Rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor

The paper shows a rotordynamic model for electromagnetic excitation caused by an eccentric and angular rotor core in an induction motor. It is shown that an eccentric rotor core leads to an electromagnetic force and an angular rotor core to an electromagnetic moment, which both force the rotor to vibrate. For these two kinds of magnetic unbalance, a rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness—radial and angular electromagnetic stiffness—the mass moment of inertia and the gyroscopic effect of the rotor. With this model, the absolute orbits of the shaft centre, the shaft journals and the bearing housings can be calculated, as well as the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be computed. In addition to the mathematical derivation of the model, also a numerical example is shown for clarification. The aim of the paper is, on the one hand, to show the mathematical coherences—based on an analytical model—between rotordynamics and the electromagnetics for an induction motor with an eccentric and angular rotor core and, on the other hand, to derive a calculation method for evaluating the vibration sensitivity regarding these two different kinds of magnetic unbalance.     

几何非线性摩擦阻尼隔振系统动力学行为研究

非线性隔振系统由于具有较线性系统更优的隔振性能,因此在工程中应用广泛.本文通过配置与被隔振对象的运动方向相垂直的库伦摩擦阻尼器,构建了几何非线性摩擦阻尼模型.由于引入了几何非线性,因此其摩擦力与位移正相关,这与传统与位移无关摩擦力模型有显著不同.首先,建立了具有几何非线性摩擦阻尼的数学模型以及隔振系统的受迫振动方程;然后,使用谐波平衡法求解了动力学方程,并使用数值仿真方法验证了谐波平衡法求解的准确性;最后,研究了几何非线性摩擦阻尼隔振器的绝对位移传递率和相对位移传递率.研究结果表明,在库伦摩擦阻尼选择适当,非线性摩擦阻尼系统可以在保持高频振动衰减效果的前提下,显著降低系统共振峰,其性能优于传统的恒定摩擦阻尼隔振模型.同时,几何非线性摩擦阻尼系统能够避免传统摩擦阻尼系统中的“锁定”现象,从传递率角度来说,不利于共振峰控制;但从激励环境改变引发隔振系统失效的角度来看,几何非线性摩擦阻尼系统可以拓宽系统对激励幅值的适应范围,避免隔振系统失效.本文的研究结果对此类隔振系统的设计和摩擦阻尼参数的选择具有通用的指导意义.      

转子系统非线性动力学DEM建模研究

将DEM方法引入转子系统非线性动力学的分析计算,对其建模过程和有关本构关系,作了比较详尽的介绍。该模型可用于碰摩、弯曲振动和扭转振动等转子系统的大部分动力学和运动学问题分析计算,不仅适用于单跨转子系统,也适用于多跨转子系统,尤其是在碰摩计算时,可考虑其摩擦特性随时间历程而变的特点,从而使分析计算更加接近实际情况。     

Load enhancement effects due to polymer thickening in a short model journal bearing

A model bearing is described which is 20.0 mm in diameter and 2.5 mm in length; a short bearing of diameter to length ratio eight. The clearance is large (500 μm) and the rotor may be run true or eccentric on its own shaft; in each case the mean load and frictional (tangential) force is measured as the centreline eccentricity is varied.Comparison is made between the lubricating performance of Newtonian and highly elastic liquids; the latter give load enhancement ratios of up to 300 and reductions in coefficient of friction by factors of the order 30. These effects are greatly in excess of those obtained when dealing with bearing of diameter to length ratio close to unity; possible reasons for this are discussed.A Newtonian oil and a polymer-thickened oil are tested in the same way, the latter oil is found to give load enhancement ratios of 1.4 (true rotor) and 3.5 (eccentric rotor) with corresponding reductions of coefficients of friction by factors of 1.5 (true rotor) and 3.0 (eccentric rotor). Such effects had not previously been observed when using oils in the internal cylinder geometry (journal bearing type) although somewhat similar effects have been found in the external cylinder and squeeze film geometries.The rheological properties of the polymer-thickened solutions are measured and the relevance of the results to friction and load bearing discussed.     

