The coupled vibration in a rotating multi-disk rotor system

The influence on coupling vibrations among shaft-torsion and blade-bending coupling vibrations of a multi-disk rotor system was investigated analytically. The natural frequencies and the mode shapes of the system were solved for one- to three-disk cases as examples. First, numerical results showed how the natural frequencies varied with blades in a disk unit. The diagrams of the coupling mode shapes were drawn. From the results, it was found that the inter-blade (BB) modes were of repeated frequencies of (N_b-1) multiplicity for number blades. At multi-disk unit, the shaft-blade (SB) modes added to N_d modes for number disks. The BB modes were of repeated frequencies of [N_d×(N_b-1)] multiplicity for number disks. Numerical calculations also revealed that the natural frequencies were affected by disk distance. In the rotation effect, the times of instability will due to the number of disk. And, the more disk rotor causes instability earlier than the less disk case.     

The coupled vibration in a rotating multi-disk rotor system with grouped blades

The influence on coupling vibrations among shaft-torsion, blade-bending and lacing wire coupling vibrations of a multi-disk rotor system with grouped blades was investigated analytically. The natural frequencies and the mode shapes of the system were solved for one-to four-disk cases as examples. First, numerical results showed how the natural frequencies varied by lacing wires and disks in a multidisk rotor system. The diagrams of the coupling mode shapes were drawn. From the results, the inter-blade (BB) modes, the shaft-blade (SB) modes and the lacing wires-blade (LB) modes change rules were given in this paper. Numerical calculation also revealed three interesting results that the natural frequencies were affected by lacing wire constant, lacing wire location and the disk distance. In the rotation effects, the multi-disk has drawn three important phenomena. The times of instability will due to the number of disk, the more disk rotor causes instability earlier than the less disk case and the lacing wires could not affect the system instability.     

基于有限元法的离心机转子系统模态分析

利用有限元分析软件ANSYS建立离心机转子系统的基本模型,对其进行模态分析,得出四阶固有频率和振型。结果显示,高阶固有振型比低阶对转子系统的振动影响大,固有频率越高其振动越剧烈,对结构影响就明显。     

基于有限元法微型涡喷发动机转子系统分析

利用商业软件Catia对微型涡喷发动机转子系统进行了3D实体造型,并利用有限元方法对转动部件进行了强度分析,得到了发动机最大工作状态下的应力分布;对转动部件及转子系统进行了模态分析,得出了其各阶固有频率及振型等主要模态参数。分析结果为发动机安全运转提供了理论依据。     

遥感器正弦振动试验的有限元法

提出了利用模态分析、谐响应分析以及载荷谱变换来实现遥感器正弦振动试验的有限元方法.简述了模态分析、谐响应分析的功能及其理论基础;说明了常用正弦振动试验载荷谱的形式及其变换方法;研究了结构系统阻尼的实现方法;最后以箱形结构为例,说明该方法的可行性.     

Three methods for studying coupled vibration in a multi flexible disk rotor system

This paper improved and developed Shaft-disk-blade (SDB) rotor system based on the previous studies of the authors in the last decade from Yang and Huang (2005) to Chiu et al. (2017). This paper also explored blade-bending, disk-transverse, and shaft-torsion coupling vibration of a multi flexible disk rotor system. Unlike the previous studies of the authors, this paper adopted three methods: (a) Assumed mode method (AMM), (b) Finite element method (FEM), and (c) experimental method. The first approach is the main method, and the two other methods are complementary. Results generated from the three methods were then compared and analyzed. Based on the previous definition of the authors, a flexible disk rotor system displays three types of coupling vibrations: Inter-blade, SDB, and diskblade modes. The system changes the rules of natural frequencies and mode shapes. This paper presents several interesting results. First, the author determined the change rules of the mode shapes and natural frequencies using the AMM, FEM (including three kinds of software), and the experimental method. Second, numerical calculation results also revealed that two phenomena regarding the distance of disk and flexible disk would be affected by the natural frequencies. Third, the experimental results would be explored in this paper. Last, the flexible disk could affect the system instability in the case study of rotation effects.     

基于有限元的风力发电机转子系统动特性分析

针对异步风力发电机转子及端部风扇进行了建模和动特性有限元分析计算.首先对风力发电机转子的运动方程进行了描述,说明了转子临界转速的理论定义.进而分别对转子和转子端部风扇建立了有限元模型,并采用分块兰索斯法对转子和风扇的前四阶固有频率和振型进行了求解,最后针对求解结果进行了分析,指出了误差决定因素.所述方法和所得结果对于风电运行人员具有参考价值.     

动力总成悬置系统隔振性能的有限元分析方法

应用有限元方法对某重型卡车的发动机悬置系统的隔振性能进行分析.首先,建立发动机和变速器的简化三维实体几何模型,使其与部件的轮廓基本符合,保证其质心基本上保持不变;再通过适当选取密度数值使质量、转动惯量也基本上保持不变.对悬置元件建立有限元分析模型,根据其生产厂家提供的参数和有限元分析结果确定悬置橡胶材料的弹性模量与泊松比.建立包括发动机、变速器及其悬置元件的动力总成悬置有限元分析模型,对该模型进行模态分析,得到悬置系统的各阶刚体模态频率与振型.分析结果证明了这种分析方法的有效性.     

