Study on Unbalanced Meshing Loads of Planetary Gear Transmission under Heavy-load Conditions

doi:10.3969/j.issn.1004-132X.2023.13.001

Abstract

Abstract: To study the gear tooth load distribution affected by the multi-flexible body deformations of planetary gear transmission under heavy-load conditions， a coupled dynamics modeling method of planetary gear transmission that taken into account the structural flexibility and dynamic contact of gear pair was proposed. Taking a certain type of megawatt-class wind turbine gearbox planetary gear train as the research object， according to the ring gear， carrier， and their boundary characteristics， the finite element reduction theory was used to establish the correlations between the ring gear teeth， carriers coupling points and the corresponding elastic supports， and the dynamic load-contact of the gear pair was used as the interface coordination condition to couple these components， to establish the planetary gear transmission coupling dynamics model. The phenomenon of unbalanced meshing loads and the effects of structural parameters on the meshing characteristics were analyzed. The results show that the comprehensive bending moment acting on the planet gear and the asymmetric structural deformations of the carrier pin are the main causes of the unbalanced meshing loads， and the resonance of the system will aggravate this phenomenon. In the resonance region， the dynamic meshing stiffness differs greatly from the static meshing stiffness. Increasing the carrier pin stiffness and the helix angle may improve the meshing condition and reduce the system vibration in the resonance region. But in low-speed region, that is not good for system vibration absorption. Increase of the rigidity of the carriers connecting plate may keep the systems vibration state in the low-speed region， and reduce the system vibration in the resonance region.

Key words: wind turbine gearbox, planetary gear train, structural flexibility, ring gear, dynamics

摘要： 为了深入研究重载行星齿轮传动多柔体变形下齿面载荷分布规律，提出一种计入结构柔性与齿轮副动态接触的行星齿轮传动耦合动力学建模方法。以某型兆瓦级风电齿轮箱行星轮系为研究对象，根据内齿圈、行星架结构及其边界特征，采用有限元缩聚理论建立内齿圈轮齿、行星架耦合点与弹性支撑之间的关联关系，利用齿轮副动态承载接触作为界面协调条件将各构件进行耦合，建立行星齿轮传动耦合动力学模型，分析了啮合偏载现象以及结构参数对啮合特性的影响。研究结果表明，作用在行星轮上的合弯矩以及行星架销轴非对称结构变形是造成啮合偏载的主要原因，系统共振会加剧啮合偏载程度；在共振区附近，齿轮动态啮合刚度与静态啮合刚度存在较大差异；增加销轴刚性、增大螺旋角可以改善啮合偏载程度，减小共振区系统振动，但在低转速区不利于系统减振，而增大行星架连接板刚性可以保持低转速区系统振动状态，同时减小共振区系统振动。

关键词: 风电齿轮箱, 行星轮系, 结构柔性, 内齿圈, 动力学

CLC Number:

TM614

TAN Jianjun, LI Hao, YANG Shuyi, ZHU Caichao, SONG Chaosheng, SUN Zhangdong. Study on Unbalanced Meshing Loads of Planetary Gear Transmission under Heavy-load Conditions[J]. China Mechanical Engineering, 2023, 34(13): 1513-1524.

谭建军, 李浩, 杨书益, 朱才朝, 宋朝省, 孙章栋. 重载工况下行星齿轮传动啮合偏载分析[J]. 中国机械工程, 2023, 34(13): 1513-1524.

