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工程设计学报  2026, Vol. 33 Issue (2): 169-181    DOI: 10.3785/j.issn.1006-754X.2026.05.257
机械设计理论与方法     
直升机主减速器传动系统振动预测孪生建模技术研究
陈龙1(),刘捷舟2,肖钊1(),陈立锋1,丁撼3,唐进元3,田一3
1.湖南科技大学 机电工程学院,湖南 湘潭 411201
2.中国航发 湖南动力机械研究所,湖南 株洲 412002
3.中南大学 高性能复杂制造国家重点实验室,湖南 长沙 410083
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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摘要:

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    
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 words: digital twin    tooth surface contact analysis    Bayesian optimization    eXtreme Gradient Boosting    vibration prediction
收稿日期: 2025-11-30 出版日期: 2026-04-28
CLC:  TH 132.41  
基金资助: 湖南省自然科学基金资助项目(2024JJ8275);湖南省自然科学基金资助项目(2024JJ8284);湖南省杰出青年基金项目(2024JJ2031)
通讯作者: 肖钊     E-mail: 18911282502@163.com;xnxzh501@hnust.edu.cn
作者简介: 陈 龙(2000—),男,硕士生,从事齿轮传动、传动系统数字孪生建模研究,E-mail: 18911282502@163.com
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引用本文:

陈龙,刘捷舟,肖钊,陈立锋,丁撼,唐进元,田一. 直升机主减速器传动系统振动预测孪生建模技术研究[J]. 工程设计学报, 2026, 33(2): 169-181.

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[J]. Chinese Journal of Engineering Design, 2026, 33(2): 169-181.

链接本文:

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

图1  弧齿锥齿轮系统振动预测数字孪生框架
图2  转子系统动力学模型
图3  传动系统数字孪生模型构建流程
图4  传动系统振动试验平台
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
表1  齿轮副结构参数和装配参数
图5  齿面接触分析结果
图6  各工况下振动强度指标
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
表2  传动系统振动预测试验数据集
图7  振动数据箱线图
图8  工况参数去噪前后对比
图9  振动数据去噪前后对比
图10  各参数间的 Pearson 相关系数
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
表3  XGBoos超参数搜索范围及最优值
图11  测试集预测结果
输出目标R2ERMS
ao, h0.991 50.443 7
ao, v0.978 90.907 2
ao, a0.987 40.169 4
表4  本文模型预测性能指标
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
表5  各模型预测性能指标
  
  
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