风力发电机行星齿轮传动系统变载荷激励动力学特性研究
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摘要
齿轮增速箱是风力发电机组的关键部件，由于其在随机自然风场和高空架设等使用环境下运行，要求比一般机械系统具有更高的可靠性和使用寿命。兆瓦级风力发电机组多采用行星齿轮传动系统，具有低速重载变载荷变转速运行的特点，在随机风的作用下受到频繁的扰动和激励，动力学特性十分复杂，对系统可靠性及机组运行稳定性有较大影响。针对风力发电传动系统的实际工况特点，研究行星齿轮传动系统动态性能，有利于突破大型风电能源装备传动装置的核心技术，推动大型风电传动装备设计制造的国产化进程。
本课题是国家自然科学基金项目（50975294）研究内容的组成部分，在引入以随机风载为主要外部激励，并考虑主要内部激励的条件下，研究风力发电机行星齿轮传动系统的动力学特性，主要研究内容包括：
①风力发电机传动系统外部载荷特性研究
根据自然风的谱特性，基于随机信号谱估计方法建立了用于随机风速模拟的AR（AutoRegressive，AR）模型；运用风力机气动理论建立了风力机气动载荷计算模型；根据电机理论，基于旋转电机矩阵分析方法推导了变速恒频发电机的能量转换关系和电磁转矩表达式，建立了双馈感应发电机（Doubly Fed InductionGenerator，DFIG）矢量控制模型；根据机械系统动力学，建立了风力发电传动系统的等效动力学模型。在此基础上，综合上述各数学模型，同时考虑DFIG及风力机叶片桨距角的控制方法，建立了反映风力发电机组运行过程的风-机-电联合仿真模型，利用该模型进行仿真计算，得到风电传动系统的外部动载荷，并分析了该动载荷的作用规律和性质。
②行星齿轮传动系统动力学模型及动态激励
根据机械振动理论，将齿轮副处理为啮合线上的阻尼弹簧，并考虑支承轴承的弹性，采用集中参数法建立行星齿轮系统的扭振-平移动力学模型，并导出其振动微分方程，并对行星齿轮系统的轮齿啮合刚度、轴承支承刚度、行星轮啮合相位和外部变载荷等主要激励因素进行了分析。
③行星齿轮系统齿轮轴承刚度变化下的固有振动特性研究
在计算系统固有频率及振型的基础上，分析了轮齿啮合刚度和各支承轴承刚度对系统固有频率的影响，以及系统刚度影响下的模态跃迁现象。采用Fourier级数表示轮齿啮合时变刚度，基于Hertzian接触理论建立轴承刚度表达式，并考虑行星轮啮合相位关系，分析了行星齿轮系统刚度的时变规律，研究了系统在刚度时变条件下的频率特征及自由振动特性。
④风电行星齿轮系统变载荷激励机理及动态响应特性研究
对于变载荷作用导致转速变化和弹性变形的行星齿轮系统，利用能量法分析了变载荷作用下系统动能和势能及转换关系，结合内容②的理论推导结果，以Lagrange函数为基础，导出了变载荷作用下考虑转速波动的行星齿轮系统振动微分方程，探讨了变载荷对系统振动的激励机理，分析了载荷激励对系统振动频率的影响。在同时考虑系统刚度时变性和变载荷激励的条件下，采用Newmark方法求解了系统的动态响应，通过对求解结果进行分析，得到系统在内外部激励下的动态响应特性。
⑤风电行星齿轮系统振动响应特性试验研究
构建了背靠背台架试验系统，制定了风力发电齿轮系统动力学性能测试方案。分别在稳定和非稳定驱动/负载载荷工况条件下测量了传动系统的振动信号，通过对比分析稳定和非稳定载荷工况下的响应结果，获得变载荷对系统振动响应的影响规律，从而验证了理论模型和研究方法的正确性。
The speed increasing gearbox is the key component of the wind turbine, whichmust has higher reliability and service life than the general mechanicalsystem because of working in the circumstances of random wind field and high altitudesetting up. The planetary gear transmission system is commonly used in the MW-levelwind turbines, and has the obvious characteristics of low speed, heavy load, varyingspeed and varying load, the dynamic characteristics are very complex due to thefrequent disturbance under the random wind and have a greater impact on reliability andstability of wind turbines. Researching the dynamic properties of planetary geartransmission of wind turbine can be advantageous to break through the key technologyof wind power energy equipment and promote the localization of manufacturing anddesign of wind turbine transmission equipment.
This topic is the important component of the National Natural Science Funds(50975294). The dynamics characteristics of the planetary gear transmission system ofwind turbine are studied in the paper, and the main research contents as follows.
