【作者】 闫志勇；

【导师】 郑铁生；

【作者基本信息】 复旦大学 ， 流体力学， 2011， 博士

【摘要】 大型组装式离心压缩机组包含多根平行转子-轴承系统,通过齿轮箱和联轴器实现动力耦合。随着机组向高速化、轻型化、复杂化方向发展,迫切需要完善系统动力学模型及进行动力学行为研究,为提高机组的稳定性、安全性和可靠性提供理论和工程指导。本文以大型组装式离心压缩机组转子动力学建模与求解为工程背景,主要围绕紊流工况非线性油膜力及其Jacobi矩阵求解、可倾瓦轴承动力学模型、多平行转子-轴承系统建模及非线性动力求解几个方面,进行动力学建模及相应高效求解算法研究。本文研究工作在理论和应用上取得了一些创新成果,对复杂转子-轴承系统动力特性研究及其工程应用具有积极的意义。具体地,本文主要研究内容和研究成果可以分为以下几方面：(1)利用二阶线性椭圆型偏微分方程等价变分不等方程理论,针对紊流工况Reynolds方程,提出了一种联合求解紊流非线性油膜力及其Jacobi矩阵快速算法。考虑到轴承侧端压力不等于零工况,选取权函数和线性插值函数乘积形式作为油膜压力函数,建立有限元离散化的一维变分不等方程。利用修正的追赶法求解油膜压力及其导数,无需迭代自动满足油膜自由边界条件。(2)考虑到瓦块绕支点摆动和沿几何预载荷方向微幅振动,对于n瓦可倾瓦轴承首次建立了包含2n+2个自由度的可倾瓦轴承完整动力学解析模型。通过建立固结与瓦块的随动坐标系和可倾瓦轴承总体坐标系,全局广义位移向量和力向量可以简练地转换到局部随动坐标系下位移向量和力向量,进而通过求解局部坐标系下的油膜力及其Jacobi矩阵扩充、叠加得到系统的广义油膜力向量及其Jacobi矩阵。对于可倾瓦轴承承受静载荷工况,给出了一种求解静平衡方程的快速算法,可以快速计算得到轴颈和瓦块的静平衡位置同时得到系统的刚度和阻尼系数矩阵。当设定轴颈和瓦块扰动频率,给出了缩聚可倾瓦轴承完整动力特性系数得到八个简化当量刚度系数和阻尼系数的计算方法。(3)利用有限元方法,建立了比较完善的齿轮啮合多平行转子轴承系统动力学模型。针对转子-轴承系统为局部高维非线性动力系统特点,考虑了广义非线性力影响,提出了一种二次规范降阶方法,通过两次规范降阶把原高维系统转化为与之等价的低维系统,采用配套的打靶法求解低维系统的周期解并通过Floquet定理来判断周期解的稳定性,周期解失稳后采用直接数值积分方法求解系统的长期动力响应。(4)针对复杂转子系统动力特性的研究,根据本文对轴承—转子系统的求解算法分析,编写了相关的计算程序,对可倾瓦轴承-转子系统和某工程组装式PTA离心压缩机组,进行了线性动力特性分析和非线性动力特性分析,验证了本文模型及算法的有效性及实用性。更多还原

【Abstract】 Study on Dynamic Behaviour of Complex Rotor SystemsLarge assembled centrifugal compressor units are comprised of multi-parallel rotor bearing system, which are dynamic coupled by gear box and coupling. With the development of compressor units towards to high speed, maximization and complication, it’s necessary to research the rotor-bearing system dynamic behavior for improving the system stability, security and reliability.On the background of rotor dynamic modeling and solution of large assembled centrifugal compressor units, this thesis studies on several aspects, such as, the model and algorithm of turbulent nonlinear oil-film forces and their Jacobian matrices, the model of tilting pad journal bearing, the model and nonlinear solution of complicated rotor bearing systems. Some achievements are acquired by current research from theory and practice, and conclusions that are reached are beneficial to study on the behavior of rotor-bearing system and engineering applications.In detail, there are the following achievements and contents in current research.(1) Based on the variational inequality of general quasilinear elliptic partial differential equation in free boundary condition, a kind of model with an efficient algorithm is presented to get the nonlinear oil-film force and its Jacobian matrices by solving turbulent Reynolds equation. Considering the condition of bearing side-pressure not equal to zero, the proper oil-film pressure function is chosen in the form of multiplier of weight function and linear interpolation function, and one-dimensional discrete variational inequality of turbulent Reynolds equation is built up. An amendatory direct-method is proposed to solve the oil-film force and its Jacobian matrices. During the process, the operations are restricted within the positive pressure region, and no iteration is involved.(2) Considering the freedom of pad tilting and pad translation along preload orientation, an analytical complete model as well as mathematical method which contains 2n+2 degrees of freedom is presented for calculating the dynamical characteristics of tilting pad journal bearing. Based on the motion relationship of shaft and pad, the local coordinate system, the generalized displacement and generalized force vector are chosen. The concise transformation of generalized displacement, generalized force and its Jacobian matrix between the local and global coordinate systems are built up in matrix form. A fast algorithm using Newton-Raphson method for calculating the equilibrium position of journal and pads is proposed. The eight reduced stiffness and damping coefficients can be obtained assuming that the journal and all pads are subject to harmonic vibration.(3) The dynamic model of gear-coupled multi parallel rotor is presented using the finite element method. A method of quadratic normal reduction is presented for complex dynamic system with local nonlinearities. The degrees of freedom are reduced and the equivalent system is obtained by quadratic normal reduction and the effects of local nonlinear forces in the modal transformation are considered. Meanwhile the supporting shooting method is proposed to solve the periodic responses and the stability is determined by the Floquet theory. When the response is unstable, the long-term response is obtained by direct numerical integration method.(4) The relevant program of current algorithm is developed. The linear and nonlinear dynamic behaviors are calculated for the industrial rotor system supported by tilting-pad journal bearing and one industrial assembled PTA centrifugal compressor train. The efficiency and reliability of the model and algorithm in this thesis is proven.更多还原