随机风作用下风力发电机齿轮传动系统动力学及动态可靠性研究
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摘要
随着能源和环境问题日趋严峻，风能作为一种清洁、可再生能源受到了广泛的关注和应用，风力发电技术也得到了快速的发展。风力发电机齿轮传动系统作为风力发电系统的关键部件之一，主要功用是将风轮在风力作用下所产生的动力传递给发电机并使其得到相应的转速，其性能好坏直接决定了风力发电机性能的好坏。由于风力发电机组工作在变载荷的恶劣工况，处于高空架设，维修困难，这就对齿轮传动系统运行的动态性能和可靠性提出了很高的要求。因此，研究在随机风速工况下风力发电机齿轮传动系统的动态特性和可靠性是风力发电机设计中的重要任务之一。
本课题结合国家自然科学基金资助项目(50975294)的主要内容，并考虑风力发电机在随机风速工况下运行的工作特点，针对风力发电机齿轮传动系统的动力学和动态可靠性问题开展了较全面深入的研究。主要研究内容包括以下方面：
1.风力发电机随机风速模型研究
为了更真实的反映传动系统的外部激励，基于风能和风资源的数学描述以及风力发电机的工作特点，研究了风力发电机齿轮传动系统的外部激励。采用基于机器学习的加权最小二乘支持向量机（Weight Sparse Least Squares Support VectorMachines，WSLS-SVM）模拟随机风速，结合风力机气动理论计算得到相应的转矩载荷作为系统的外部激励，为风力发电机齿轮传动系统的动力学分析奠定基础。
2.风力发电机齿轮传动系统齿轮-轴承耦合动力学研究
基于齿轮啮合理论和Lagrange方程，考虑了轮齿啮合误差、齿轮副的时变啮合刚度及滚动轴承的时变啮合刚度等因素，运用集中参数法建立了MW级风力发电机齿轮传动系统的耦合动力学模型，计算了风力发电机齿轮传动系统的固有特性，系统地分析了风力发电机齿轮传动系统的内部激励特征。在模拟真实风场随机风速的基础上，将由随机风速变化引起的随机风载荷作为系统的外部激励，求解了风力发电机齿轮传动系统的动态响应，并对齿轮传动系统振动特性进行了分析。求得了在随机风载作用下系统各齿轮和各轴承的动载荷，对比分析了系统动态响应随外部激励变化的规律，为风力发电机动态可靠性分析和疲劳寿命预测提供了基础。
3.风力发电机齿轮传动系统的动态可靠性分析
根据随机风作用下各齿轮和轴承的动载荷，基于有限元方法、赫兹接触理论和准静态方法，求得了系统各齿轮副和各轴承的动态接触应力。采用雨流计数法和数理统计理论，得到系统各构件动态接触应力的概率分布形式，并利用MonteCarlo仿真试验得到零件疲劳强度的概率分布。将载荷作用过程视为随机过程，强度视为随机变量，建立零件的随机过程功能函数，利用一次二阶矩和摄动法求得关键零部件的可靠性指标及可靠度随时间变化关系，根据传动系统的结构形式，建立风力发电机齿轮传动系统的动态可靠性模型，进而得到系统的可靠度随时间变化规律。对系统输入随机载荷进行统计分析和分级处理，编制了用于疲劳寿命试验的试验载荷谱，为可靠性动态设计和疲劳破坏试验提供基础。
4.考虑失效相关的风电齿轮传动系统动态可靠性分析
在对风力发电机齿轮传动系统各齿轮副和各滚动轴承应力-时间历程统计分析的基础上，考虑在齿轮和轴承的相互耦合作用、零件失效相关性以及强度退化等因素，从系统层面上应用应力-强度干涉模型，将载荷作用过程看作随机过程，建立了考虑失效相关性的风力发电机齿轮传动系统动态可靠性模型，得到了系统可靠性随时间变化规律，研究了强度退化对系统可靠性的影响规律，并与不考虑失效相关性的动态可靠性模型进行对比，揭示出失效相关性对传动系统的可靠度具有正相关的特性。
5.风力发电机齿轮传动系统疲劳寿命预测
应用雨流计数法统计循环参量，结合Goodman公式将工作循环应力水平按等寿命原则转换为对称循环下的疲劳应力谱。考虑影响零件疲劳强度的各种因素，由材料的P-S-N曲线得到零件的P-S-N曲线，基于Palmgren-Miner线性累积损伤法则建立了关键零件的疲劳寿命预测模型，对系统各齿轮和轴承的疲劳寿命进行估算，为风力发电机齿轮传动系统的疲劳寿命预测提供了理论方法。
6.风力发电机齿轮传动系统动态性能与疲劳寿命试验研究
基于相似原理设计制造了用于试验的风电齿轮箱，搭建了风电试验齿轮箱动态测试和疲劳寿命试验台，开展了试验齿轮箱的动态测试试验和疲劳寿命试验，将仿真模型计算结果和试验结果进行了对比分析，验证了仿真模型的正确性和有效性，对随机风作用下风力发电机齿轮传动系统动力学和可靠性试验研究进行了初步探索，为风力发电机齿轮箱的设计和应用提供了理论和试验基础。
With the increasingly serious problem of energy and environment, the wind energyas a clean and renewable energy has been widely applied and concerned, and the windpower technology also obtained the fast development. As one of key components ofwind turbine, the main function of gear transmission system is to deliver the powergenerated by the wind wheel rotating to the generator and make it obtain thecorresponding speed, which performance directly determines the wind turbineperformance. As the wind turbine working in stochastic load condition, aerial erectingand repair difficulties, the higher dynamic performance and reliability of wind turbinegear transmission system are required. Therefore, research on the dynamic characteristicand the reliability design of wind turbine gear transmission system in stochastic windcondition is one of the important tasks.
According to the research task of The National Natural Science Fund Project(50975294), and considering the practical operating characteristics of wind turbine instochastic wind conditions, the dynamic and the fatigue reliability problems of windturbine gear transmission system in complex load are investigated fairlycomprehensively and deeply in this dissertation. The main researches are as following:
