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.     

电火花机床主轴头的模态分析与减振设计

针对某机床厂生产的SH50电火花机床在实际工作中主轴头振动较大的问题,通过实验测试和有限元仿真相结合的方法,分析了主轴头的模态特性,并通过测试主轴头的工作振型(operating deflection shapes,简称ODS),找出了主轴头实际工作中的薄弱环节。理论模态、实验模态和ODS三种结果相互印证,增加了有限元模型的可信度,并以此模型为基础对主轴头进行了减振设计。模态实验中改进了传统模态实验依靠经验选取测点或均匀布点时,对经验高度依赖且实验效率较低的弊端,采用有效独立法和模态置信度(modal assurance criterion,简称MAC)矩阵相结合的方法,实验前先进行测点优化,然后根据优化结果布置传感器和力锤位置,提高了模态实验的精度和效率。结果显示,在主轴头结构上增加一个背板,能够提高主轴头频率,远离工作频率的共振范围,起到减振的目的。     

An assumed mode method and finite element method investigation of the coupled vibration in a flexible-disk rotor system with lacing wires

The Assumed mode method (AMM) and Finite element method (FEM) were used. Their results were compared to investigate the coupled shaft-torsion, disk-transverse, and blade-bending vibrations in a flexible-disk rotor system. The blades were grouped with a spring. The flexible-disk rotor system was divided into three modes of coupled vibrations: Shaft-disk-blade, disk-blade, and blade-blade. Two new modes of coupled vibrations were introduced, namely, lacing wires-blade and lacing wires-disk-blade. The patterns of change of the natural frequencies and mode shapes of the system were discussed. The results showed the following: first, mode shapes and natural frequencies varied, and the results of the AMM and FEM differed; second, numerical calculation results showed three influencing factors on natural frequencies, namely, the lacing wire constant, the lacing wire location, and the flexible disk; lastly, the flexible disk could affect the stability of the system as reflected in the effect of the rotational speed.     

超高速磨削机床主轴系统模态分析

针对液体动静压轴承支撑的超高速磨削主轴系统工作的特殊性,在机床工作过程中,主轴高速旋转,动静压轴承的支撑刚度随转速动态变化.为了解主轴系统工作过程中的动态特性,应用Flunent软件求解液体动静压轴承的动态支撑刚 度,而后在此基础上利用有限元分析软件ANSYS建立超高速磨床主轴系统的三维有限元模型,并对其进行模态分析,得到了各阶固有频率和振型.通过设置不同转速下轴承的支撑刚度,获得主轴系统模态分析结果,并利用图解法求解出主轴系统的临界转速.分析结果表明主轴系统在高速旋转状态下,系统的结构刚度会发生变化,使主轴系统的固有频率改变,并且随着转速提高差异越显著.通过振动试验测试验证仿真分析的可靠性,经分析可知,试验与仿真的误差主要来源于支撑模型的简化.     

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bernoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method (DTM) has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.     

硬盘驱动器的冲击振动响应与控制

硬盘驱动器是计算机最重要的外存储设备。由于硬盘抗冲击振动问题的重要性和复杂性,许多研究者对此问题从各个方面进行了研究。本文从硬盘的基本结构与工作原理入手,分析了硬盘的头盘系统在冲击振动作用下的响应特点及其失效机理,并对国内外有关提高硬盘抗冲击振动性能的研究进行了较为系统的回顾与分析,最后阐述了硬盘冲击振动的控制方法和原理。     

Vibration characteristics of a piezoelectric disk laminated with an elastic disk

This paper theoretically and experimentally deals with the vibration characteristics of a piezoelectric disk polarized in the thickness direction and laminated with an elastic disk. Axisymmetric vibration modes include radial and axial motions. Theoretically, in this study, the differential equations of piezoelectric motions were derived in terms of radial and axial displacements and electric potential. The differential equations of elastic motions were expressed in terms of radial and axial displacements. Solving the governing equations and boundary conditions for a coupled structure produced characteristic equations that provided natural frequencies and mode shapes. Experimentally, the natural frequencies were measured using an impedance analyzer and the radial in-plane motions of the fundamental mode were measured using an in-plane laser interferometer. The results of the theoretical analysis were compared with those of a finiteelement analysis and experiments; moreover, the theoretical analysis was verified on the basis of this comparison. It appeared that the natural frequencies of the radial modes of the piezoelectric disk were not affected by the elastic disk; however, those of the thickness modes were reduced by the elastic disk owing to the added mass effect.     

