journal Bearing Coupling System in Wind Turbine Gearboxes under Multiple Operating Conditions

doi:10.3969/j.issn.1004-132X.2026.10.019

Abstract

Abstract:

The combined effects of complex low-speed heavy-load conditions， component deformations， and dynamic bending moments from helical gear meshing can easily induce bearing edge contact and gear mesh misalignment， compromising system reliability. Taking a 6 MW wind turbine gearbox with journal bearings as the research object， a tribodynamic coupling model was established considering the elastohydrodynamic lubrication of the planet gear journal bearings and the deformation of key components. Then， a surrogate modeling method was employed to reconstruct the mapping relationships among multiple operating conditions， gear modification parameters， and system responses， and the optimal gear modification parameters were obtained. Finally， the optimized results were substituted into the dynamic coupling model， and the mapping relationships among multiple operating conditions， journal bearing parameters， and system responses were reconstructed to obtain the optimal bearing parameters， thereby achieving a hierarchical optimization in which gears were optimized first followed by journal bearings. The effectiveness of the approach was validated through experiments. The results show that increasing input torque aggravates bearing edge contact and gear mesh misalignment. Gear modification alone improves tooth load distribution but hardly alleviates bearing edge contact. The hierarchical optimization strategy can not only improve optimization efficiency but also effectively reduce bearing edge contact， increase the minimum oil film thickness， and improve tooth load distribution and system load-sharing performance.

Key words: wind turbine, gearbox, journal bearing, dynamic characteristic, multi-objective optimization

摘要：

风电齿轮箱复杂低速重载工况、构件复杂变形及斜齿轮动态啮合弯矩的综合作用易引发滑动轴承边缘接触与齿轮啮合偏载，影响系统可靠性。以某型6 MW级风电滑动轴承齿轮箱为研究对象，考虑行星轮滑动轴承弹流润滑与关键构件变形，建立风电滑动轴承齿轮箱摩擦动力学耦合模型；采用代理模型方法重构多工况-齿轮修形参数-系统响应映射关系，求解最优齿轮修形参数；将优化结果代入动力学耦合模型，重构多工况-滑动轴承参数-系统响应映射关系，求解最优滑动轴承参数，实现先齿轮-后滑动轴承的分层优化，并通过试验进行验证。结果表明：增大输入扭矩会加剧滑动轴承边缘接触与齿轮啮合偏载；仅通过齿轮修形虽然可改善齿面载荷分布，但难以改善滑动轴承边缘接触；先齿轮-后滑动轴承的分层优化策略不仅可以提高优化效率，还可以有效减少滑动轴承边缘接触、增大最小油膜厚度、改善齿面偏载与系统均载性能。

关键词: 风电机组, 齿轮箱, 滑动轴承, 动态特性, 多目标优化

CLC Number:

TM614

DU Honghan, TAN Jianjun, SUN Yizhong, SONG Chaosheng, LI Hao, GUAN Yuan. Hierarchical Optimization of Meshing and Lubrication for Planetary Journal Bearing Coupling System in Wind Turbine Gearboxes under Multiple Operating Conditions[J]. China Mechanical Engineering, 2026, 37(10): 2566-2576.

杜虹汗, 谭建军, 孙义忠, 宋朝省, 李浩, 关远. 多工况下风电齿轮箱行星轮滑动轴承耦合系统啮合与润滑分层优化[J]. 中国机械工程, 2026, 37(10): 2566-2576.

Figures/Tables 31

Fig.1 Structure of wind turbine gearbox with journal bearings

Tab.1 Main design parameters of the wind turbine

参数	数值	参数	数值
额定功率	6250 kW	切出风速	22 m/s
塔筒高度	125 m	额定风速	10 m/s
叶片数量	3	额定扭矩	6500 kN·m
风轮直径	220 m	额定转速	9.6 r/min
切入风速	3 m/s	传动比	1∶68.6

Tab.2 Main design parameters of the gear transmission system in a wind turbine gearbox

类别		模数/mm	齿数	压力角/（°）
低速级	太阳轮	18	50	22.5
	行星轮		27
	内齿圈		104
中间级	太阳轮	12.8	47	22.5
	行星轮		34
	内齿圈		115
高速级	太阳轮	10.68	26	22.5
	行星轮		57
	内齿圈		142

Fig.2 Tribodynamic model of a gearbox with journal bearings

Fig.3 Optimization variables of gears and journal bearings

Fig.4 Optimization variables of gears and journal bearings

Tab.3 Load cases of the wind turbine gearbox simulation model

工况	n_r/（r·min^-1）	F_x /kN	F_y /kN	F_z /kN	M_x /（kN·m）	M_y /（kN·m）	M_z /（kN·m）	概率/%
L01	6.66	464	-169	-1084	1547	-812	189	18.4
L02	7.78	621	-352	-999	3432	-903	574	16.4
L03	7.98	699	-613	-968	5312	-2476	1919	43.8
L04	7.74	518	-439	927	6515	49	2411	21.3

Fig.5 Sequential optimization process of meshing and lubrication for the coupled system

Fig.6 Pressure distributions under different operating conditions

Fig.7 Tooth load distribution of the low-speed stage planetary gear train

Fig.8 Load sharing coefficient and vibration response of the low-speed stage

Fig.9 Data samples （dimensionless）

Fig.10 Comparison of prediction accuracy of various surrogate models under multiple operating conditions

Fig.11 Pareto frontier solution set for gears

Fig.12 Pareto frontier solution set for journal bearings

Fig.13 Pressure distributions under L04 condition before（left） and after（right） gear-only optimization

Fig.14 Film and contact pressure distributions before （left） vs. after （right） optimization

Fig.15 Minimum oil film thickness before and after optimization

Fig.16 Tooth load distribution coefficient before and after optimization

Fig.17 Tooth load distribution of the low-speed stage under L04 condition before and after optimization

Fig.18 Load sharing coefficient before and after optimization

Fig.19 Maximum value of load sharing coefficient before and after optimization

Fig.20 Vibration acceleration of the ring gear before and after optimization

Tab.4 RMS vibration acceleration of ring gear before and after gear-bearing optimization

工况	L01	L02	L03	L04
x向优化前/（m·s^-2）	0.118	0.466	0.757	0.868
x向优化后/（m·s^-2）	0.120	0.465	0.747	0.870
对比/%	2.50	-0.20	-1.32	0.23
y向优化前/（m·s^-2）	0.121	0.510	0.836	0.979
y向优化后/（m·s^-2）	0.122	0.537	0.849	0.984
对比/%	0.82	5.18	1.53	0.56

Fig.21 Wind turbine gearbox bench test rig

Fig.22 Vibration testing system and measurement points of wind turbine gearbox

Fig.23 Comparison of time‑domain and frequency‑domain results of simulated and measured vibration acceleration at each measuring point

Tab.5 RMS vibration acceleration at each measuring point

额定工况	低速级内齿圈x方向	中间级内齿圈y方向	高速级内齿圈x方向
仿真值/（m·s^-2）	1.33	2.04	3.03
试验值/（m·s^-2）	1.37	2.46	3.06
误差/%	2.92	17.07	0.98

Fig.24 Principle of load‑sharing test and strain‑gauge layout for wind turbine gearbox

Fig.25 The micro-strain at the tooth root of the ring gear at positions a2 and a4 under rated operating conditions

Tab.6 Simulation and test load sharing coefficient calculation results under 25%~100% rated torque

工况	25%	50%	75%	100%
仿真值	1.12	1.07	1.06	1.05
试验值	1.14	1.13	1.11	1.05
误差	1.48%	5.04%	4.94%	0.42%

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