三自由度齿轮传动系统混沌振动及其智能控制

【作者】 高阳；

【导师】 王三民；

【作者基本信息】 西北工业大学 ， 机械电子工程， 2004， 硕士

【摘要】 齿轮传动是机械系统中应用最为广泛的传动形式，其动力学分析和振动控制一直受到人们的重视。特别是近几年来为满足航空、航天、机器人等工业技术发展的需要，对齿轮传动的精度、振动、噪声和可靠性等提出了更为苛刻的要求。齿轮传动系统实质是一个非线性系统，因此只有对它进行非线性的动力学分析和非线性振动控制研究，才能满足对齿轮传动系统提出的高精度、小振动和低噪音的要求。 本文针对三自由度齿轮传动系统，利用集中质量法建立了齿轮传动系统的非线性动力学模型。并针对现有的增量谐波平衡法在求解周期解时存在收敛速度慢的缺点，将最小二乘法原理与增量过程组合，提出了一种改进的增量谐波平衡算法，并推导了这种算法的计算公式，进行了程序实现。将此方法应用于三自由度齿轮非线性系统中，求出了位于混沌吸引子内部的不稳定周期轨道。通过数值分析，证实了这种改进的增量谐波平衡法的有效性和可靠性。 针对BP神经网络在进行非线性系统控制时存在着跟踪误差较大、收敛速度较慢和需要大量系统先验数据的缺点，本文基于傅里叶级数理论和齿轮非线性振动的特点，提出了一种简化的RBF网络；并以这种简化的RBF网络为基础，建立了三自由度齿轮传动系统的智能控制模型；分别以单周期轨道和多周期轨道为控制目标，对系统的混沌振动控制进行了数字模拟，取得了满意的控制效果。 通过对齿轮传动系统的非线性动力学的分析和混沌振动控制的研究，发现齿轮传动系统随系统参数改变会产生复杂的动力学行为，而且借助力矩加载控制器可以达到抑制齿轮传动系统的混沌振动的目的。更多还原

【Abstract】 In the mechanical systems, gear driving is one of the most widely used driving ways, so the analysis and control of its dynamics is the focus of the current research. In recent years, the requirement of these fields, such as aeronautic, aerospace and robot, demands more on the accuracy, vibration, noise and reliability in the gear driving system. In essence, the gear driving system is a non-linear system. Then to meet the requirement of high precision, small vibration and low noise in the system, the nonlinear analysis and control should be adopted.Given the 3-degree gear driving system, the non-linear system model is built in this thesis by using mass centralized method. Because the general incremental harmonic balance method deals with periodic solutions at slower convergence rate, an improved incremental harmonic balance method has been put forwarded. This improved method is based on least-square method and incremental disposal. A computing formulas and program of the improved incremental harmonic balance are performed. When this method is used to deal with the non-linear system, we obtain periodic solutions in chaos attractor. The numerical solution proves that this method is valid and credible.We find slow convergence rate, a great number of data needed to train BP neural network when the network deals with the nonlinear system identification. To avoid these disadvantages, this thesis has put forward a simplified RBF neural network based on Fourier- progression. Based on this simplified RBF neural network, the intellectualized control model of 3-degree gear driving system is set up. When the single-periodic solution and multi-periodic solution is regarded as control target, the digital simulation of chaotic vibration control has been done and the control-results can satisfy with our requirement.Through the analysis of non-linear dynamics and studies of controlling chaos vibration for the gear driving system, we find that complex actions will be get following with the changing of parameters in this system. Furthermore, we also find that the chaotic vibration can be controlled by using the torques loaded controller.更多还原