风力发电机齿轮传动系统随机振动分析及动力可靠性概率优化设计
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摘要
风力发电机工作环境恶劣，常年经受无规律的变向变负荷的风力作用及强阵风的冲击，加之高空架设、维修困难等原因，对其可靠性和使用寿命都提出了比一般机械系统高得多的要求。作为风力发电机传动系统的关键部件，齿轮传动系统需要承受高度不稳定的随机动载荷和比其他传动机构高得多的疲劳循环，是风力发电机失效率最高的部件之一。因此，研究风力发电机齿轮传动系统的动力学行为和可靠性对提高风力发电机的稳定可靠运行有重要的现实意义。
本文结合国家自然科学基金资助项目（50975294）——“基于柔性多体动力学的风电传动系统可靠性研究”的研究任务，依据风力发电机的实际工况，针对其齿轮传动系统的动力学和可靠性等问题进行了深入研究。主要研究内容包括以下几个方面：
①风力发电机齿轮传动系统固有特性分析。
基于齿轮动力学理论和Lagrange方程，运用集中参数法建立了某1.5MW风力发电机齿轮传动系统的纯扭转动力学模型。将风力发电机齿轮传动系统中齿轮的弹性模量、质量密度、工作齿宽和分度圆直径视为随机变量，根据随机摄动理论推导了系统特征值统计特征的表达式。应用随机摄动法研究了齿轮物理参数和几何参数随机变异时系统固有频率的统计特征，定量分析了各参数随机变异对系统固有频率的影响。
②风力发电机齿轮传动系统随机振动分析。
考虑齿轮时变啮合刚度、综合传递误差和阻尼等因素，建立了考虑制造误差的风力发电机齿轮传动系统纯扭转动力学模型。基于随机波动(SV)模型来获取风场的随机风速序列，根据空气动力学理论得到了齿轮传动系统的外部激励。系统地分析了风力发电机齿轮传动系统的内部激励特征，对刚度激励和传递误差进行了分析和模拟。提出了风力发电机齿轮传动系统外部载荷和参数随机变异时系统动态响应的求解方法。通过数值仿真得到了载荷和参数随机变异时系统各响应量和齿轮副间动态啮合力的统计特征，并分析了载荷和参数随机变异对系统动态响应的影响。
③载荷和参数随机性对系统动力可靠性的影响分析。
依据雨流计数原则，对各齿轮副的动态啮合力进行循环计数，得到变幅疲劳载荷的频次数。采用Geber二次曲线等效方法计算得到了随机风载作用下传动系统等效应力幅值和频次。建立了基于概率疲劳累积损伤理论的风电齿轮传动系统动力可靠度模型，利用概率疲劳累计损伤理论推导计算了零件及系统的动力可靠度。研究了各参数随机变异时系统动力可靠度随时间的变化规律。分析了参数随机性对传动系统动力可靠度的影响，并将计算结果与Monte-Carlo法的计算结果进行了对比。
④基于动力可靠性的系统概率优化设计
根据风力发电机齿轮传动系统的结构模型，以传动系统各构件扭转位移均值和体积最小为优化目标，以影响传动系统动态性能和可靠性的参数为优化设计变量，以传动系统的可靠度、参数随机性对可靠性的影响、以及各轮齿正常啮合的条件和强度等为约束条件，建立了用于风力发电机齿轮传动系统可靠性概率优化设计的数学模型。对系统优化问题的求解方法进行了探讨。对风力发电机齿轮传动系统进行了实例优化，并将优化结果与设计结果和Monte Carlo法的优化结果进行了对比，验证了本文优化方法的可行性。
⑤风力发电机齿轮增速箱随机振动测试
根据相似理论设计制造了风力发电机齿轮增速箱，并搭建了振动测试试验台。根据风力发电机齿轮传动系统的工作特点，测量了各种随机载荷工况下各测点的动态响应，经过数值积分和统计分析得到了风力发电机齿轮传动系统随机振动的统计特征。将理论分析结果与试验结果进行对比分析，发现理论分析结果与试验结果比较吻合，从而验证了本文随机振动分析方法的正确性。
As wind turbine working condition is bad, and withstand the variable wind loads orstrong gusts, coupled with installed overhead and difficult to maintain requests higherreliability and longer service life than the general mechanical system. Gear transmissionsystem need to withstand the highly fluctuating load and much higher cyclic fatiguethan other transmission mechanism as the key components of drive system of windturbine, and it is one of the highest failure rate components of wind turbine. Therefor,the study of dynamic behavior and reliability of gear transmission system of windturbine has an important practical significance to improve the stable and reliableoperation of the wind turbine.
According to the research task of the National Natural Science Foundation ofChina (50975294)“Reliability research of wind turbine transmission besed on theflexible multi-body dynamics”, and considering the practical operating condition ofwind turbine, the dynamics and the reliability problems are investigated fairlycomprehensively and deeply in this dissertation. The main researches are as following:
①Inherent characteristic analysis of gear transmission system of wind turbine.
