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Chinese Journal of Engineering Design  2026, Vol. 33 Issue (2): 169-181    DOI: 10.3785/j.issn.1006-754X.2026.05.257
Theory and Method of Mechanical Design     
Research on twin modeling for vibration prediction of transmission system of helicopter's main gearbox
Long CHEN1(),Jiezhou LIU2,Zhao XIAO1(),Lifeng CHEN1,Han DING3,Jinyuan TANG3,Yi TIAN3
1.School of Mechanical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
2.Hunan Aviation Powerplant Research Institute, Aero Engine Corporation of China, Zhuzhou 4120021, China
3.State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China
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Abstract  

Spiral bevel gears in the helicopter's main gearbox exhibit pronounced spatial meshing characteristics. Under the combined effects of complex loads as well as manufacturing and assembly errors, the key excitations such as mesh stiffness and transmission error are difficult to obtain online, which limits the high-accuracy prediction of vibration responses. To address this issue, a digital twin method for vibration prediction was proposed by integrating tooth surface contact analysis with mechanism-guided data-driven modeling. The proposed method adopted collaborative modeling along physical and data paths. On the physical path, a tooth surface with geometric errors was constructed based on the three-coordinate measurement data, and the tooth surface contact analysis was carried out to extract time-varying mesh stiffness and composite transmission error. A condition-related vibration intensity index was then obtained through torsional dynamics analysis and used as an interpretable mechanism-informed feature. On the data path, a Bayesian-optimized XGBoost (eXtreme Gradient Boosting) mapping model BO-XGBoost was constructed to fuse the measured operating parameters with the mechanism features for nonlinear prediction of three-dimensional vibration of the output-shaft. The verification results based on the test-rig data of the transmission system of the main gearbox demonstrated that the model had a higher prediction accuracy for the three-dimensional vibration of the output-shaft, with the determination coefficient R2 being higher than 0.97. Compared with baseline models such as BO-XGBoost, SVR (support vector regression), LSTM (long short-term memory), and GRU (gated recurrent unit), its prediction accuracy was the highest. The research results provide a physically interpretable modeling approach for vibration monitoring and performance evaluation of the transmission system of the helicopter's main gearbox.



Key wordsdigital twin      tooth surface contact analysis      Bayesian optimization      eXtreme Gradient Boosting      vibration prediction     
Received: 30 November 2025      Published: 28 April 2026
CLC:  TH 132.41  
Corresponding Authors: Zhao XIAO     E-mail: 18911282502@163.com;xnxzh501@hnust.edu.cn
Cite this article:

Long CHEN,Jiezhou LIU,Zhao XIAO,Lifeng CHEN,Han DING,Jinyuan TANG,Yi TIAN. Research on twin modeling for vibration prediction of transmission system of helicopter's main gearbox. Chinese Journal of Engineering Design, 2026, 33(2): 169-181.

URL:

https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.257     OR     https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/169


直升机主减速器传动系统振动预测孪生建模技术研究

直升机主减速器弧齿锥齿轮系统的空间啮合特性显著,在复杂工况载荷与制造及装配误差的共同作用下,其啮合刚度和传动误差等关键激励难以在线获取,限制了振动响应的高精度预测。针对上述问题,提出了一种融合齿面接触分析与机理引导-数据驱动建模的振动预测数字孪生方法。采用物理路径与数据路径协同建模方式:在物理路径上,基于三坐标测量数据构建了含几何误差的齿面并开展齿面接触分析,提取时变啮合刚度和综合传动误差,并结合扭转动力学分析得到与工况相关的振动强度指标,将它作为可解释的机理先验特征;在数据路径上,构建了贝叶斯优化XGBoost(eXtreme Gradient Boosting,极限梯度提升)映射模型BO-XGBoost,将实测工况参数与机理特征融合,实现输出轴三向振动非线性预测。基于主减速器传动系统台架试验数据的验证结果表明,所提出的模型对输出轴三向振动的预测精度较高,决定系数R2均高于0.97。与BO-XGBoost、SVR(support vector regression,支持向量回归)、LSTM(long short-term memory,长短期记忆)、GRU(gated recurrent unit,门控循环单元)等基线模型相比,其预测精度最高。研究结果为直升机主减速器传动系统振动监测与性能评估提供了具有物理可解释性的建模方法。


关键词: 数字孪生,  齿面接触分析,  贝叶斯优化,  XGBoost,  振动预测 
Fig.1 Digital twin framework for vibration prediction of spiral bevel gear system
Fig.2 Dynamics model of rotor system
Fig.3 Construction process of digital twin model for transmission system
Fig.4 Vibration test platform for transmission system
参数小齿轮大齿轮
齿数2670
节锥角/(°)17.053.0
面锥角/(°)18.253.5
根锥角/(°)16.351.6
齿宽/mm40.040.0
齿顶高/mm4.02.5
齿根高/mm2.55.0
外锥距/mm180.0180.0
弧齿厚/mm6.53.8
轴向误差/mm00
偏置距误差/mm00
轴交角误差/(°)00
滚切修正系数-2C0.1760
滚切修正系数-6D-0.0990
Table 1 Structural parameters and assembly parameters of gear-pair
Fig.5 Results of tooth surface contact analysis
Fig.6 Vibration intensity indices under different operating conditions
参数数值
ni/(r/min)20 08519 89119 8922 000
Mi/(N·m)355522682695
pi/MPa0.430.420.420.42
qi/(L/min)24.824.924.824.9
Ti/℃71.071.071.071.0
T1/℃116.7116.9107.097.3
T2/℃109.8102.0102.092.2
T3/℃57.369.372.052.5
ao, h/g8.410.614.319.5
ao, v/g5.49.815.718.4
ao, a/g5.75.98.49.5
ARMS/g6.105.5210.1310.13
Table 2 Data set for vibration prediction of transmission system
Fig.7 Box plots of vibration data
Fig.8 Comparison of operating condition parameters before and after denoising
Fig.9 Comparison of vibration data before and after denoising
Fig.10 Pearson correlation coefficients among parameters
超参数名称搜索范围最优值
学习器数量100~500218
树的最大深度3~2013
学习率0.01~0.300.033
正则化系数0~10.489
子集最小权重1~101.117
样本采样比例0.5~1.00.634
Table 3 Search ranges and optimal values of XGBoost hyperparameters
Fig.11 Prediction results on test set
输出目标R2ERMS
ao, h0.991 50.443 7
ao, v0.978 90.907 2
ao, a0.987 40.169 4
Table 4 Prediction performance indicators of proposed model
模型ao, hao, vao, a
R2ERMSR2ERMSR2ERMS
BO-XGBoost0.983 20.623 10.964 11.184 60.974 60.241 1
BO-XGBoost+Mech0.991 50.443 70.978 90.907 20.987 40.169 4
SVR0.963 40.918 30.919 01.778 90.946 60.349 5
LSTM0.953 81.005 30.895 01.975 20.923 80.406 8
GRU0.954 80.994 90.900 61.921 90.920 70.414 9
Table 5 Prediction performance indicators of different models
 
 
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