Stability analysis of a ball-rod-spring automatic balancer

The traditional ball-type automatic balancer, which consists of several balls moving along a fixed circular orbit, has been applied to different fields for rotational vibration reduction. Under proper working conditions, the balls will counter-balance the rotor by positing to appropriate locations. This particular equilibrium configuration is referred to as the perfect balancing configuration. The unbalance vibrations at steady state can be totally suppressed only if the perfect balancing configuration is stable. The stability of the perfect balancing configuration depends on the parameters of the system. To achieve perfect balancing, the system parameters must lie in the stable region of the perfect balancing configuration in the parameter space. An automatic balancer with a larger stable region of the perfect balancing configuration will be more robust. This paper provides a detailed analysis of a new design of auto-balancer, the ball-rod-spring balancer, which is aimed to increase the stable region of the perfect balancing configuration. A theoretical model of a rotor packed with a two-unit ball-rod-spring balancer is constructed. Closed form formulae of the equilibrium configurations are presented. The stability of each equilibrium configuration is investigated both analytically and numerically. Results of numerical analysis confirm that the stable region of the perfect balancing configuration of the new design is larger than that of the traditional fixed orbit balancer.     

转子在线自动平衡研究

研究了转子在工作转速下实现在线自动平衡的方法。以电磁执行器作为施力装置,运用傅里叶分析和线性系统的叠加原理,对不停车的情况下转子不平衡振动的识别和抑制的算法进行了推导,并在一滚珠轴承支承的转子系统上进行了试验研究。结果证明该方法和装置能够使旋转工作频率下转子的不平衡振动大大减小。     

Theoretical and experimental motion analysis of Self-Compensating Dynamic Balancer

A theoretical and experimental approach was used to investigate the motion and effectiveness of a Self-Compensating Dynamic Balancer (SCDB). This is a device intended to minimize the effects of rotor imbalance and vibratory forces on a rotating system during normal operation. The basic concept of an automatic dynamic balancer has been described in many U.S. patents. The SCDB is composed of a circular disk with a groove containing massive balls and low viscosity damping fluid. The objective of this research is to, determine the motion of the balls and how this ball motion is related to the vibration of the rotating system using both theoretical and experimental methods. The equations of motion of the balls were derived by the Lagrangian method. Static and dynamic solutions were derived from the analytic model. To consider the dynamic stability of the motion, perturbation equations were investigated by two different methods: Floquet theory and direct computer simulation. On the basis of the results of the stability investigation, ball positions which result in a balance system are stable above the critical speed and unstable at critical speed and below critical speed. To determine the actual critical speed of the rotating system used in the experimental work, a modal analysis was conducted. Experimental results confirm the predicted ball positions. Based on the theoretical and experimental results, when the system operates below and near the first critical speed, the balls do not balance the system. However, when the system operates above the first critical speed the balls can balance the system.     

Analytical study of the effect of a circumferential feeding groove on the unbalance response of a rigid rotor in a squeeze film damper

In recent years, a series of researchers have shown that a circumferential feeding groove of a squeeze film damper (SFD) has an evident effect on the forces of fluid film in SFD. Therefore, the feeding groove also affects the dynamic responses of a rotor in SFD. The present work studies the effect of the feeding groove on the unbalance response of a rigid rotor in a squeeze film damper based on the film force models that include effects of the feeding groove and fluid inertia on dynamic characteristics of the fluid film in SFD. Comparisons with the published work show that the feeding groove increases the orbit radius of rotor whirling and affects the unbalance response of a rotor system. The effect of the feeding groove on the unbalance response is also related to the action of fluid inertia.     

新型智能砂轮半自动平衡仪

介绍新研制成功的精密磨床砂轮半自动平衡仪。该仪器利用数字相敏检波技术提取砂轮的不平衡振动信号及最小二乘技术识别砂轮不平衡量;设计出友善的人机界面,用于提示、指导识别与平衡过程;仪器的绝大部分功能均由软件完成,成本低,可靠性高。试验表明仪器原理正确,平衡精度高。     

A dynamic model and numerical study on the liquid balancer used in an automatic washing machine

The rotational system of an automatic washing machine has two major technical difficulties. One is the collision of the tub against the frame at the beginning of its early spinning stage. A factor that causes such instability of the rotational object can be attributed to the deflection of the liquid inside the liquid balancer due to the unbalance mass. This study proposes the installation of a middle plate to avoid the deflection of the liquid and a CFD method is used to verify its effectiveness. The other is the whirling vibration occurred during the high speed rotation of the basket and it shakes the center of its rotational axis. This is because the balancer cannot generate enough restoration forces during its high speed rotation. It is necessary to employ the multi-race in the balancer in order to increase restoration forces. The analysis for the configuration has been performed using a dynamic model.     