Evaluation of gas turbine rotor dynamic analysis using the finite element method

Rotors in general have complex geometries which make analytical modeling of the rotor to determine its dynamic behavior difficult. For this purpose, strong approaches such as finite element method are used to analyze the system. Finite element method saves time and money by allowing reductions in equations while solving the equation systems. Besides, it is possible to obtain faster solutions by using software that can solve these equations. Investigating the Campbell diagrams and deformations caused by critical speeds is very important in investigation of the dynamic behaviors of rotors. For this reason, obtaining the Campbell diagrams of the rotating systems and determining the critical speeds are very useful for us to observe the system behaviors. There are several programs based on finite element method to obtain these data and diagrams. In this study, a program named Dynrot was used to make dynamic analysis and the evaluation of the results and how the software was used are presented in the study. For this purpose, a gas turbine rotor with certain geometrical and mechanical properties is modeled and its dynamic analysis was made by Dynrot program.     

The finite element method application to linear closed loop steady system vibration analysis

An original method for steady, linear, mechanical closed loop system vibration analysis is presented in the paper. The finite element method, the abilities of which are extended, including the coupling element term, is applied to modelling. The problem of excited periodic vibration has been formulated and resolved numerically using the Fast Fourier Transform (FFT) for this purpose. An illustrative example is presented using a computer model of a real milling machine to consider stationary cutting conditions. Some comparative calculations for various types of feedback interaction are performed and time plots for steady-state vibration are obtained.     

Multi-scale simulation method with coupled finite/discrete element model and its application

The existing research on continuous structure is usually analyzed with finite element method (FEM) and granular medium with discrete element method (DEM), but there are few researches on the coupling interaction between continuous structure and discrete medium. To the issue of this coupling interaction, a multi-scale simulation method with coupled finite/discrete element model is put forward, in their respective domains of discrete and finite elements, the nodes follow force law and motion law of their own method, and on the their interaction interface, the touch type between discrete and finite elements is distinguished as two types: full touch and partial touch, the interaction force between them is calculated with linear elastic model. For full touch, the contact force is proportional to the overlap distance between discrete element and finite element patch. For partial touch, first the finite element patch is extended on all sides indefinitely to be a complete plane, the full contact force can be obtained with the touch type between discrete element and plane being viewed as full touch, then the full overlap area between them and the actual overlap area between discrete element and finite element patch are computed, the actual contact force is obtained by scaling the full contact force with a factor which is determined by the ratio of the actual overlap area to the full overlap area. The contact force is equivalent to the finite element nodes and the force and displacement on the nodes can be computed, so the ideal simulation results can be got. This method has been used to simulate the cutter disk of the earth pressure balance shield machine (EPBSM) made in North Heavy Industry (NHI) with its excavation diameter of 6.28 m cutting and digging the sandy clay layer. The simulation results show that as the gradual increase of excavating depth of the cutter head, the maximum stress occurs at the roots of cutters on the cutter head, while for the soil, the largest stress is distributed at the region which directl     

An investigation on the micro cutting performance of diamond-like carbon coatings using finite element method

In an effort to prolong the tool life and improve the tooling performance in micro cutting, it is attractive and promising to apply diamond-like carbon (DLC) coatings on micro tools. Comprehensive understandings of micro cutting performance under various coating circumstances are essential for choosing optimum coating conditions so as for potentially improving cutting tool designs. In the study, the cutting characteristics of a DLC-coated tool has been extensively evaluated and compared with those of an uncoated tool under constant and various uncut chip thickness (UCT) using 2D plane-strain finite element method (FEM). The thermo-mechanical modelling approach has been validated at different UCT in micro milling. Besides, the influence of coating friction coefficient, coating thickness as well as UCT on the cutting forces and tool temperatures has been determined and analysed through design of experiment. It is found that appropriate UCT in micro cutting is of the greatest importance for achieving desirable coating performance of micro tools.     

Free vibration analysis of aboveground LNG-storage tanks by the finite element method

Recently, in proportion to the increase of earthquake occurrence-frequency and its strength in the countries within the circum-pan Pacific earthquake belt, a concept of earthquake-proof design for huge structures containing liquid has been growing up. This study deals with the refinement of classical numerical approaches for the free vibration analysis of separated structure and liquid motions. According to the liquid-structure interaction, LNG-storage tanks exhibit two distinguished eigenmodes, the sloshing mode and the bulging mode. For the sloshing-more analysis, we refine the classical rigid-tank model by reflecting the container flexibility. While, for the bulging-mode analysis, we refine the classical uncoupled structural vibration system by taking the liquid free-surface fluctuation into consideration. We first construct the refined dynamic models for both problems, and present the refined numerical procedures. Furthermore, in order for the efficient treatment of large-scale matrices, we employ the Lanczos iteration scheme and the frontal-solver for our test FEM program. With the developed program we carry out numerical experiments illustrating the theoretical results.     

