【作者】 王睿；

【导师】 郭杏林； 王跃方；

【作者基本信息】 大连理工大学 ， 工程力学， 2016， 博士

【摘要】 泵是一种把机械能转换成势能和动能的设备。泵类设备应用广泛,是能源,电力,石化,航空航天等领域的重要设备。大部分泵都属于旋转机械。旋转机械的核心是转子系统。转子系统的组成部分一般包括转子,轴承,密封和基础。随着人们对转子动力学研究的深入,转子系统的设计不仅要满足对高效率运行的追求,还要考虑转子系统的性质。只有充分了解转子系统的非线性性质,才能准确的设计转子安全运行的工作转速区间,才能更好的识别转子的运行状态。区别于传统的线性研究，转子系统的非线性研究不再将轴承力和密封力分解成八个线性化系数,而是在非线性模型内综合考虑小间隙内流体惯性力效应和外阻尼引起的循环力效应等。此外,旋转机械运行时转子与流体相互作用,具有明显的流固耦合特征。粘性流体以压力的形式作用于固体表面,固体的运动又时刻改变着流场的边界。考虑到转子系统受非线性力作用后响应的复杂性,尽管人们对转子动力学研究已有数十年,但是仍有许多非线性问题值得深入研究。研究的成果不仅能对解释转子动力学现象提供理论依据,还可以更好的为转子系统的设计提供参考基础。本文以泵转子系统作为研究对象,并使用Lagrange法建立了多自由度转子系统运动方程。应用能自适应时间步长的Runge-Kutta-Fehlberg法求解微分运动方程组。考察转子系统的一阶临界转速,计算转子系统的可运行区间,研究在基础振动情况下系统的响应,基于计算流体动力学法(Computational Fluid Dynamics-CFD)和径向基函数法(Radial Basic Function-RBF)得到与流场相关的密封动力学系数的响应曲面并进行转子动力学分析,还完成了带有叶片的叶轮在流体中转动的流固耦合分析。本文的主要工作有如下几个方面：1.建立带有非线性油膜力轴承模型的泵转子-轴承系统运动微分方程。使用Matlab编程求解微分运动方程组。采用诸如分岔图,庞加莱图和相图等非线性方法,分别研究了水平放置转子和竖直放置转子的动力学性质。通过考察系统随转速变化的振幅,找到系统的一阶临界转速。综合幅频曲线图,轴心轨迹图和瀑布图结果考察轴承处的油膜失稳,分别识别出“油膜涡动”和“油膜振荡”现象,给出油膜涡动的失稳角速度。计算结果证明了建模方法的适用性,该方法既可以应用于对称转子,也适用于质量偏置的情况。计算得到的一阶临界转速,分岔点和失稳转速,为泵转子运行区间和隔离裕度设计提供了理论依据。2.建立了考虑基础运动的泵转子-轴承系统的运动微分方程。采用时程分析法,将地震波和正弦型激励作为基础振动加载,分别研究了水平放置转子和竖直放置转子在基础振动作用时的非线性响应。选用的水平放置转子一阶临界转速较低,在地震波作用时，在频域内得到一阶临界转速。而竖直放置转子因为一阶临界转速相对较高,在地震波作用时,在频域内没有得到一阶临界转速。但是竖直放置转子出现转速半频成分的最低转速降低了。当非线性系统受到离心力和正弦型基础振动共同作用时,得到了多自由度系统的组合共振现象,即系统的频率响应包含多个有内在联系的成份。这些成分中不仅包含转速的频率和基础振动频率,还包含转速的频率和基础振动的频率的整数倍数的代数和。计算结果不仅证明了在一定条件下,多自由度的非线性系统存在组合共振的现象；还可以为转子系统在基础运动作用时的运行状态识别提供理论依据：3.基于CFD和RBF法得到泵密封内与流场相关系数的近似函数曲面,研究了变系数的转子-轴承-密封系统的非线性性质。Muszynska(?)线性密封力模型因为其形式简洁,物理意义明确等特点,得到了广泛的应用。求解该模型中所用的系数,例如进口损失系数、轴向流速和流体周向平均流速比都与流场状态密切相关。但之前在该密封力模型的使用中,这些系数通常采用常数或者经验公式代替。在进、出口边界条件一定的情况下,密封内的流场由转子转速和相对偏心率决定。本文中使用CFD方法得到了不同转速、不同偏心率时的系数：再使用RBF方法拟合出这些系数的近似函数曲面。这些曲面作为系数,在求解运动方程的过程中每一步都根据对应的转速和对应的偏心率调用近似函数曲面上的数值,实现了比传统方法更为精确的瞬态分析。该方法为分析转子-轴承-密封系统的非线性性质提供了新的思路。4.使用有限元软件ADINA完成了流固耦合模拟计算,研究了轴流式泵转子的动力学响应。在流固耦合面使用非滑移条件,采用迭代方法计算固体域的变形和流体域的流动。与传统的流固耦合研究不同的是,本文基于运动网格技术,实现了转子结构网格和周围流体网格的真实转动。在不同轴向流速条件下,得到了转子中心轨迹,位移和加速度信号的频率响应和瞬态流动,识别出转子“湿态”临界频率。通过对比转子是否绕转轴涡动的结果可以看出流固耦合界面的变化对流场压力的影响。通过与传统计算方法的对比,还证明了本文采用方法的有效性。本文提供了同时考虑转子真实转动和流固耦合条件下,研究复杂的旋转机械转子动力学问题的新思路。更多还原