①Study on external load characteristics of wind turbine transmission
The AR wind speed model is build on the basis of random signal spectrumestimation method and the spectrum characteristics, and the pneumatic load calculationmodel is build using the wind turbine pneumatic theory. According to the active powerbalance, the Doubly Fed Induction Generator vector control model is build，the electromagnetism torque expression and the Energy conversion relationship ofconstant frequency variable speed motor are deduced based on the matrix analysismethod of rotating electrical machines. The equivalent dynamics model is set upaccording to the mechanical system dynamics. Based on the above, considering thepitch angle control method of wind turbine blade, the wind-mechanical-electrical unitedsimulation model is build and the calculation for the simulation model is carried out, theexternal dynamic load of is obtained and its rule and properties are analyzed.
②Dynamics model and dynamic excitation of planetary gear transmission
Considering the bearing’s flexibility and making the gear pair as spring in meshingline, the torsion-translation dynamics model of planetary gear transmission system isbuild using the lumped parameter method and the differential equations of system arederived based on the mechanical vibration theory and many factors are analyzed such as mesh stiffness, bearing stiffness, planetary gear mesh phase, internal and externalincentive.
③Research on the natural vibration characteristics of the planetary gear systemwith time-varying stiffness of gear and bearing
The influences of gear mesh stiffness and bearing supporting stiffness on systemnatural frequency and the modal transition phenomenon are analyzed based oncalculating the natural frequency and vibration modes. The gear mesh stiffness isexpressed by Fourier series, the bearing stiffness expression is build by Hertz contacttheory, and the mesh phasing is considered, the tine-varying rules are analyzed ofsystem stiffness of planetary gear system，the frequency features and the vibrationcharacteristics are researched in the condition of time-varying.
④Research on the varying load excitation mechanism and the dynamic responsecharacteristic of wind turbine planetary gear system.
Aiming at the speed variation and elastic deformation caused by varying load forplanetary gear system, the transformational relation between the kinetic energy and thepotential energy in varying load conditions are analyzed by energy method, thevibration differential equations of planetary gear system are derived based on theLagrange function and the results part②, the varying load excitation mechanism arediscussed and the influence of load excitation on vibration frequency of system isanalyzed. Taking into account the time-varying characteristicsthe of system stiffness andthe varying load excitation, the dynamic responses are solved by the Newmark methodand the dynamic responses characteristics are obtained.
⑤Experimental study of the vibration response characteristics of wind turbineplanetary gear system.
The test rig of back-to-back energy feedback was setup and the dynamics propertytesting program of wind turbine was established. The vibration signal of transmissionsystem was measured under the working conditions of steady and unsteady drive/loadtorque. The influence regulations of varying load on the system vibration response wereobtained, the theory model and the research methods were validated by comparing tworesults of steady and unsteady working conditions.
本课题是国家自然科学基金项目（50975294）研究内容的组成部分，在引入以随机风载为主要外部激励，并考虑主要内部激励的条件下，研究风力发电机行星齿轮传动系统的动力学特性，主要研究内容包括：
①风力发电机传动系统外部载荷特性研究
根据自然风的谱特性，基于随机信号谱估计方法建立了用于随机风速模拟的AR（AutoRegressive，AR）模型；运用风力机气动理论建立了风力机气动载荷计算模型；根据电机理论，基于旋转电机矩阵分析方法推导了变速恒频发电机的能量转换关系和电磁转矩表达式，建立了双馈感应发电机（Doubly Fed InductionGenerator，DFIG）矢量控制模型；根据机械系统动力学，建立了风力发电传动系统的等效动力学模型。在此基础上，综合上述各数学模型，同时考虑DFIG及风力机叶片桨距角的控制方法，建立了反映风力发电机组运行过程的风-机-电联合仿真模型，利用该模型进行仿真计算，得到风电传动系统的外部动载荷，并分析了该动载荷的作用规律和性质。
②行星齿轮传动系统动力学模型及动态激励
根据机械振动理论，将齿轮副处理为啮合线上的阻尼弹簧，并考虑支承轴承的弹性，采用集中参数法建立行星齿轮系统的扭振-平移动力学模型，并导出其振动微分方程，并对行星齿轮系统的轮齿啮合刚度、轴承支承刚度、行星轮啮合相位和外部变载荷等主要激励因素进行了分析。
③行星齿轮系统齿轮轴承刚度变化下的固有振动特性研究
在计算系统固有频率及振型的基础上，分析了轮齿啮合刚度和各支承轴承刚度对系统固有频率的影响，以及系统刚度影响下的模态跃迁现象。采用Fourier级数表示轮齿啮合时变刚度，基于Hertzian接触理论建立轴承刚度表达式，并考虑行星轮啮合相位关系，分析了行星齿轮系统刚度的时变规律，研究了系统在刚度时变条件下的频率特征及自由振动特性。
④风电行星齿轮系统变载荷激励机理及动态响应特性研究
对于变载荷作用导致转速变化和弹性变形的行星齿轮系统，利用能量法分析了变载荷作用下系统动能和势能及转换关系，结合内容②的理论推导结果，以Lagrange函数为基础，导出了变载荷作用下考虑转速波动的行星齿轮系统振动微分方程，探讨了变载荷对系统振动的激励机理，分析了载荷激励对系统振动频率的影响。在同时考虑系统刚度时变性和变载荷激励的条件下，采用Newmark方法求解了系统的动态响应，通过对求解结果进行分析，得到系统在内外部激励下的动态响应特性。
⑤风电行星齿轮系统振动响应特性试验研究
构建了背靠背台架试验系统，制定了风力发电齿轮系统动力学性能测试方案。分别在稳定和非稳定驱动/负载载荷工况条件下测量了传动系统的振动信号，通过对比分析稳定和非稳定载荷工况下的响应结果，获得变载荷对系统振动响应的影响规律，从而验证了理论模型和研究方法的正确性。