1. Stochastic wind speed model of wind turbine
The external load of wind turbine gear transmission system is researched based onthe working characteristics and the mathematical description of wind energy and windresource. The Weight Sparse Least Squares Support Vector Machines (WSLS-SVM)based on the machine learning language is used to simulate the actual wind speed.Combining with the aerodynamics theory, the torque load is obtained and be used asexternal excitation, which layings the foundation for dynamics analysis of wind turbinegear transmission system.
2. Dynamic analysis of wind turbine gear transmission system coupled withbearings in stochastic wind condition
Considering the influences such as the time-vary mesh stiffness, comprehensivemeshing error and time-varying bearing stiffness, a translational-torsional coupleddynamics model of MW level wind turbine gear system is built by usinglumped-parameter method based on the gear meshing theory and the Lagrange function,and the system's natural frequency is calculated. The dynamic response of gear transmission system is obtained and the vibration characteristic is analysed by solvingdynamics differential equation with numerical simulation method based on thestochastic wind prediction model have been built，the change rules of system dynamicresponse with the external excitation are analyzed, the dynamic mesh force of each gearand the nonlinear bearing force of each rolling element bearing are obtained, whichprovide foundation for dynamic reliability analysis and fatigue life prediction of windturbine gear transmission system.
3. Time-dependent reliability analysis of gear transmission system of wind turbinein stochastic wind condition
The finite element method, Hertz contact theory and Quasi-static method are usedto obtain the the dynamic contact stress of each gear pairs and each rolling elementbearing on the basis of dynamic load of each gear and each bearing. The rain-flowcounting method and the mathematical statistic theory are used to obtain theprobabilistic distribution function of dynamic contact stress of each gear pair and eachbearing, and the Monte Carlo method is used to obtain the probabilistic distribution ofparts strength. Regarding the load process as random process and considering thestrength as random variable, the random process function is built, and thetime-dependent reliability and the reliability index are calculated by using first-ordersecond-moment and perturbation method. The time-dependent reliability model is builtbased on the series parallel connection between the components in gear transmissionsystem and the rules of system’s reliability changing with time are obtained. Thestatistical analysis and classification of input stochastic load of gear transmission systemare carried out and the test loading spectrum used as fatigue life test is made, thisprovides the research foundations for reliability dynamic design and fatigue lifeprediction.