Analytical study of the stability of a two-ball automatic balancer

A ball-type automatic balancer, which consists of several balls moving on a circular orbit, can effectively reduce the imbalance vibrations of an optical-disk drive. Under proper working conditions, the balls can counter-balance the imbalance of a disk by positioning the appropriate angles relative to the mass center of the disk. These particular positions are referred to as the perfect balancing positions. The proper working conditions depend on the stability of the perfect balancing positions. Much work has been done to determine the stability of the equilibrium positions numerically for some specific values of the system parameters. This paper, in contrast, analytically studies the stability characteristics of the equilibrium positions under several conditions. A theoretical model of an optical-disk drive packed with a two-ball automatic balancer is constructed first. The governing equations of the theoretical model are derived using Lagrange's equations. The closed-form formulae and the existence conditions for the equilibrium positions are presented. Experiments are conducted to verify the theoretical model. The stability of each equilibrium position is determined by Routh's criterion. Finally, general guidelines on the stability of the equilibrium positions are proposed.     

一种新型电磁平衡头的静态磁特性研究

传统机上动平衡和现场动平衡无法适应高速旋转机械智能化和精密化的发展趋势,因此具有不停机和高精度优势的在线主动动平衡成为当前旋转机械抑制失衡的重要手段.针对某高速磨削电主轴,设计了一款具有环形对称结构、依靠电磁和永磁原理实现驱动和自锁的在线主动平衡头.基于此,研究了它的磁路和磁场分布,采用有限元法获得了其静态自锁力、力矩和静态驱动力、力矩.研究结果可指导平衡头的优化,进而以获得最佳的平衡效果.     

ANALYSIS OF METHOD FOR DETERMINING AZIMUTH OF PRINCIPAL AXIS OF INERTIA BASED ON DYNAMIC BALANCE MEASUREMENT

The dynamic balance quality of a rotating object is an important factor to maintain the stability and accuracy for motion. The azimuth of the principal axis of inertia is a major sign of dynamic balance. A usual method is measuring moment of inertia matrix relative to some base coordinates on a rotary inertia machine so as to calculate the azimuth of principal axis of inertia. By using the measured unbalance results on the two trimmed planes on a vertical hard bearing double-plane dynamic balancing machine, the dimension and direction of couple unbalance can be found. An azimuth angle formula for the principal axis of inertia is derived and is solved by using unbalance quantities. The experiments indicate that method based on dynamic balancing measurement is proved rational and effective and has a fine precision.     

非线性油膜力作用下联轴器耦合转子系统的稳定性和分岔

在非线性油膜力作用下 ,建立了转子 -联轴器系统的运动微分方程。非线性油膜力则采用有限差分法求解 ,对联轴器耦合的刚性转子系统和柔性转子系统分别进行了计算和分析。结果表明对于平衡转子系统在平衡点失稳后 ,在一个较大的转速范围内存在着稳定的涡动轨迹 ,联轴器两侧转子的质量相差越大 ,则发生 Hopf分岔所对应的转速越高。对于不平衡转子系统 ,在同步涡动轨道失稳后 ,系统将产生准周期和倍周期等一系列的分岔现象 ,并且质量偏心的位置对系统的动力学行为有影响。     

Analytical study on effect of a circumferential feeding groove on unbalance response of a flexible rotor in squeeze film damper

Of recent years, a series of researches have shown that a circumferential feeding groove of squeeze film damper (SFD) has evident effect on fluid film forces in SFD. Therefore, the feeding groove also affects dynamic responses of a rotor in SFD. Present work studies the effect of the feeding groove on unbalance response of a flexible rotor in SFD based on new film force models that include effects of the feeding groove and fluid inertia on dynamic characteristics of the fluid film in SFD. Compared with the published work, unbalance responses predicated under considering effect of the feeding groove on the dynamic characteristics in SFD are small, and rotor speed region for unbalance responses with multiple solutions is different, affecting the stability of a rotor system. And the effect of the feeding groove on the unbalance response is related to action of fluid inertia.     

