齿轮系统监控一体参数空间解域界及混沌振动控制方法研究

High-performance gear transmission system is a significant guarantee to contribute to the upgrading of equipment manufacturing industry to our country. The vibration problem is one of the critical factors restricting the dynamic performance and service life of gear system, various incentive elements occurring during driving period are closely related to the dynamic responses of the system, while the solution domain structure in parameter space is a theoretical basis for implementation of vibration control and anti-vibration design. An analytical technique regarding the exploration of solution domain structure in parameter space and global behaviors of basin of attraction inside state space is developed by adopting Cell mapping method, consequently, intrinsic mechanism of chaotic behavior can be further revealed. Correlation dimension (G-P algorithm) along with improved Lyapunov exponent algorithm are jointly employed to precisely depict the numerical characteristics of variety complicated fractal of attractors, the traditional bifurcation evolution route research under single parameter has been extended on the two-dimensional solution domain structure plane, then, comprehensive explorations in terms of dynamic evolution can be realized, and it turns out be efficiently on dynamical parameter configuration. In order to deal with the problem of stable dimension variation of saddle point as well as non-hyperbolic characteristics of high dimensional gear system while controlling the chaotic attractor onto periodic orbit, based on stable manifold theorem and diffeomorphism transformation theory, multi-parameter multi-step chaos control method which can be adopted for solving the complex conjugate eigenvalue problem of Jacobian matrix, is proposed and applied for the high periodic orbits. These work would provide the theoretical and technical support that promoting the designing work of gear transmissions with low vibration, high stability as well as durable service life.

高性能的齿轮传动系统是促进我国装备制造产业升级的重要保障。振动问题是制约齿轮系统动力学性能和服役寿命的关键因素，齿轮传动中的各类激励要素与系统动态响应息息相关，其参数空间解域界是实施振动控制和减振设计的理论基础。基于胞映射建立齿轮系统参数空间解域界结构及状态空间全局吸引域性态解析方法，揭示混沌行为内在机理。联合关联维数（G-P算法）和Lyapunov指数改进算法精确刻画吸引子复杂形变结构数值特征，将传统单参量分岔图路径提升到二维解域界层面实现系统动态演化全面监控，促进动力学参数间优化配置。针对高维齿轮系统混沌吸引子周期轨道控制时普遍具有非双曲性的特点和不动点处稳定维数变异问题，基于稳定流形定理与微分同胚映射理论，提出多参数多步式混沌控制方法，解决Jacobian矩阵产生复共轭特征值时高周期轨道稳定控制的难题。相关成果旨在为推动设计研发具有低振动、高稳定和长寿命的齿轮系统提供理论和技术支持。

随着我国制造产业日益深刻地融入国际分工，特别是工业化进程的推进和装备产业的快速升级，对高稳定性齿轮装置提出了更迫切需求。齿轮装置是较为复杂的动力传动系统，由于各类间隙的存在使轮齿啮合间产生接触、脱离、再接触的反复冲击载荷激励，致使解域内呈现出强非线性特征，尤其非线性混沌的内禀随机性，使混沌振动极难规避，影响设备振动噪声品质。本项目开展齿轮系统振动解域界与混沌控制研究，首先，建立了计入齿侧间隙及时变啮合刚度等非线性激励要素的多自由度齿轮-轴承系统动力学模型，引入量化指标从不同维度精确刻画了形态复杂吸引子结构的数值特征，特别扭曲、缠绕和折叠剧烈的混沌相轨迹，追踪了单参量激励下分岔路径与最大Lyapunov指数演变的同步性。其次，采用区域离散与胞映射等全局技术手段，建立了齿轮系统参数空间解域界与状态空间吸引域解集构造与解析方法，实现了将传统单向分岔图路径提升到更广域的二维解域界层面，研究了混沌行为渐变演化机理，揭示了多吸引子共存及吸引域间的扩张收敛机制。进一步在吸引子骨架上搜寻了稳健的目标不稳定周期轨道不动点，基于稳定流形定理发展了多参数多步式混沌控制策略，解决了鞍点维数变异长周期轨道驱动控制难题，破解了信源单调且尺度有限等配置局限，探索了灵活、持续多阶段的周期跳变控制技巧，建立了摄动轨道偏移微小波动误差衡量的定量评价准则。最后，搭建了分流型齿轮传动系统啮合振动测试实验平台，基于啮合关系设计了沿啮合线方向齿轮副相对振动信号采集方案，验证了所建模型和解域界分析方法的正确性。项目研究成果形成了齿轮系统多源激励监控一体全局性域分析法，丰富了高周期非双曲型鞍点激扰微摄混沌控制理论，促进了研发具有低振动、高稳定和长寿命的高品质齿轮装置理论和技术的形成。

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