【Abstract】 Pump is a device that converts mechanical energy into potential energy and kinetic energy. Pump is widely used. It is the important equipment in energy, electric power, petrochemical, aerospace and other fields. Most pumps are rotating machinery. Rotor system, which consists of rotor, bearing, seal and base, is the core of the rotating machinery. With further research of the rotor dynamics, design of the rotor system has not only pursue efficiency of the whole system, but also considers the nonlinear characteristics of the rotor system. Only by fully understanding of the nonlinear characteristics of the rotor system, safe operation speed range of the rotor can be designed more accurately, as well as running state of the rotor can be identified better. Different from the traditional linear research, the bearing force and the sealing force no longer be simplify into eight linear coefficients during investigation of nonlinear rotor system. The effect of inertia force of fluid in small gap and the effect of cyclic force caused by external damping are taken into account in the nonlinear model. Moreover, rotor interacts with fluid as rotating machinery running which has distinct characteristics of fluid-structure interaction. Viscous fluid act on the solid surface in the form of pressure, and movement of the solid changes boundary of the flow field during the running of machinery. In consideration of complexity of response of the rotor system subjected to nonlinear force action, although people have been studied for several decades, there are still many nonlinear problems worthy of further research. The results of the research can not only provide theoretical basis for interpretation of the rotor dynamics, but also provide reference for design of the rotor system.Rotor system of pump is investigated in this paper. The motion equations are proposed for rotor system with multi-degree of freedom. The Runge-Kutta-Fehlberg, which is adaptive time step method, is applied to solve the differential equations of motion. The first critical frequency of the rotor system is investigated; the running speed range of the rotor system is calculated; the respondes when the rotor system subjected to base movements are studied. Furthermore, based on the Computational Fluid Dynamics (CFD) and Radial Basis Function (RBF) method, the respond surfaces of dynamics parameters of the seal which are closely relevant to fluid field are obtained and the rotordynamic analysis is completed. The analysis of the Fluid Solid Interaction (FSI) as a rotor which has blades rotated in fluid is accomplished. The major contents are as follows:1. The differential motion equations of rotor-bearing system of pump with nonlinear oil film force are proposed. The software of Matlab is used to program and solve the equations. The nonlinear methods, such as bifurcation maps, Poincare maps, phase diagrams, etc, are employed to investigate dynamics behaviors of horizontal and vertical rotor. The first critical frequency of the system is found by observing the amplitude of the system vs. variation of rotation speed. Based on the results of amplitude frequency curves, axis trajectories and cascade diagrams, oil film instability of the bearing is gained. The phenomena of "oil whirl" and "oil whip"’are identified and the speed of oil film instability is achieved. The results proved the modeling approach is "robust". The proposed method can be applied to the case of a symmetric rotor, and also to the case of mass bias. The results of critical speed, bifurcation point and speed of instability provide a theoretical basis to designs of both operation speed range and separation margin of pump.2. The differential equations of motion of rotor-bearing system of pump which subjected to base movements are build. The seismic wave and sinusoidal wave are used as base movements by time history analysis method. The nonlinear responses of horizontal rotor and vertical rotor are investigated, separately. Due to the critical frequency of the horizontal rotor is lower, the first critical frequency in the frequency domain is observed when the seismic wave happened. While the first critical frequency of the vertical rotor is higher, there is not exist the critical frequency in the frequency domain. Nevertheless, the lowest speed when the peak of half frequency of rotational speed emerged for the vertical rotor becomes lower. The phenomena of combination resonance of multi-degree of freedom system are obtained when the nonlinear system subjected to both centrifugal force and sinusoidal base movements. There are several peaks which have relevances in the results of the FFT. These peaks include not only the two peaks of the rotational speed and the frequency of base movements, but also the the peaks of algebraic sum of integer multiple of both the rotational speed and the frequency of base movements. The results proved the phenomena of combination resonance of multi-degree of freedom system may happen at some cases, as well as provide a theoretical basis to identify status of the rotor system subjected to base movements.3. Nonlinear characteristics of rotor-bearing-seal system of pump with varying coefficients based on CFD and RBF is investigated. Approximate function surfaces of coefficients which are relevant to fluid of the seal are obtained. The Muszynska nonlinear seal force model has been widely applied because of its simple form, clear physical meaning and so on. The coefficients of the model, such as inlet loss coefficient, axial velocity and fluid average circumferential velocity ratio, are closely related to status of the flow field. In the former researches, these coefficients often replaced by constants or emprical formula. The fluid field is decided by rotational speed and relative eccentric rate in case of the conditions both of inlet and outlet are given. The CFD method is applied to compute the coefficients of fluid field as different rotational speed and different relative eccentric rate. The RBF method is employed to fit the approximate function surfaces of the coefficients. According to the values of rotational speed and relative eccentric rate, call the corresponding data of the approximate function surfaces in each steps during solving process of motion equations. This method of transient analysis is more accurate than the formers. The approach in this paper provides a new way to investigate the nonlinear characteristics of the rotor-bearing-seal system.4. The rotordynamics of an axial flow pump considering the effect of FSI are numerically investigated using finite element software ADINA. The non-slip condition is applied on the fluid solid interaction surface. The iterative method is adopted in computation of coupled fields of displacement and fluid. What distinguishes the present study from previous ones is the use of moving meshes and the FSI interface that separates the rotor surface from its surrounding fluid. The rotor"s center orbit and frequency response as well as the transient fluid dynamics are obtained with various axial flow speeds. The "wet" critical frequency is obtained. The change of the FSI interface affects the pressure of fluid field. This can be approved by comparing with the results of rotor as it never whirls around Z axis. Moreover, by comparing with the traditional method, it is proved that the method of simulation in this paper is effective. By including real rotating motion of the rotor, this paper presents a better way to solve complicated rotordynamic problems of rotating mechinary that are operated in FSI circumstances.更多还原