摘要
本文重点以航空涡轮发动机的轴承-转子系统设计为应用背景,研究滚动轴承-转子系统非线性动力学分析与优化设计问题,这类滚动轴承-转子系统在其他工程领域如电力、机械、运输也有广泛应用。由于该轴承-转子系统分析存在复杂的非线性动力学耦合因素,造成建模和求解困难。目前理论研究与工程实际尚有差距,我国的有关研究与国际先进水平也有差距。研究建立更为接近工程实际的滚动轴承-单(双)转子系统非线性动力学模型,提供更为高效的分析方法,并在此基础上进行该系统动力学优化设计,具有理论意义和工程应用价值。本文重点研究滚动轴承-单转子系统非线性动力学分析方法,滚动轴承-双转子系统的非线性动力学建模,以及考虑滚动轴承非线性动力学的轴承-转子系统优化设计。
论文的主要工作如下：
(1)提出一种滚动轴承-单转子系统动力学分析的改进的打靶法。打靶法是一类滚动轴承-不平衡单转子系统的非线性动力学分析重要方法。针对现有方法求解时存在积分区间较长,积分效率较低的问题。基于Poincare映射理论和问题特点,本文给出一种新的高阶Poincare映射方法,并结合Newton-Raphson迭代构成一种新的求解非线性动力学系统周期解的改进打靶法,结合Floquet理论判断周期解的稳定性和分岔形式。仿真结果表明本文方法与当前的打靶法和平衡点的典型方法相比,在同等精度条件下,积分区间更短,求解效率更高。
(2)提出一种新的滚动轴承-双转子系统5自由度非线性动力学分析模型。与现有的3自由度模型相比,增加引入转子的2个旋转自由度和中介轴承的非线性动力学模型,构成5自由度模型,对各轴承的非线性位移、弹性变形和非线性轴承作用力进行了数学描述。采用Runge-Kutta-Fehlberg算法求解。定量给出了转子5个自由度和轴承非线性动力学模型对该系统仿真结果的影响。与当前典型3自由度模型的仿真结果不同,表明了本文增加考虑上述影响因素的必要性。并将本文5自由度模型数值仿真结果与Gupta(1993年)双转子系统实验结果对比验证,同时也验证了著名学者Gupta(1993年)对5自由度模型双转子相互影响预测的正确性。
(3)给出一种考虑滚动轴承非线性动力学的滚动轴承-转子系统优化模型和求解方法。与现有同类工作相比,在模型上增加引入轴承游隙的非线性动力学影响；在优化方法上针对目前线性优化算法存在的问题,提出一种演化算法／线性搜索混合优化算法。经典型的算例验证结果表明,引入轴承游隙对系统的优化方案有较大影响；克服了单纯采用线性搜索方法难以确定初始解的缺点和演化算法在后期早熟问题。在同等精度和耗时情况下,本文方法的求解成功率更高。最后采用本文优化方法实现某航空燃气涡轮发动机轴承-转子实例的优化设计,达到了优化设计的目的。
期望本文工作有助于一类滚动轴承-单(双)转子系统非线性动力学的建模、求解和优化设计的研究,期望为轴承-转子系统动力学分析与优化设计提供理论和软件工具支持。
On the background of design of aviation turbine engine, nonlinear dynamic analysis and optimization of bearing-rotor system are studied in this dissertation. This system is a very important component in engineering and it is widely used in power, mechanical, and transportation project fields. Due to many complicated nonlinear factors existing in the system and coupling among these factors, there are still quite great gaps between theoretical research on nonlinear dynamics analysis, optimal design and practical engineering. Thus theoretical researches on model, method for nonlinear dynamic analysis and optimal dynamical design have important theoretical signficances and practical engineering value to modern machine production of rotating machinery. Several aspects as nonlinear dynamic analysis method for bearing-single rotor system, nonlinear dynamic model of rolling bearing-dual rotor system and dynamical optimization of bearing-rotor system are focused on in this thesis.
The contents of the dissertation are as follows:
(1) We propose an improved shooting method for nonlinear dyanmic analysis of rolling bearing-unbalanced single rotor system.The unbalanced rotor bearing system is excited by two periodic forces with different periods, eccentric force of the rotor and nonlinear varying bearing force. When the shooting method is used to obtain the periodic solutions of the system, the integral interval is long and the computation efficiency is low because the integral interval should be the least common multiple of the above two exciting periods. Aiming at the above problems, an improved shooting method is proposed based on combination of higher Poincare map and Newton-Raphson iteration. The stability and bifurcation are judged through Floquet theory. Compared with current shooting method and fixed point algorithm, the proposed method has shorter integral interval and higher efficiency under the same solving precision.
(2) We develop a new five-degree-freedom dynamical analysis model of rolling bearing-dual rotor system, which is widely used in aerospace engineering. Compared with current models, rotational freedoms of rotors are introduced. Furthermore, in the proposed model, the nonlinear displacement, deformation and load of bearings are formulated mathematically considering five degrees of freedom and coupling of dual rotors. The nonlinear equations of motions of dual rotors with five degrees of freedom are solved using Runge-Kutta-Fehlberg algorithm. In order to investigate the effect of introduced five degrees of freedom and nonlinear dynamic bearing model, we compare the simulation results of proposed model with two present models. The quantitative results are given. The simulation results show the rotational freedom of rotors and nonlinear dynamic model of deep groove ball bearings have great effects on the system dynamic simulation and verify Gupta's prediction (1993).
(3) We propose an optimization model of rotor-bearing system with bearing nonlinear dynamics constraints and an optimization method. Comparing with present similar works, we make following improving works. Firstly, influence of clearance is involved in the optimization model. Secondly, a hybrid algorithm based on evolutionary algorithm/line search method is proposed. Numerical results of classic example show: the clearance has great influence on optimization results. The proposed algorithm overcomes the difficulty in choosing initial value of line search method and the premature of evolutionary algorithm. The proposed method has higher success rate under the same calculation accuracy. At the end of the dissertation, we adopt the proposed optimization method to optimize an aero-gas-turbine-engine bearing-rotor system in engineering and the optimal results are obtained.
This study is helpful to the model, solution and optimization of the rolling bearing-rotor system. And also this work can provide theoretical and software support for dynamic analysis and optimal design of bearing-rotor system.
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