Free vibration analysis of point-supported plates by vibration testing technique

Sweep sine-wave testing is applied for the identification of dynamic characteristics of a four-point-supported square plate with free edges. The idea behind the method is to make use of free vibration time-response data such as acceleration to determine the natural frequencies and associated mode shapes. To compare with the theoretical results, detailed experimental results have been obtained for the various support locations lying at specified positions along the plate diagonals. The natural frequencies and associated mode shapes for the first five modes have been predicted, and the variation of natural frequencies with various support positions have been analyzed for the first symmetric and antisymmetric modes. It is found that the experimental results are generally in reasonable agreement with the theoretical ones.     

Continuous Scan, a method for performing modal testing using meaningful measurement parameters; Part I

This paper presents the first part of a work about modal testing using meaningful measurement parameters. Scanning Laser Doppler Vibrometer (SLDV) systems are becoming largely used both in industry and university for performing vibration measurements. A reason for the success of SLDV systems can be found in their capability of measuring vibration remotely and under different environmental conditions which, when hostile, can inhibit other transducers to work correctly. Hence, SLDV system can be very practical and useful in many engineering applications. SLDV systems are being used as a contactless transducer measuring vibrations from a discrete number of measurement positions marked on the specimen whenever an optical access to it is available. Hence, the advantage of a modal test carried out using accelerometers and one carried out using a SLDV system can be: (i) the automation of the measurements and (ii) the increase of the spatial resolution of the measured modes. This suggests that SLDV systems can be used as a practical replacement of accelerometers operating the same measurement method. Continuous Scanning method is a novel approach of using contactless transducers for measuring vibrations. The most important difference between a discrete and a continuous approach is the method of measuring a vibration pattern. A discrete method measures the level of vibrations at discrete positions on a structure whereas a continuous method captures the modulation of the vibrations produced by the excited modes. This is possible when a transducer can travel across a vibrating surface. This first part of the work presents a new approach of continuous scanning measurement method using a multi-tonal excitation waveform. The paper starts from a comparison between a step and continuous scan mode to introduce a novel approach of continuous scan and multi-tonal excitation waveform. The objective of this first part of work is to present and understand that measurement parameters, such as measurement positions, and can be carefully chosen to improve the measurement technique. A laboratory test piece and a helicopter tail cone are used as examples for the application of this new measurement method approach.     

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.     

计算机磁头/磁盘超薄气膜润滑稳定性

以任意拉森数的超薄气体润滑方程为基础,给出磁头刚体小扰动对空气轴承滑块 (ABS)气膜压强摄动方程。采用算子分裂法求解气膜压强和非结构三角网格的有限元法解压强摄动方程,得到气膜的刚度系数和阻尼系数矩阵。模态分析得到磁头气固耦合系统的固有频率,衰减率和振型。以Ω型磁头为例,分析了在不同气膜厚度和磁盘转速下的磁头稳定性。研究结果表明,磁头稳定性对气膜厚度很敏感,在小气膜厚度运行时,系统固有频率高,稳定性好;磁头升沉和纵倾运动的动力耦合,使磁头系统固有频率和衰减率降低,对稳定性不利;高转速的磁盘对磁头稳定性不利,但影响不大。     

混合单频激励下连续扫描激光多普勒振动测试

提出了一种混合单频激励下激光连续扫描振动测试方法,提高了连续扫描激光多普勒振动测试效率。首先,基于单频激励下连续扫描激光多普勒振动测试的原理,研究了混合单频激励下连续扫描激光多普勒振动测试技术,提出了适合混合单频激励的结构工作变形提取方法;其次,通过仿真测试,从理论上验证了方法的有效性;最后,以悬臂梁结构为例,进行了连续扫描和离散点扫描测试的试验验证。结果表明,混合单频激励下的连续扫描激光振动测试及分析方法可准确获得结构工作变形,具有效率高、空间分辨率高等优点,对进一步的工程应用具有实用价值。     

大型分体式磁轴承电动机系统定子模态分析

准确分析定子固有模态对低振动噪声电机系统优化设计和控制有十分重要的意义。针对大型分体式磁轴承电动机系统,采用有限元仿真方法分析轴向磁轴承定子绕组、径向磁轴承定子叠片结构、机座螺栓连接以及底座附加质量对大型分体式磁轴承电动机系统定子模态的影响。结果表明:轴向轴承定子绕组对定子固有频率影响较大,宜采用质量计入铁心的方式处理;径向轴承定子叠片结构对定子固有频率的影响较小,可按各向同性处理;机座螺栓连接刚度对机座固有频率有一定影响,但当连接刚度远大于机座刚度时,影响较小;底座附加质量对整机模态频率有一定的影响,但对不同振型的固有频率的影响效果相差较大。计算了整机的模态频率,并与振动试验结果进行了对比验证。     