References

［1］ABOUSLEIMAN V， VELEX P. A Hybrid 3D Finite Element/Lumped Parameter Model for Quasi-Static and Dynamic Analyses of Planetary/Epicyclic Gear Sets［J］. Mechanism and Machine Theory， 2006， 41（6）：725-748.
［2］ZHANG C， WEI J， WANG F， et al. Dynamic Model and Load Sharing Performance of Planetary Gear System with Journal Bearing［J］. Mechanism and Machine Theory， 2020， 151：103898.
［3］许华超，秦大同. 内激励下弹性边界柔性直齿内齿圈振动响应研究［J］. 机械工程学报， 2018， 54（9）：161-167.
XU Huachao， QIN Datong. Vibration Response of Flexible Spur Ring Gear with Elastic Foundation under Internal Excitation［J］. Journal of Mechanical Engineering， 2018， 54（9）：161-167.
［4］张俊，宋轶民，王建军. 计入齿圈柔性的直齿行星传动动力学建模［J］. 机械工程学报， 2009， 45（12）：29-36.
ZHANG Jun， SONG Yimin， WANG Jianjun. Dynamic Modeling for Spur Planetary Gear Transmission with Flexible Ring Gear［J］. Journal of Mechanical Engineering， 2009， 45（12）：29-36.
［5］刘向阳，周建星，章翔峰，等. 考虑齿圈柔性的风电机组行星传动均载特性与灵敏度分析［J］. 太阳能学报， 2021， 42（7）：340-349.
LIU Xiangyang， ZHOU Jianxing， ZHANG Xiangfeng， et al. Analysis of Load Sharing Characteristics and Sensitivity of Planetary Transmission of Wind Turbine Considering Flexibility of Gear Ring［J］. Acta Enerciae Solaris Sinica， 2021， 42（7）：340-349.
［6］SAADA A， VELEX P. An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains［J］. Journal of Mechanical Design， 1995， 117（2A）：241-247.
［7］VELEX P， MAATAR M. A Mathematical Model for Analyzing the Influence of Shape Deviations and Mounting Errors on Gear Dynamic Behaviour［J］. Journal of Sound and Vibration， 1996， 191（5）：629-660.
［8］RACLOT J P， VELEX P. Simulation of the Dynamic Behaviour of Single and Multi-stage Geared Systems with Shape Deviations and Mounting Errors by Using a Spectral Method［J］. Journal of Sound and Vibration， 1999， 220（5）：861-903.
［9］LIU C， QIN D， LIAO Y. Dynamic Model of Variable Speed Process for Herringbone Gears Including Friction Calculated by Variable Friction Coefficient［J］. Journal of Mechanical Design， 2014， 136（4）：041006.
［10］YOUNES E B， CHANGENET C， BRUYERE J， et al. Multi-objective Optimization of Gear Unit Design to Improve Efficiency and Transmission Error［J］. Mechanism and Machine Theory， 2022， 167：104499.
［11］CHAPRON M， VELEX P， BRUYRE J， et al. Optimization of Profile Modifications with Regard to Dynamic Tooth Loads in Single and Double-helical Planetary Gears with Flexible Ring-gears［J］. Journal of Mechanical Design， 2016， 138（2）：023301.
［12］AJMI M， VELEX P. A Model for Simulating the Quasi-static and Dynamic Behaviour of Solid Wide-faced Spur and Helical Gears［J］. Mechanism and Machine Theory， 2005， 40（2）：173-190.
［13］GUILBERT B， VELEX P， DUREISSEIX D， et al. Modular Hybrid Models to Simulate the Static and Dynamic Behaviour of High-speed Thin-rimmed Gears［J］. Journal of Sound and Vibration， 2019， 438：353-380.
［14］白恩军，谢里阳，佟安时，等. 考虑齿轮轴变形的斜齿轮接触分析［J］. 兵工学报， 2015， 36（10）：1975-1981.
BAI Enjun， XIE Liyang， TONG Anshi， et al. The Contact Analysis of Helical Gear in Considering Gear Shaft Deformation［J］. Acta Armamentarii， 2015， 36（10）：1975-1981.
［15］袁冰，常山，刘更，等. 大齿宽齿轮耦合转子系统准静态接触分析及动态特性［J］. 机械工程学报， 2020， 56（3）：96-105.