According to gear mesh theory and Lagrange equation, the torsional dynamicmodel for gear transmission system of1.5MW wind turbine is developed bylumped-parameter method. The expression of the statistical characteristics of the systemeigenvalues is derived based on the stochastic perturbation theory. The statisticalcharacteristics of system eigenvalues are researched taking the elastic modulus, massdensity, tooth width and pitch diameter as random variables, and the influence of theseparameters on the system natural frequency are also studied.
②Random vibration analysis of gear transmission system of wind turbine
A dynamic model of planetary gear transmission system of wind turbine wasdeveloped with considering the time-varying mesh stiffness, transmission error anddamp. Random wind velocity is obtained based on the Stochastic Volatility (SV) model,and the external excitation of the gear transmission system is got according toaerodynamic theory on the basis of the dynamic model of the system. Thecharacteristics of internal excitation of the multi-stage gear transmission system areanalysed, and a solving algorithm for system response of wind turbine gear transmissionsystem when the external loads and design parameters are random variable. The statistical characteristics of the vibration displacement and dynamic dynamic meshingforce are obtained by numuerical simulation, and the influence of these parameters onsystem dynamics are also be analysed.
③The influence of randomness of loadings and parameters on dynamic reliabilityof gear transmission system.
According to rain flow counting principle, the dynamic meshing forces have beenconverted into a series of amplitude fatigue load spectrum blocks. Then, the equivalentamplitude and frequency will be get using equivalent method of Geber quadratic curve.Finally, the dynamic reliability model of components and system have been set upaccording the theory of probability fatigue damage cumulative. The change laws withtime of system reliability with the random variation of parameters has been calculated,and the influence of random parameters on dynamic reliability of components havebeen studied and compared with the results of Monte Carlo method.
④Probability optimization design of wind turbine gear transmission system basedon dynamic reliability
A probability optimal mathematic model of wind turbine gear transmission systemis built with goals of the maximum of the mean vibration displacement of systemcomponents and minimum volume, design variables of parameters which have aninfluence on system dynamics and reliability, comstrains of the reliability of geartransmission system, and the influence of random parameters on system reliability andthe normal meshing conditions and strength of gears. A solving algorithm for systemprobability optimal model is presented based on the system dynamic reliability analysisand probability optimal mathematic model. Then, an optimized example of geartransmission system of wind turbine is given. The optimization results is compared todesign results and the Monte Carlo optimization results to verify the feasibility of theoptimization method.
⑤Random vibration test of wind turbine gearbox
The wind turbine gearbox used testing is designed and manufactured based on thesimilitude theory，and the test fig is set up for dynamic characteristics testing of windturbine gearbox. According to the working characteristics of wind turine geartransmission system, the dynamic responses of each point have been measured under avariety of random load conditions, and the statistical characteristics of the randomvibration of wind turine gear transmission system have been obtained through statistical analysis and numerical integration. The comparison analysis between theory calculationand test results shows that the theory model is correct and effective.
本文结合国家自然科学基金资助项目（50975294）——“基于柔性多体动力学的风电传动系统可靠性研究”的研究任务，依据风力发电机的实际工况，针对其齿轮传动系统的动力学和可靠性等问题进行了深入研究。主要研究内容包括以下几个方面：
①风力发电机齿轮传动系统固有特性分析。
基于齿轮动力学理论和Lagrange方程，运用集中参数法建立了某1.5MW风力发电机齿轮传动系统的纯扭转动力学模型。将风力发电机齿轮传动系统中齿轮的弹性模量、质量密度、工作齿宽和分度圆直径视为随机变量，根据随机摄动理论推导了系统特征值统计特征的表达式。应用随机摄动法研究了齿轮物理参数和几何参数随机变异时系统固有频率的统计特征，定量分析了各参数随机变异对系统固有频率的影响。
②风力发电机齿轮传动系统随机振动分析。
考虑齿轮时变啮合刚度、综合传递误差和阻尼等因素，建立了考虑制造误差的风力发电机齿轮传动系统纯扭转动力学模型。基于随机波动(SV)模型来获取风场的随机风速序列，根据空气动力学理论得到了齿轮传动系统的外部激励。系统地分析了风力发电机齿轮传动系统的内部激励特征，对刚度激励和传递误差进行了分析和模拟。提出了风力发电机齿轮传动系统外部载荷和参数随机变异时系统动态响应的求解方法。通过数值仿真得到了载荷和参数随机变异时系统各响应量和齿轮副间动态啮合力的统计特征，并分析了载荷和参数随机变异对系统动态响应的影响。
③载荷和参数随机性对系统动力可靠性的影响分析。
依据雨流计数原则，对各齿轮副的动态啮合力进行循环计数，得到变幅疲劳载荷的频次数。采用Geber二次曲线等效方法计算得到了随机风载作用下传动系统等效应力幅值和频次。建立了基于概率疲劳累积损伤理论的风电齿轮传动系统动力可靠度模型，利用概率疲劳累计损伤理论推导计算了零件及系统的动力可靠度。研究了各参数随机变异时系统动力可靠度随时间的变化规律。分析了参数随机性对传动系统动力可靠度的影响，并将计算结果与Monte-Carlo法的计算结果进行了对比。
④基于动力可靠性的系统概率优化设计
根据风力发电机齿轮传动系统的结构模型，以传动系统各构件扭转位移均值和体积最小为优化目标，以影响传动系统动态性能和可靠性的参数为优化设计变量，以传动系统的可靠度、参数随机性对可靠性的影响、以及各轮齿正常啮合的条件和强度等为约束条件，建立了用于风力发电机齿轮传动系统可靠性概率优化设计的数学模型。对系统优化问题的求解方法进行了探讨。对风力发电机齿轮传动系统进行了实例优化，并将优化结果与设计结果和Monte Carlo法的优化结果进行了对比，验证了本文优化方法的可行性。
⑤风力发电机齿轮增速箱随机振动测试
根据相似理论设计制造了风力发电机齿轮增速箱，并搭建了振动测试试验台。根据风力发电机齿轮传动系统的工作特点，测量了各种随机载荷工况下各测点的动态响应，经过数值积分和统计分析得到了风力发电机齿轮传动系统随机振动的统计特征。将理论分析结果与试验结果进行对比分析，发现理论分析结果与试验结果比较吻合，从而验证了本文随机振动分析方法的正确性。
