【作者】 宋清华；

【导师】 唐委校；

【作者基本信息】 山东大学 ， 化工过程机械， 2006， 硕士

【摘要】 随着工业的发展和社会的进步，旋转机械转速不断增加，性能不断提高。特别是像燃汽轮机、航空发动机、工业压缩机及各种电动机等过程装备及机械装置，由于其转速加大，推重比提高，带来了零部件重量的减轻和负荷的增加，从而导致了振动的加剧。旋转机械的振动历来是人们极为关注的问题，高速旋转机械的振动则尤其复杂，其研究工作更显得重要。因此，高速旋转系统动态特性分析及优化方法研究是促进高速旋转机械发展和推广应用的重要应用基础课题，对充分发挥高速旋转机械的技术优势、经济优势和社会优势具有重要的理论意义和现实意义。 探讨适合高转速特点的高速旋转系统动力学建模及其建模方法，基于Timoshenko连续梁理论，运用有限单元法和第二类Lagrange方程，建立高速旋转系统(轴承-转子系统)多自由度动力学模型。此模型考虑转动惯量、陀螺力矩、剪切变形、不平衡和材料阻尼等因素的影响。 针对所建立的动力学模型，分别讨论系统的固有频率、临界转速、频响函数和动力响应等动态特性。重点探讨反对称特征值的求解方法—由广义Arnoldi法推导的本质缩减算法。其中，在应用广义Arnoldi法推导陀螺特征值时，引入针对对称特征值问题提出的重起动概念，使此减缩方法成为完善的大型特征值问题的求解方法。另外，运用上述动特性分析方法对一实际转子系统的动态特性进行数值计算。 基于所建立的动力学模型和对模型的动态特性分析，运用Lyapunov稳定性定理和稳定性判据，研究陀螺力(陀螺力矩)与高速旋转系统稳定性的关系，分析陀螺力对高速旋转系统动态稳定性的影响。探讨基于频响函数的高速旋转系统稳定性评价方法和理论体系，给出基于频响函数的高速旋转系统稳定性预测分析方法。 将结构动力修改技术引入高速旋转系统动态优化的“逆问题”求解并给予延伸和发展，探讨并研究了基于结构动力修改的高速旋转系统动态优化方法，把在保证系统稳定性基础上寻求高转速、高生产率、低成本为优化目标的动态优化“逆问题”，通过采用结构动力修改方法转换为分步修改和重分析的“正问题”。提出重点针对能够综合反映系统动态特性的频响函数进行优化的结构动力修改更多还原

【Abstract】 With the development of industries and the society, the rotating machines are speeding up and their performances are enhanced greatly, such as the steamers, aeroengines, compressors and other kinds of machines. As the speed up of rotating and the better performaces, the weight of components is lightened and load increased. The vibrations of rotating machines became the key issues to pay people’s attentions. Vibrations of high-speed rotating machines are so complex that the researchs of them become more important. Therefore, it is an important application foundation subject for promoting the developments and applications of high-speed rotating machines and has a very important theorial and realistic meaning to bring high-speed rotating machines into technological advantage, economic advantage and society advantage further.Studying the dynamics model and modeling method suit to the characteristics of high-speed rotating, based on Timoshenko theory, and using finite element method (FEM) and Lagrange’s equation, the dynamics model of high-speed rotating system with muti-degrees of freedom is set up, with respect to the influence of rotating inertia, gyroscopic moment, cutting deformation, unbalance and damping of materials.Based on the model proposed previously, the natural frequencies, frequency response function (FRF), critical speed and impetus responses are studied which prepares for the researchs of system stabilities and optimization. Thereinto, the resoluting method of the unsymmetric eigenvalues of undamped and damped linear systems—essential reducing method (ERM) educing from the generalized Arnoldi method (GAM), is discussed emphasizedly. In addition, the conception of restart-up is proposed, and the reducing arithmetic turns into the perfect method for determining the unsymmetric eigenvalues. The dynamics characteristics of an example are analysed with ANSYS software by the method proposed previously.Be based upon the dynamics model established and dynamics characteristics analysis of the model, handling Lyapunov stability theorem and stability criterion, the connections between gyroscopic moment and the stability of high-speed system are更多还原