GCr15钢-CVDCr_7C_3镀层摩擦副摩擦振动的研究

本文系统地研究了GCr15钢球-CVDCr_7C_3镀层钢盘摩擦副滑动干摩擦引起的摩擦力(切向力)振动特性及其对材料摩擦磨损性能的影响。试件系统在垂直和水平方向上均处于低刚度、小阻尼状态。试验信号由微机采集、处理并进行频谱分析。结果表明,摩擦力振动的类型与正压力有关,而与拖动速度无关;摩擦力呈周期性自持振动时具有与相对滑动速度典型的非线性关系,振动频率接近(略低)于系统在切向的固有频率,而与拖动速度无关;摩擦力呈非平稳随机振动时,振动频率与系统在法向的振动频率有关,而与系统在切向的固有频率及拖动速度都无关;摩擦偶件运动的平稳性与摩擦力振动的类型有关,而与平均摩擦系数无关;摩擦力所耗费的能量与正压力呈比例关系。     

一种测量TBM滚刀受力的实验方法研究

为探索测量TBM掘进机滚刀受力特性的方法,本文提出了一种能够测试滚刀三向受力的方案。选择滚刀装配体上的垫块作为弹性体,以粘贴应变片的方式实现测量。利用数值计算方法找出垫块底端面和侧端面对所测力敏感而对作用力位置变化不敏感的区域作为贴片位置,分析了锁紧楔块对测试结果的影响。对滚刀装配体在不同工况下的受力情况进行了数值分析和实验测试。结果显示,若根据数值计算选定的位置贴片,垫块底端面和侧端面桥路应变总值的实验和数值结果相对误差介于1.06%和5.62%之间。滚刀强烈振动或更换刀具后可能使中心轴与垫块之间受力位置发生变化,结果确定其影响不超过2.75%。该方案不仅可以测出三个力的信号,还可用于分析滚刀振动状态,特别是滚刀发生偏磨后,刀刃与岩石之间强烈摩擦,振动状态与未偏磨时必然不同,因此还可通过分析由该方法测得的动态信号来识别偏磨。     

Sliding friction in the presence of ultrasonic oscillations: superposition of longitudinal oscillations

Summary  It was often observed that friction forces can be reduced significantly if ultrasonic oscillations are superposed to the macroscopic sliding velocity. This phenomenon can be used to improve machining processes by addition of ultrasonic vibration to tools or workpieces, and forms the basis for many processes of ultrasonic machining. On the other hand, ultrasonic vibrations can be used to generate motion. The thrusting force of ultrasonic motors is provided to the rotor through friction. In the present paper, a simple theoretical model for friction in the presence of ultrasonic oscillations is derived theoretically and validated experimentally. The model is capable of predicting the reduction of the macroscopic friction force as a function of the ultrasonic vibration frequency and amplitude and the macroscopic sliding velocity. Received 22 November 2000; accepted for publication 6 February 2001     

Nonlinear lateral-torsional coupled motion of a rotor contacting a viscoelastically suspended stator

Interaction of a rotor with a stationary part is a kind of serious malfunction that could result in a catastrophic failure if remained undetected. Past analytical and numerical simulation work on rotor?Cstator interactions mainly focus on the vibrations along the lateral directions. The torsional degree of freedom (dof) is usually ignored. The present work is aimed to study the influence of a rotor to stator contact on the lateral-torsional coupled vibrations. A mathematical model consisting of interacting vibratory systems of rotor and stator is presented. The contact is modeled using contact stiffness, damping and Coulomb friction. Equations derived for kinetic, potential and dissipation energies and non-conservative external forces are used in the Langrange??s equations for deriving the motion equations for the rotor?Cstator system. Equations revealed that the lateral-torsional motion coupling exists twofold for the rotor. The unbalance couples lateral-torsional motion of rotor through inertia and damping matrices. Coupling due to the rotor?Cstator friction occurs through a force vector. The nonlinear equations are solved using a Runge?CKutta fourth-order numerical integration scheme using relatively small time step. Results obtained through the proposed model are compared with the identical rotor?Cstator system without torsional dof and differences are identified. Effect of several parameters such as speed, relative inertia, coefficient of friction and contact damping on the bifurcation behavior of the rotor?Cstator motion has been investigated. Vibration motions presented in the forms of spectrum cascade of the coast-up response, and orbit and Poincaré plots of the steady-state response are exhibiting rich dynamic behavior of the system.     

行波型超声波电机摩擦特性的实验研究

超声波电机是通过逆压电效应产生高频振动并通过摩擦实现驱动的电机,其定转子摩擦接触面的高频、微幅的行波振动有其特殊性,跟以往的摩擦接触显著不同,并对电机的换能效率、电机寿命和摩擦材料的选择等都有影响.本文建立了超声波电机定转子接触面摩擦系数测量装置,通过试验比较了摩擦接触面在常规、定子驻波振动以及行波振动下的动态摩擦系数,分析了定子相对转速(速度)、预紧力以及温度对定转子接触面摩擦系数的影响.根据摩擦二项式和电机定转子表面弹塑性接触状态对摩擦系数与预紧力等的对应关系进行了说明,分析了驻波振动和行波振动的超声减摩效果以及温度对摩擦系数的影响,确定了适合行波型超声波电机的摩擦系数计算模型.超声波电机的驱动摩擦特性是1项基础性工作,有助于行波形超声波电机设计、建模和驱动控制等.     