多级柔性水泵转子的动力学有限元分析

利用ANSYSIO．0软件,建立水泵转子的三维模型并进行模态分析和谐响应分析。得出水泵转子前四阶的固有频率和振型,并得到转子在前两阶固有频率下对不同盘加简谐激振力时的振型图,与转子理论振型对比,验证了转子动力学的合理性。有限元法建立的模型为多级水泵柔性转子系统的振动提供了一定的理论依据。     

Exact analysis of resonance frequency and mode shapes of isotropic and laminated composite cylindrical shells; Part I: analytical studies

In order to study the free vibration of simply supported circular cylindrical shells, an exact analytical procedure is developed and discussed in detail. Part I presents a general approach for exact analysis of natural frequencies and mode shapes of circular cylindrical shells. The validity of the exact technique is verified using four different shell theories 1) Soedel, 2) Flugge, 3) Morley-Koiter and 4) Donnell. The exact procedure is compared favorably with experimental results and those obtained using a numerical finite element method. A literature review reveals that beam functions are used extensively as an approximation for simply supported boundary conditions. The accuracy of the resonance frequencies obtained using the approximate method are also investigated by comparing results with those of the exact analysis. Part II presents effects of different parameters on mode shapes and natural frequencies of circular cylindrical shells.     

汽轮机叶片——叶轮系统耦合振动特性的理论计算和实验研究

对汽轮机叶片—叶轮系统（轮系）耦合振动特性进行了理论和实验研究。首先介绍了一种简便实用的计算轮系振动特性的数值积分方法。此方法考虑了叶片的剪切变形、转动惯量、叶轮轮孔处支承柔度、叶片和叶轮连接处的叶根柔度及离心力等影响轮系振动的各种主要因素，给出了焊拉筋和松拉筋的处理方法，可供计算各种结构轮系振动的静、动频谱和相应的振型。其次，本文利用锤击法对叶片—叶轮系统模型进行了模态分析和参数识别，得到系统各阶固有频率和振型，理论计算结果与实验值的比较较为吻合。     

叶盘结构频率转向特征及失谐敏感性实验研究

搭建了用于失谐叶盘结构固有特性及失谐敏感性研究的实验平台,对谐调叶盘结构的频率转向现象进行了实验研究,验证了以往理论分析和有限元仿真中发现的频率转向特征和模态振型转换现象;通过在叶尖粘贴不同的质量块,模拟了三种典型的叶片失谐形式,实验研究了失谐叶盘结构的模态局部化问题;针对同一叶片失谐形式下不同的模态密度区域,实验研究了模态密度对失谐敏感性的影响规律。实验结果与有限元实验仿真结果吻合较好。     

ANSYS在数控机床模态分析中的应用

建立了主轴的三维有限元模型，并利用大型有限元分析软件ANSYS，对主轴部件进行了模态分析，得出了主轴前五阶固有频率和振型，了解主轴部件的各阶振动模态的特点，对于研究主轴部件的动态特性是十分必要的，有利于机床主轴系统的整体设计及其制造。     

ANSYS在数控机床模态分析中的应用

建立了主轴的三维有限元模型,并利用大型有限元分析软件ANSYS,对主轴部件进行了模态分析,得出了主轴前五阶固有频率和振型,了解主轴部件的各阶振动模态的特点,对于研究主轴部件的动态特性是十分必要的,有利于机床主轴系统的整体设计及其制造。     

计入齿圈柔性的直齿行星传动动力学建模

为揭示齿圈柔性对传动系统动态性能的影响,在系杆随动坐标系下建立计入齿圈柔性的直齿行星传动精细化动力学模型,建模中计入时变啮合刚度、支承刚度、陀螺效应和齿圈柔性等诸多影响因素。采用有限段单元的离散化建模方法,将连续体的柔性齿圈离散成由等效虚拟弹簧连接的刚性齿圈段,并推导齿圈段与行星轮的啮合判据。通过分析各构件间的相对位移关系及其受力,最终建立系统的运动微分方程。以三行星轮的NGW型直齿行星传动为例对其进行固有特性分析,得出系统的低阶固有频率分布及相应的振动模式,并进一步分析齿圈柔性和安装方式对系统固有特性的影响。研究结果表明,直齿行星传动的振型可归结为中心构件(太阳轮、系杆)扭转振动和中心构件平移振动两种模式,两种模式下齿圈和行星轮均做复杂平面振动;齿圈的柔性会降低系统的低阶固有频率,且其影响程度与齿圈安装方式有关,齿圈完全固定时其影响最小,径向浮动或周向转动时影响较明显。