4. Time-dependent reliability analysis of gear transmission system of wind turbineconsidering dependent failure
Considering the factors such as the dependent failure，coupling effect between thegear and the bearing and strength degradation, using the stress strength interferencemodel at the system level, regarding the load process as random process, thetime-dependent reliability model of gear transmission system of wind turbineconsidering dependent failure is built on the basis of the statistical analysis to thedynamic contact stress of each gear pairs and each bearing in gear transmission system,the rules of system reliability varying with time are obtained, the influences of strength degenerate to system reliability are studied, and the results are compared with dynamicreliability model without considering dependent failure.
5. Fatigue life prediction of wind turbine gear transmission system
The rain-flow counting method is used to statistics cycle parameters and theworking cycle stress is converted to fatigue stress spectrum in the condition ofsymmetrical cyclic stress in the principle of equal life combining with the Goodmanformulation. Considering all kinds of factors that affect part’s fatigue strength, theP-S-N curve of part is obtained by the P-S-N curve of material, the model for predictingthe fatigue life of key parts and components is set up, and the fatigue life of each gearsand bearing of gear transmission system is estimated on the basis of Palmgren-MinerLinear accumulative damage law, this research supplies theory and method for fatiguelife prediction wind turbine gear transmission system.
6. Study on the dynamic property testing and the fatigue life experiment of windturbine gear transmission system
The wind turbine gearbox used testing is designed and manufactured based on thesimilitude theory，the test fig is set up for dynamic characteristics testing and fatigue lifetesting of wind turbine gearbox, the dynamic characteristics testing and fatigue lifetesting of wind turbine gearbox are carried out. The comparison analysis between theorycalculation and test results shows that the theory model is correct and effective. Apreliminary testing research for dynamics and reliability of wind turbine geartransmission system in random wind condition is explored and the research resultsprovide the theory and experiment foundation for design and apply of wind turbinegearbox.
本课题结合国家自然科学基金资助项目(50975294)的主要内容，并考虑风力发电机在随机风速工况下运行的工作特点，针对风力发电机齿轮传动系统的动力学和动态可靠性问题开展了较全面深入的研究。主要研究内容包括以下方面：
1.风力发电机随机风速模型研究
为了更真实的反映传动系统的外部激励，基于风能和风资源的数学描述以及风力发电机的工作特点，研究了风力发电机齿轮传动系统的外部激励。采用基于机器学习的加权最小二乘支持向量机（Weight Sparse Least Squares Support VectorMachines，WSLS-SVM）模拟随机风速，结合风力机气动理论计算得到相应的转矩载荷作为系统的外部激励，为风力发电机齿轮传动系统的动力学分析奠定基础。
2.风力发电机齿轮传动系统齿轮-轴承耦合动力学研究
基于齿轮啮合理论和Lagrange方程，考虑了轮齿啮合误差、齿轮副的时变啮合刚度及滚动轴承的时变啮合刚度等因素，运用集中参数法建立了MW级风力发电机齿轮传动系统的耦合动力学模型，计算了风力发电机齿轮传动系统的固有特性，系统地分析了风力发电机齿轮传动系统的内部激励特征。在模拟真实风场随机风速的基础上，将由随机风速变化引起的随机风载荷作为系统的外部激励，求解了风力发电机齿轮传动系统的动态响应，并对齿轮传动系统振动特性进行了分析。求得了在随机风载作用下系统各齿轮和各轴承的动载荷，对比分析了系统动态响应随外部激励变化的规律，为风力发电机动态可靠性分析和疲劳寿命预测提供了基础。