与冲蚀有关的粘着与犁沟摩擦系数

提出一种与冲击磨损有关的有效摩擦系数，它被定义为冲击过程中，每一瞬间的切向有效摩擦力与法向载荷之比．有效摩擦力被表示为剪切项与犁沟项之组合．剪切项依赖于剪切金屑接合点的状态——滑移或滚动．犁沟项依赖于冲击物在冲击途中使靶材料发生移动的状态．此有效摩擦系数被应用于研究刚性球自由斜冲击延性靶问题．在忽略剪切项仅计及犁沟项的情况下，研究表明，Hutchings实验中的有效冲击摩擦系数是冲击过程与初始冲击角的函数，就时间平均而言，大于Hutchins为拟合计算与实验结果所取的摩擦系数常值0.05．有迹象表明，对于与固粒延性冲蚀有关的刚性球自由斜冲击延性靶问题，在一定条件下，有效摩擦系数主要由犁沟效应确定．     

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque-speed curves as well as torque-efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.     

电磁作用激发的水电机组转子轴系振动研究

水轮发电机组的振动问题是长期困扰广大科研工作者的一个难题,也一直是学术界研究的热点.本文针对某大型水轮发电机转子轴系,首先建立了轴系扭振的微分方程组,给出了轴系整体扭振零频的计算公式,并计算了零频数值.接着在考虑了转子静偏心、振动偏心和转动偏心的综合影响后,求得了气隙磁场能量和单边电磁拉力的表达式,并应用机电耦联系统的能量法,求得了系统由电磁力激发的组合强迫共振响应的一次近似解.最后并应用奇异性理论对分岔方程进行了分析,求得了分岔集、滞后集、双极限集和转迁集的参数区间,给出了普适开折平面和物理参数平面上的分岔图,求得了机组稳定运行区域的电磁参数.本文所得结论对水电机组的工程设计人员具有重要的指导意义.     

复合干摩擦的准零刚度隔振系统的亚谐共振

利用增量平均法研究了复合干摩擦阻尼器的准零刚度非线性隔振系统在外部简谐激励作用下的1/3次亚谐共振. 首先利用平均法得到了复合干摩擦的准零刚度隔振系统的主共振近似解析解, 然后在系统主共振近似解析解的基础上将系统的亚谐共振响应看作增量, 并利用平均法得到了准零刚度隔振系统的亚谐共振近似解析解. 利用李雅普诺夫方法得到了准零刚度隔振系统主共振和亚谐共振稳态解的稳定性条件, 并推导了系统1/3次亚谐共振的存在条件. 根据近似解析解分别得到了复合干摩擦的准零刚度隔振系统的主共振和亚谐共振力传递率. 利用数值解验证了准零刚度隔振系统主共振和亚谐共振近似解析解的准确性. 利用系统的近似解析解详细分析了准零刚度参数和干摩擦力对系统主共振和亚谐共振的幅频响应以及力传递特性的影响. 分析结果表明, 通过选取合适的干摩擦力参数, 可以消除准零刚度隔振系统在主共振区域的亚谐共振. 通过复合干摩擦阻尼器不但可以提高准零刚度隔振系统在低频区域的振幅抑制效果, 而且可以降低准零刚度隔振系统的起始隔振频率, 但是会增大系统在有效隔振频带内的力传递率.      

复杂机车振动环境下牵引电机轴承服役寿命评估

牵引电机是铁路机车的动力源, 其关键零部件(支承轴承等)的服役性能直接影响机车传动系统的稳定性和可靠性. 对于重载机车, 传统轴承服役寿命评估方法主要基于定载荷工况, 难以准确评估轨道不平顺等复杂外部激励作用下电机轴承的服役寿命. 因此, 本文根据车辆-轨道耦合动力学理论, 考虑轨道车辆运行过程中的轮轨相互作用和齿轮啮合作用, 建立了具有牵引动力传动系统的机车-轨道耦合动力学模型; 采用线性损伤累积准则和ISO 281标准计算方法, 评估了复杂机车振动环境下牵引电机轴承的服役寿命. 结果表明, 在轨道随机不平顺激励下, 机车轮轨垂向力、齿轮啮合力、牵引电机内部转子离心力、不平衡磁拉力等明显增大; 在复杂机车振动环境中, 电机轴承内部滚子-滚道相互作用加剧, 传动端与非传动端轴承的疲劳寿命缩短; 随着线路状态的不断恶化和机车运行速度的提高, 牵引电机轴承的预测寿命里程不断减小; 由于传动端轴承承受较大的外部动态载荷, 传动端轴承的服役寿命明显低于非传动端轴承. 本文提出的评估方法可为机车牵引电机轴承的设计、选型和寿命评估提供理论指导.      