YUAN Bing， CHANG Shan， LIU Geng， et al. Quasi-static Contact and Dynamic Behaviors Analysis of Wide-faced Gear Coupled with Rotor System［J］. Journal of Mechanical Engineering， 2020， 56（3）：96-105.
［16］王涛，唐增宝. 齿轮传动的动态啮合刚度［J］. 华中理工大学学报， 1992， 20（3）：39-44.
WANG Tao， TANG Zengbao. The Dynamic Meshing Stiffness of Gear Transmission［J］. Journal of Huazhong University of Science and Technology， 1992， 20（3）：39-44.
［17］CAI Y， HAYASHI T. The Linear Approximated Equation of Vibration of a Pair of Spur Gears Theory and Experiment［J］. Journal of Mechnical Design， 1994， 20（3）：558-564.
［18］MATSUMURA S， UMEZAWA K， HOUJOH H. Rotational Vibration of a Helical Gear Pair Having Tooth Surface Deviation during Transmission of Light Load［J］. JSME International Journal. Ser. C， Dynamics， Control， Robotics， Design and Manufacturing， 1996， 39（3）：614-620.
［19］CAO Z， CHEN Z， JIANG H. Nonlinear Dynamics of a Spur Gear Pair with Force-dependent Mesh Stiffness［J］. Nonlinear Dynamics， 2020， 99：1227-1241.
［20］PARKER R G， VIJAYAKAR S M， IMAJO T. Non-linear Dynamic Response of a Spur Gear Pair：Modelling and Experimental Comparisons［J］. Journal of Sound and Vibration， 2000， 237（3）：435-455.
［21］ZHANG C， DONG H， WANG D， et al. A New Effective Mesh Stiffness Calculation Method with Accurate Contact Deformation Model for Spur and Helical Gear Pairs［J］. Mechanism and Machine Theory， 2022， 171：104762.
［22］赵百顺，李娜，马辉，等. 混合修形斜齿轮转子系统振动特性分析［J］. 振动工程学报， 2021， 34（4）：704-711.
ZHAO Baishun， LI Na， MA Hui， et al. Vibration Characteristics of the Helical Gear Rotor System Considering Mixed Modification［J］. Journal of Vibration Engineering， 2021， 34（4）：704-711.
［23］常乐浩，田宏炜，贺朝霞，等. 结合有限元法和接触理论的内齿轮副啮合刚度计算方法［J］. 机械传动， 2018， 42（8）：61-64.
CHANG Lehao， TIAN Hongwei， HE Zhaoxia， et al. A Method for Determining the Mesh Stiffness of Internal Gearby Combining Finite Element Method and Contact Theory［J］. Mechanical Transmission， 2018， 42（8）：61-64.
［24］TAN Jianjun， LI Hao， TANG Hao， et al. Dynamic Modeling and Analysis of Planetary Gear Train System Considering Structural Flexibility and Dynamic Multi-teeth Mesh Process［J］. Mechanism and Machine Theory， 2023， 186：105348.
［25］HELSEN J， VANHOLLEBEKE F， MARRANT B， et al. Multibody Modelling of Varying Complexity for Modal Behaviour Analysis of Wind Turbine Gearboxes［J］. Renewable Energy， 2011， 36（11）：3098-3113.
［26］WANG J. Rayleigh Coefficients for Series Infrastructure Systems with Multiple Damping Properties［J］. Journal of Vibration and Control， 2015， 21（6）：1234-1248.
［27］TAN J， ZHU C， SONG C， et al. Dynamic Modeling and Analysis of Wind Turbine Drivetrain Considering Platform Motion［J］. Mechanism and Machine Theory， 2019， 140：781-808.
［28］CHEN K， MA H， CHE L， et al. Comparison of Meshing Characteristics of Helical Gears with Spalling Fault Using Analytical and Finite-element Methods［J］. Mechanical Systems and Signal Processing， 2019， 121：279-298.
［29］NATALI C， BATTARRA M， DALPIAZ G， et al. A Critical Review on FE-based Methods for Mesh Stiffness Estimation in Spur Gears［J］. Mechanism and Machine Theory， 2021， 161：104319.
［30］WAN X， ZHI Q. Precise Integration Method for LQG Optimal Measurement Feedback Control Problem［J］. Applied Mathematics and Mechanics， 2000， 21：1417-1422.

