风力发电机系统动态特性与参数匹配规律研究

The gear transmission systems in the wind turbine have high failure rate, due to insufficient investigation of wind power equipment dynamics and failure mechanisms. In practice, the inter-related intersections and the combination nonlinear response behaviors of both planetary gear and parallelaxes gear with various non-linear factors, such as friction of tooth surface, gear backlash, meshing error and time-varying stiffness, should be taken into account comprehensively by means of multi-parameter approach. Hence it's essential that we build some multi-parameter, non-smooth multi-body differential inclusions for modeling the gear-rotor-bearing systems. And some qualitative analysis methods of set-valued solutions play a central role in the analysis of this kind of differential inclusions, such as the existence, stability and controllability should be discussed by using theory of set-valued analysis. More specifically, there are some significant topics will be involved, devoting to designing set-valued functions for friction, impact, engaging force and torsion, updating Poincaré-Cell-to-Cell mapping comprehensive algorithm, formatting nonlinear numerical simulation methods for differential inclusions dynamical systems, and developing computational formulas for several characteristic indices such as Lyapunov-exponent spectra and Floquet multiplier. The co-existences and bifurcation types of attractors, the transient process of route to chaos in differential inclusion dynamical system will be studied by means of comprehensive analysis and numerical methods， and the basins of attraction associated with ever-changing parameters also will be demonstrated in the sketch. By depicting global bifurcation curves of two-parameter and dynamic variable, the culminating effect on systems' oscillatory when subjected to friction, gear backlash and damping force will be analyzed, the incidence relationship between dynamical evolutions and system parameters will be discussed, and the optimal matching rules of system parameters will be explored. The ultimate goals of this research are to optimize the wind turbine design and to provide theoretical principles for fault detections.

风力发电机齿轮传动系统故障率高，源于对风电装备动力学和失效机理的研究不足。考虑齿轮传动中齿面摩擦、齿侧间隙、啮合误差、时变刚度等的影响，建立齿轮－转子－轴承高维多参数非光滑多体系统。运用集值分析理论，研讨一类微分包含动力系统集值解的存在、稳定、可控等定性分析方法；针对摩擦、冲击、啮合力、扭矩等设计集值函数、改进Poincaré-胞映射综合算法、构造微分包含动力系统非线性数值仿真方法、修订Lyapunov指数谱、Floquet特征乘子等若干特征指标计算公式。综合运用解析分析与数值模拟研究微分包含动力系统吸引子共存、吸引子分岔等；揭示分岔类型，描绘通向混沌的转迁过程、吸引子的吸引域及随参数变化的规律。描绘二维参数与动态变量的全局分岔图，分析摩擦、齿侧间隙、阻尼力等对系统振动的影响,探讨系统动力学演化与系统参数的关联关系，寻求系统参数的合理匹配规律，为优化风力机设计及故障检测提供理论基础。

在项目执行过程中，项目组主要针对多种复杂非线性动力系统，如齿轮传动系统等高维多参数动力系统，深入研究了整数阶与分数阶奇异微分方程、积分-微分方程理论、以及微分包含理论。针对不同的定解条件，运用理论分析与数值模拟相结合的手段，深入探讨了复杂非线性动力系统解的定性理论分析方法。通过设计Poincaré映射、改进Poincaré-胞映射综合算法、修订Lyapunov 指数谱、Floquet 特征乘子等若干特征指标计算公式，深入分析系统在外部扰动下的周期运动、拟周期运动，运动稳定性、奇异性、各类分岔特性、混沌运动等复杂动力学行为。针对动力系统动力学复杂的演化规律设计非线性动力系统混沌同步与控制方法。借助CUDA并行计算编程及多GPU并行计算技术，我们针对齿轮传动、转子系统以及离心调速器等机械系统，在双参数空间深入探讨了全局振动行为结构特征，绘制了大量高质量相图，展现了系统的全局动态特征。我们发现了一个有趣的现象“混沌之眼”，展现了正向和逆向倍周期分岔序列的极限状况；在一定尺度的参数范围内振动响应呈现出分形的自相似性，周期响应和阵法混沌交替产生组织一种周期数保持不变的齿状分形结构；系统的锁模模式即阿诺德舌则按照等级排列的法里树组织。. 齿轮传动、转子系统以及离心调速器等机械系统均为高维多参数非线性动力系统，其稳定性与参数有密切的关系，探索随参数的变化系统的周期及混沌运动规律仍然是突出的问题。揭示各种振动响应在参数空间中局部与局部、局部与整体之间的本质联系，研究参数的关联关系及匹配规律，这些规律将为高维复杂动力系统参数优化设计，安全运行提供更广泛的动力学参考。.