The speed increasing gearbox is the key component of the wind turbine, whichmust has higher reliability and service life than the general mechanicalsystem because of working in the circumstances of random wind field and high altitudesetting up. The planetary gear transmission system is commonly used in the MW-levelwind turbines, and has the obvious characteristics of low speed, heavy load, varyingspeed and varying load, the dynamic characteristics are very complex due to thefrequent disturbance under the random wind and have a greater impact on reliability andstability of wind turbines. Researching the dynamic properties of planetary geartransmission of wind turbine can be advantageous to break through the key technologyof wind power energy equipment and promote the localization of manufacturing anddesign of wind turbine transmission equipment.
This topic is the important component of the National Natural Science Funds(50975294). The dynamics characteristics of the planetary gear transmission system ofwind turbine are studied in the paper, and the main research contents as follows.
①Study on external load characteristics of wind turbine transmission
The AR wind speed model is build on the basis of random signal spectrumestimation method and the spectrum characteristics, and the pneumatic load calculationmodel is build using the wind turbine pneumatic theory. According to the active powerbalance, the Doubly Fed Induction Generator vector control model is build，the electromagnetism torque expression and the Energy conversion relationship ofconstant frequency variable speed motor are deduced based on the matrix analysismethod of rotating electrical machines. The equivalent dynamics model is set upaccording to the mechanical system dynamics. Based on the above, considering thepitch angle control method of wind turbine blade, the wind-mechanical-electrical unitedsimulation model is build and the calculation for the simulation model is carried out, theexternal dynamic load of is obtained and its rule and properties are analyzed.
②Dynamics model and dynamic excitation of planetary gear transmission
Considering the bearing’s flexibility and making the gear pair as spring in meshingline, the torsion-translation dynamics model of planetary gear transmission system isbuild using the lumped parameter method and the differential equations of system arederived based on the mechanical vibration theory and many factors are analyzed such as mesh stiffness, bearing stiffness, planetary gear mesh phase, internal and externalincentive.
③Research on the natural vibration characteristics of the planetary gear systemwith time-varying stiffness of gear and bearing
The influences of gear mesh stiffness and bearing supporting stiffness on systemnatural frequency and the modal transition phenomenon are analyzed based oncalculating the natural frequency and vibration modes. The gear mesh stiffness isexpressed by Fourier series, the bearing stiffness expression is build by Hertz contacttheory, and the mesh phasing is considered, the tine-varying rules are analyzed ofsystem stiffness of planetary gear system，the frequency features and the vibrationcharacteristics are researched in the condition of time-varying.
④Research on the varying load excitation mechanism and the dynamic responsecharacteristic of wind turbine planetary gear system.
Aiming at the speed variation and elastic deformation caused by varying load forplanetary gear system, the transformational relation between the kinetic energy and thepotential energy in varying load conditions are analyzed by energy method, thevibration differential equations of planetary gear system are derived based on theLagrange function and the results part②, the varying load excitation mechanism arediscussed and the influence of load excitation on vibration frequency of system isanalyzed. Taking into account the time-varying characteristicsthe of system stiffness andthe varying load excitation, the dynamic responses are solved by the Newmark methodand the dynamic responses characteristics are obtained.
⑤Experimental study of the vibration response characteristics of wind turbineplanetary gear system.
The test rig of back-to-back energy feedback was setup and the dynamics propertytesting program of wind turbine was established. The vibration signal of transmissionsystem was measured under the working conditions of steady and unsteady drive/loadtorque. The influence regulations of varying load on the system vibration response wereobtained, the theory model and the research methods were validated by comparing tworesults of steady and unsteady working conditions.
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