[1]	LU Kai-Jiang, SHI Dun-Beng, ZHANG Feng-Chao. Dynamics Optimization Design of Planar 3-DOF Parallel Mechanism [J]. J4, 201016, 21(16): 1926-1931.
[2]	TANG Hao, TAN Jianjun, LI Hao, ZHU Caichao, YE Wei, SUN Zhangdong. Research on Dynamic Modeling and Decoupling Methods of Planetary Gear Trains in Wind Turbine Gearboxes with Journal Bearings [J]. China Mechanical Engineering, 2024, 35(04): 591-601.
[3]	WEN Zhiwei, LOU Junqiang, CHEN Tehuan, CUI Yuguo, WEI Yanding, LI Guoping. Vibration Mimicking Fish Body Wave and Flow Distribution of Underwater Flexible Structure with Resonant Actuation of Macro Fiber Composites [J]. China Mechanical Engineering, 2024, 35(03): 405-413.
[4]	HUI Jizhuang, LUO Wei, ZHANG Zeyu, ZHANG Jun, WANG Jie. Research on Energy Transfer Model and Optimisation of Operating Parameters of Vibratory Rollers [J]. China Mechanical Engineering, 2024, 35(03): 541-547.
[5]	WANG Bo, LUO Shihui, MA Weihua, WANG Chen, QU Tianwei, LEI Cheng. Research on Curve Passing of Large Axle-load Diesel Locomotive with Radial Bogie [J]. China Mechanical Engineering, 2024, 35(01): 93-101,143.
[6]	SHU Xiayun, WANG Ce, CHANG Xuefeng, ZHONG Zhidong, TANG Yiquan, . Experimental Study of Dry Aerosol Jet Printing with Sheath Gas-assisted Aerodynamics Lens Focusing [J]. China Mechanical Engineering, 2024, 35(01): 152-159.
[7]	YU Shubo, LIU Zhansheng, ZHAO Chen. Dynamics Simulation Data Driven Domain Adaptive Intelligent Fault Diagnosis [J]. China Mechanical Engineering, 2023, 34(23): 2832-2841.
[8]	ZHANG Xiao, CHI Maoru, XIE Yuchen, WANG Huansheng, CAI Wubin, DAI Liangcheng. Optimization of Variable Gauge Train Wheel Treads Based on Reverse Design Method [J]. China Mechanical Engineering, 2023, 34(22): 2746-2757.
[9]	ZHU Zongming, JI Suqiang, WANG Hao, TANG Puhua, LIANG Liang. Hemodynamics Analysis of Interventional Robots in Diagnosis and Treatment Based on Fluid-structure Interaction [J]. China Mechanical Engineering, 2023, 34(21): 2592-2599.
[10]	DU Zhongqiu, SHEN Huiping, MENG Qingmei, LI Tao, YANG Tingli. Design and Performance Analysis of 8R Two-translational Spatial Parallel Mechanism with Motion Decoupling and Symbolic Positive Solutions [J]. China Mechanical Engineering, 2023, 34(12): 1425-1435.
[11]	LEI Xinpei, FENG Libo, ZHANG Hang, FENG Kai. Influences of Magnetic-Gas Load Ratio on Supporting Characteristics and Rotor Dynamics Characteristics of Foil-Magnetic Hybrid Bearings [J]. China Mechanical Engineering, 2023, 34(11): 1287-1295,1305.
[12]	PAN Ling, LIN Guobin, HAN Yuqing, YU Hui. Molecular Dynamics Simulation for Effect of Nanoparticle Additives on Boundary Lubrication [J]. China Mechanical Engineering, 2023, 34(10): 1140-1156.
[13]	ZHOU Song, CHEN Yu, DONG Hongliang, GAO Xiang, SHEN Juan, ZHOU Jia, WAN Xinming. Research on Multi-axis Road Simulation Test of a New Type of Commercial Vehicle Cab [J]. China Mechanical Engineering, 2023, 34(10): 1241-1250.
[14]	FU Xiang, LIU Zexuan, , LIU Daoyuan, LI Dongyuan, . Pivot Steering Control of Off-road Vehicles Driven by In-wheel Motors [J]. China Mechanical Engineering, 2023, 34(10): 1251-1259.
[15]	ZHU Chen, CHI Maoru, ZHAO Minghua, DAI Liangcheng, CHEN Shiqi. Applicability Analysis of Connected Transverse Damper in Metro Vehicles [J]. China Mechanical Engineering, 2023, 34(06): 660-667，676.