基于行波型超声马达的超声波振动减摩试验研究

提出了行波型超声马达振动减摩的几何模型,采用电磁电机驱动、电磁电机结合一路驻波振动驱动及行波型超声马达驱动3种驱动方式模拟行波型超声马达摩擦驱动特点,借助超声马达摩擦特性模拟试验装置,引入摩擦系数降低率的概念,研究了电机转速、预压力、超声波激励电压和摩擦材料等对定、转子摩擦副摩擦系数的影响.结果表明:在较高相对滑动速度、小预压力及大振幅条件下,超声波振动减摩现象显著.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

Dynamics of rotating conveying mud drill string subjected to torque and longitudinal thrust

In the view of fluid-structure interactions and rotor dynamics, this paper models the lateral vibration of a vertical downward rotating elastic drill string conveying mud subjected to supporting stabilizers, bit torque and longitudinal thrust. The dynamic model involves the rotational inertia of the drill string tube cross section, the gyroscopic effect caused by rotation, the damping due to friction with the surrounding fluid, the gravity force and mud buoyancy. Damped natural frequency, stability and resonance of the drill string system are determined by quadratic eigenvalue problem and investigated at influences of the stabilizer, rotational angular speed, mud flowing velocity, bit torque and thrust. As a result, the drill string can lose stability both at simultaneous and separate influences of the mud conveying, bit torque and thrust, whereas the rotation, stabilizer and gravity of the drill string can improve system stability; the rotational angular speed causing system resonance decreases with the increase of the mud flowing velocity, bit torque and thrust.     

干摩擦控制振动的应用

干摩擦能衰减机械振动的现象早为人们所熟悉。但是很长一段时期,干摩擦应用到控制振动上的例子不多见。这是由于干摩擦的性能不好掌握和干摩擦会使系统变为非线性,设计、计算就很复杂。 干摩擦振动系统是非线性系统。以振动系统中的一个干摩擦接头来说明。当接头上的力     

COMPUTATIONAL METHOD FOR DYNAMICS SIMULATION OF PAYLOAD SEPARATION FROM SATELLITE WITH RAIL CLEARANCE

传统在轨分离载荷动力学分析未考虑实际导轨的实时接触,无法准确分析分离时刻载荷的速度和角速度。针对半圆形双导轨,研究了空间导轨与定向器接触的特点及形式,基于分离装置的几何构型提出了一种确定发生相对轴向运动时导轨与定向器潜在接触对的方法,所提方法考虑了载荷轴线与导轨轴线的空间夹角,保证了分离后期接触检测的准确性,并可推广至多导轨接触计算。基于Lankarani与Nikravesh的连续接触力模型计算法向碰撞力,采用修正的Coulomb模型计算切向摩擦力。最后对飘浮基挠性航天器在轨分离载荷模型进行数值分析,验证了方法的有效性。结果表明导轨间隙增大了接触碰撞力,且随间隙的增大垂直于载荷分离方向的速度和角速度增大,导轨间隙使基座的转动与挠性附件强烈耦合,对航天器的稳定性造成影响。     

Theoretical rotor dynamic analysis of two-pole induction motors regarding excitation due to static rotor eccentricity

The paper shows a theoretical rotor dynamic analysis of two-pole induction motors regarding excitation due to static rotor eccentricity, which causes an oscillating magnetic force in the air gap of the machine. The hereby caused rotor vibrations are mathematically described, showing the orbit movements of the rotor centre, the shaft journals and the bearing housings. The influence of the rotor speed as well as influence of the direction of the magnetic force on the vibration behavior is investigated, based on a numerical example. On the one hand the aim of the paper is to derive the mathematical coherences—based on a simplified rotor dynamic model—between rotor dynamics, electromagnetic and the oil film characteristics of the sleeve bearings for two-pole induction machines, considering electromagnetic excitation due to a static rotor eccentricity. On the other hand the aim is to derive a method for calculating the maximum height of the shaft vibrations—as a worst case—caused by a static rotor eccentricity. Therefore the paper shall prepare the basis for implementing this method into more detailed numerical programs, e.g., finite element programs.