Coupled bending and torsional vibration of a rotor system with nonlinear friction

Unacceptable vibrations induced by the nonlinear friction in a rotor system seriously affect the health and reliability of the rotating machinery. To find out the basic excitation mechanism and characteristics of the vibrations, a coupled bending and torsional nonlinear dynamic model of rotor system with nonlinear friction is presented. The dynamic friction characteristic is described with a Stribeck curve, which generates nonlinear friction related to relative velocity. The motion equations of unbalance rotor system are established by the Lagrangian approach. Through numerical calculation, the coupled vibration characteristics of a rotor system under nonlinear friction are well investigated. The influence of main system parameters on the behaviors of the system is discussed. The bifurcation diagrams, waterfall plots, the times series, orbit trails, phase plane portraits and Poincaré maps are obtained to analyze dynamic characteristics of the rotor system and the results reveal multiform complex nonlinear dynamic responses of rotor system under rubbing. These analysis results of the present paper can effectively provide a theoretical reference for structural design of rotor systems and be used to diagnose selfexcited vibration faults in this kind of rotor systems. The present research could contribute to further understanding on the self-excited vibration and the bending and torsional coupling vibration of the rotor systems with Stribeck friction model.     

Modeling and vibration characteristics analysis of a DMF rotor system

To analyze the vibration response of a rotor system with circumferential short spring dual mass flywheel (DMF) when the primary flywheel speed changes, the interactions (forces and torques) between the primary flywheel, spring seat, spring, and secondary flywheel are analyzed in detail, and the dynamic analysis model of the DMF rotor system is established considering the influence of clearance and friction between parts in the DMF in this study. The vibration response of the DMF is investigated by numerical method. By analyzing the bifurcation diagram, time history, phase trajectories, Poincaré section, and frequency domain of the relative angular displacement, the variation of vibration form of the system under different excitation frequencies are discussed. Besides, the effects of load, primary flywheel speed amplitude, and spring stiffness on system vibration are also analyzed. Finally, some of the results from the analytical study are verified through the DMF rotor system experiments.

     

Modeling of diffraction of electromagnetic waves on periodic inhomogeneities by a finite element method coupled with the Rayleigh expansion

Implementation of a coupled finite element method of modeling of diffraction of electromagnetic waves on periodic inhomogeneities on substrates and in free space is discussed. The region including a periodic distribution of permittivity and permeability is covered with a finite element mesh. The variational equation incorporating field values in mesh nodes is minimized in accordance with the finite element method. The Rayleigh expansion is applied to field values in homogeneous half-space domains below and above the calculation domain including the inhomogeneity. Numerical experiments are performed to analyze the solution convergence dependence on the element size.     

An experimental and coupled thermo-mechanical finite element study of heat partition effects in machining

A better understanding of heat partition between the tool and the chip is required in order to produce more realistic finite element (FE) models of machining processes. The objectives are to use these FE models to optimise the cutting process for longer tool life and better surface integrity. In this work, orthogonal cutting of AISI/SAE 4140 steel was performed with tungsten-based cemented carbide cutting inserts at cutting speeds ranging between 100 and 628 m/min with a feed rate of 0.1 mm/rev and a constant depth of cut of 2.5 mm. Cutting temperatures were measured experimentally using an infrared thermal imaging camera. Chip formation was simulated using a fully coupled thermo-mechanical finite element model. The results from cutting tests were used to validate the model in terms of deformed chip thickness and cutting forces. The coupled thermo-mechanical model was then utilised to evaluate the sensitivity of the model output to the specified value of heat partition. The results clearly show that over a wide range of cutting speeds, the accuracy of finite element model output such as chip morphology, tool–chip interface temperature, von Mises stresses and the tool–chip contact length are significantly dependent on the specified value of heat partition.     

离心力作用下电机转子强度接触有限元分析

永磁同步电机高转速运行时,在离心力作用下,转子与内嵌磁钢呈现非线性接触状态。介绍了此类非线性接触问题的有限元求解方法。以某分数槽集中绕组永磁同步电机转子与磁钢的接触分析为例,应用Ansys软件建立了三维有限元模型,对高速旋转工况下转子与磁钢的接触情况进行三维有限元分析,得出了应力和变形结果。结果表明该转子结构可满足电机设计转速时的机械强度要求。     

Numerical analysis of projection welding on auto-body sheet metal using a coupled finite element method

A comprehensive finite element method employing a subroutine to link up submodules of commercial code ANSYS is proposed to perform analysis of projection welding in quantitative detail. In order to solve the complexity due to dynamic changes in heat and electrical current flow paths, as well as temperature-dependent material properties, information about contact interfaces and the geometry of the projection areas have been taken into account. By updating parameter information among these submodules in an incremental manner, a truly thermal-electrical-mechanical coupled numerical analysis is realized for projection welding simulation. A case study of an automotive door assembly welding process is carried out and a series of experiments is conducted to confirm the validity of the newly developed method. The agreement between the experimental and numerical results is satisfactory, indicating that the incrementally coupled finite element method may be suitable for projection welding research. Finally, future work to extend this method in optimizing projection welding process design is also presented.     

A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots

Journal of Mechanical Science and Technology - Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is...