As wind turbine working condition is bad, and withstand the variable wind loads orstrong gusts, coupled with installed overhead and difficult to maintain requests higherreliability and longer service life than the general mechanical system. Gear transmissionsystem need to withstand the highly fluctuating load and much higher cyclic fatiguethan other transmission mechanism as the key components of drive system of windturbine, and it is one of the highest failure rate components of wind turbine. Therefor,the study of dynamic behavior and reliability of gear transmission system of windturbine has an important practical significance to improve the stable and reliableoperation of the wind turbine.
According to the research task of the National Natural Science Foundation ofChina (50975294)“Reliability research of wind turbine transmission besed on theflexible multi-body dynamics”, and considering the practical operating condition ofwind turbine, the dynamics and the reliability problems are investigated fairlycomprehensively and deeply in this dissertation. The main researches are as following:
①Inherent characteristic analysis of gear transmission system of wind turbine.
According to gear mesh theory and Lagrange equation, the torsional dynamicmodel for gear transmission system of1.5MW wind turbine is developed bylumped-parameter method. The expression of the statistical characteristics of the systemeigenvalues is derived based on the stochastic perturbation theory. The statisticalcharacteristics of system eigenvalues are researched taking the elastic modulus, massdensity, tooth width and pitch diameter as random variables, and the influence of theseparameters on the system natural frequency are also studied.
②Random vibration analysis of gear transmission system of wind turbine
A dynamic model of planetary gear transmission system of wind turbine wasdeveloped with considering the time-varying mesh stiffness, transmission error anddamp. Random wind velocity is obtained based on the Stochastic Volatility (SV) model,and the external excitation of the gear transmission system is got according toaerodynamic theory on the basis of the dynamic model of the system. Thecharacteristics of internal excitation of the multi-stage gear transmission system areanalysed, and a solving algorithm for system response of wind turbine gear transmissionsystem when the external loads and design parameters are random variable. The statistical characteristics of the vibration displacement and dynamic dynamic meshingforce are obtained by numuerical simulation, and the influence of these parameters onsystem dynamics are also be analysed.
③The influence of randomness of loadings and parameters on dynamic reliabilityof gear transmission system.
According to rain flow counting principle, the dynamic meshing forces have beenconverted into a series of amplitude fatigue load spectrum blocks. Then, the equivalentamplitude and frequency will be get using equivalent method of Geber quadratic curve.Finally, the dynamic reliability model of components and system have been set upaccording the theory of probability fatigue damage cumulative. The change laws withtime of system reliability with the random variation of parameters has been calculated,and the influence of random parameters on dynamic reliability of components havebeen studied and compared with the results of Monte Carlo method.
④Probability optimization design of wind turbine gear transmission system basedon dynamic reliability
A probability optimal mathematic model of wind turbine gear transmission systemis built with goals of the maximum of the mean vibration displacement of systemcomponents and minimum volume, design variables of parameters which have aninfluence on system dynamics and reliability, comstrains of the reliability of geartransmission system, and the influence of random parameters on system reliability andthe normal meshing conditions and strength of gears. A solving algorithm for systemprobability optimal model is presented based on the system dynamic reliability analysisand probability optimal mathematic model. Then, an optimized example of geartransmission system of wind turbine is given. The optimization results is compared todesign results and the Monte Carlo optimization results to verify the feasibility of theoptimization method.
⑤Random vibration test of wind turbine gearbox
The wind turbine gearbox used testing is designed and manufactured based on thesimilitude theory，and the test fig is set up for dynamic characteristics testing of windturbine gearbox. According to the working characteristics of wind turine geartransmission system, the dynamic responses of each point have been measured under avariety of random load conditions, and the statistical characteristics of the randomvibration of wind turine gear transmission system have been obtained through statistical analysis and numerical integration. The comparison analysis between theory calculationand test results shows that the theory model is correct and effective.
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