3.风力发电机齿轮传动系统的动态可靠性分析
根据随机风作用下各齿轮和轴承的动载荷，基于有限元方法、赫兹接触理论和准静态方法，求得了系统各齿轮副和各轴承的动态接触应力。采用雨流计数法和数理统计理论，得到系统各构件动态接触应力的概率分布形式，并利用MonteCarlo仿真试验得到零件疲劳强度的概率分布。将载荷作用过程视为随机过程，强度视为随机变量，建立零件的随机过程功能函数，利用一次二阶矩和摄动法求得关键零部件的可靠性指标及可靠度随时间变化关系，根据传动系统的结构形式，建立风力发电机齿轮传动系统的动态可靠性模型，进而得到系统的可靠度随时间变化规律。对系统输入随机载荷进行统计分析和分级处理，编制了用于疲劳寿命试验的试验载荷谱，为可靠性动态设计和疲劳破坏试验提供基础。
4.考虑失效相关的风电齿轮传动系统动态可靠性分析
在对风力发电机齿轮传动系统各齿轮副和各滚动轴承应力-时间历程统计分析的基础上，考虑在齿轮和轴承的相互耦合作用、零件失效相关性以及强度退化等因素，从系统层面上应用应力-强度干涉模型，将载荷作用过程看作随机过程，建立了考虑失效相关性的风力发电机齿轮传动系统动态可靠性模型，得到了系统可靠性随时间变化规律，研究了强度退化对系统可靠性的影响规律，并与不考虑失效相关性的动态可靠性模型进行对比，揭示出失效相关性对传动系统的可靠度具有正相关的特性。
5.风力发电机齿轮传动系统疲劳寿命预测
应用雨流计数法统计循环参量，结合Goodman公式将工作循环应力水平按等寿命原则转换为对称循环下的疲劳应力谱。考虑影响零件疲劳强度的各种因素，由材料的P-S-N曲线得到零件的P-S-N曲线，基于Palmgren-Miner线性累积损伤法则建立了关键零件的疲劳寿命预测模型，对系统各齿轮和轴承的疲劳寿命进行估算，为风力发电机齿轮传动系统的疲劳寿命预测提供了理论方法。
6.风力发电机齿轮传动系统动态性能与疲劳寿命试验研究
基于相似原理设计制造了用于试验的风电齿轮箱，搭建了风电试验齿轮箱动态测试和疲劳寿命试验台，开展了试验齿轮箱的动态测试试验和疲劳寿命试验，将仿真模型计算结果和试验结果进行了对比分析，验证了仿真模型的正确性和有效性，对随机风作用下风力发电机齿轮传动系统动力学和可靠性试验研究进行了初步探索，为风力发电机齿轮箱的设计和应用提供了理论和试验基础。
With the increasingly serious problem of energy and environment, the wind energyas a clean and renewable energy has been widely applied and concerned, and the windpower technology also obtained the fast development. As one of key components ofwind turbine, the main function of gear transmission system is to deliver the powergenerated by the wind wheel rotating to the generator and make it obtain thecorresponding speed, which performance directly determines the wind turbineperformance. As the wind turbine working in stochastic load condition, aerial erectingand repair difficulties, the higher dynamic performance and reliability of wind turbinegear transmission system are required. Therefore, research on the dynamic characteristicand the reliability design of wind turbine gear transmission system in stochastic windcondition is one of the important tasks.
According to the research task of The National Natural Science Fund Project(50975294), and considering the practical operating characteristics of wind turbine instochastic wind conditions, the dynamic and the fatigue reliability problems of windturbine gear transmission system in complex load are investigated fairlycomprehensively and deeply in this dissertation. The main researches are as following:
1. Stochastic wind speed model of wind turbine
The external load of wind turbine gear transmission system is researched based onthe working characteristics and the mathematical description of wind energy and windresource. The Weight Sparse Least Squares Support Vector Machines (WSLS-SVM)based on the machine learning language is used to simulate the actual wind speed.Combining with the aerodynamics theory, the torque load is obtained and be used asexternal excitation, which layings the foundation for dynamics analysis of wind turbinegear transmission system.
2. Dynamic analysis of wind turbine gear transmission system coupled withbearings in stochastic wind condition
Considering the influences such as the time-vary mesh stiffness, comprehensivemeshing error and time-varying bearing stiffness, a translational-torsional coupleddynamics model of MW level wind turbine gear system is built by usinglumped-parameter method based on the gear meshing theory and the Lagrange function,and the system's natural frequency is calculated. The dynamic response of gear transmission system is obtained and the vibration characteristic is analysed by solvingdynamics differential equation with numerical simulation method based on thestochastic wind prediction model have been built，the change rules of system dynamicresponse with the external excitation are analyzed, the dynamic mesh force of each gearand the nonlinear bearing force of each rolling element bearing are obtained, whichprovide foundation for dynamic reliability analysis and fatigue life prediction of windturbine gear transmission system.
3. Time-dependent reliability analysis of gear transmission system of wind turbinein stochastic wind condition
The finite element method, Hertz contact theory and Quasi-static method are usedto obtain the the dynamic contact stress of each gear pairs and each rolling elementbearing on the basis of dynamic load of each gear and each bearing. The rain-flowcounting method and the mathematical statistic theory are used to obtain theprobabilistic distribution function of dynamic contact stress of each gear pair and eachbearing, and the Monte Carlo method is used to obtain the probabilistic distribution ofparts strength. Regarding the load process as random process and considering thestrength as random variable, the random process function is built, and thetime-dependent reliability and the reliability index are calculated by using first-ordersecond-moment and perturbation method. The time-dependent reliability model is builtbased on the series parallel connection between the components in gear transmissionsystem and the rules of system’s reliability changing with time are obtained. Thestatistical analysis and classification of input stochastic load of gear transmission systemare carried out and the test loading spectrum used as fatigue life test is made, thisprovides the research foundations for reliability dynamic design and fatigue lifeprediction.
4. Time-dependent reliability analysis of gear transmission system of wind turbineconsidering dependent failure
Considering the factors such as the dependent failure，coupling effect between thegear and the bearing and strength degradation, using the stress strength interferencemodel at the system level, regarding the load process as random process, thetime-dependent reliability model of gear transmission system of wind turbineconsidering dependent failure is built on the basis of the statistical analysis to thedynamic contact stress of each gear pairs and each bearing in gear transmission system,the rules of system reliability varying with time are obtained, the influences of strength degenerate to system reliability are studied, and the results are compared with dynamicreliability model without considering dependent failure.
5. Fatigue life prediction of wind turbine gear transmission system
The rain-flow counting method is used to statistics cycle parameters and theworking cycle stress is converted to fatigue stress spectrum in the condition ofsymmetrical cyclic stress in the principle of equal life combining with the Goodmanformulation. Considering all kinds of factors that affect part’s fatigue strength, theP-S-N curve of part is obtained by the P-S-N curve of material, the model for predictingthe fatigue life of key parts and components is set up, and the fatigue life of each gearsand bearing of gear transmission system is estimated on the basis of Palmgren-MinerLinear accumulative damage law, this research supplies theory and method for fatiguelife prediction wind turbine gear transmission system.
6. Study on the dynamic property testing and the fatigue life experiment of windturbine gear transmission system
The wind turbine gearbox used testing is designed and manufactured based on thesimilitude theory，the test fig is set up for dynamic characteristics testing and fatigue lifetesting of wind turbine gearbox, the dynamic characteristics testing and fatigue lifetesting of wind turbine gearbox are carried out. The comparison analysis between theorycalculation and test results shows that the theory model is correct and effective. Apreliminary testing research for dynamics and reliability of wind turbine geartransmission system in random wind condition is explored and the research resultsprovide the theory and experiment foundation for design and apply of wind turbinegearbox.
引文
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