离心压缩机蜂窝阻尼密封动力特性及转子稳定性*

新一代蜂窝阻尼密封在提升透平机械转子稳定性方面有优越的表现,其动力特性是评价转子稳定性的重要参数。应用非定常动网格技术和多频涡动模型,研究蜂窝密封动特性系数随转子涡动频率的变化规律,并与迷宫密封进行对比。结果表明：蜂窝密封动特性受转子涡动频率影响较大,直接刚度系数和交叉阻尼系数随涡动频率增大而增大,交叉刚度和直接阻尼系数随涡动频率增大而减小;迷宫密封动特性系数随涡动频率变化特征不明显;在低频率区蜂窝密封的有效阻尼远高于迷宫密封。在实际压缩机转子上的应用结果表明,蜂窝密封能显著提升转子稳定性。     

转子在线动平衡嵌入式控制系统开发与验证

为了快速、有效抑制由于质量不平衡引起的转子振动并在线监测转子的实时平衡状态,基于模块化设计思想设计了一种针对电磁式主动平衡装置的嵌入式在线自动平衡控制系统。使用数字信号处理器(digital signal processor,简称DSP)和现场可编程门阵列(field programmable gate array,简称FPGA)构建了一种快速平衡控制器,基于影响系数法建立了自适应平衡控制模型,采用C和C#语言分别开发了多线程的平衡控制软件和人机交互界面,针对某国产电主轴完成了整个系统功能的试验验证。结果表明:当主轴在3kr/min平稳运行时,通过该自平衡系统可将其振动大约降低43%。     

某X波段机场场面监视雷达现场动平衡试验研究

文中对某X 波段机场场面监视雷达天线样机的动平衡性能进行了测试和分析。通过动平衡测试出不平衡的位置和大小,然后在对称方向加上相应的质量来配平衡,将不平衡引起的振动及振动力减少到允许范围内。试验表明,现场动平衡试验操作简便,降低了试验成本,并且可以避免二次装配带来的误差。现场动平衡试验及分析表明,该天线转子动平衡性能满足精度要求。这说明样机在设计、加工过程中对质量偏心问题处理得较好,并且在增加配重后能获得较好的动平衡性能。这种对大型转子的现场动平衡试验技术作为一种成熟和实用的技术为企业带来了可观的经济效益。     

The stability of active balancing control using influence coefficients for a variable rotor system

High-speed rotating machines can be very sensitive to rotating mass unbalance that is a major source of harmful vibration for many types of rotating machinery. A balancing procedure is therefore needed for all high-speed rotating systems. To save the time and cost of off-line balancing, many researchers have developed on-line balancing devices and methods. In this paper, an active balancing device, which is of an electro-magnetic type, has been developed and an active balancing method using the influence coefficient method is proposed. The stability of active balancing control is studied in this paper. A stable condition for active balancing control is derived by estimating the errors of influencing coefficients. A gain scheduling control using influence coefficients of the standard model is proposed when the dynamic characteristics of a rotor system are changed. The stability of the balancing method is verified by experiments.     

Lateral Vibration Analysis of Flexible Shafts Supported on Elliptical Journal Bearings

This paper presents the development of a finite element procedure for the dynamic analysis of flexible rotors supported on fluid-film elliptical journal bearings operating under several operating conditions. The rotating shaft is modeled by using Timoshenko beam theory and the coupled rotating components, such as disks and impellers, are modeled by using lumped masses. The modeling of the elliptical journal bearings is performed by solving the lubrication equations generated from the application of a linearized perturbation method on the classical Reynolds equation. The bearing carrying-load capacity and the linearized dynamic force coefficients can be predicted for elliptical bearings with different preloads and journal eccentricities. The rotor transient whirling unbalance response is estimated by performing the time integration of the finite element equations using Newmark method. Experimental whirling unbalance response of a rotating shaft supported at two identical journal bearings is used to validate the finite element procedure. A comparative analysis of the dynamic response of flexible rotors supported on both cylindrical and elliptical journal bearings is performed to show that some elliptical bearings are capable of attenuating the rotor unbalance response more efficiently than cylindrical bearings are.     

The nonlinear and ball pass effects of a ball bearing on rotor vibration

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.     

数控有源磁力轴承对转子不平衡振动抑制的一种新方法

有源磁力轴承在高转速场合应用时,由于转子的不平衡响应,降低了转子的旋转精度。我们借鉴转子现场平衡的两平面影响系数法,设计了一种利用数字控制的有源磁力轴承对不平衡补偿的方法,实验表明,这种方法使转子绕几何中心平稳旋转,能极大地提高转子的旋转精度     

THEORY OF MUM FOR METAL SPHERICAL ROTOR WITH CONTACTLESS SUSPENSION

Based on the motion equations of an unbalanced spherical rotor with contactless suspension,three methods of MUM (mass unbalance measurement) are put forward to measure the total massunbalance, radical mass unbalance and radical mass unbalance of the rotor. Total mass unbalance isobtained when the unbalanced rotor plays as a simple pendulum in static situation. The pendulant pe-riod and pendulant midpoint indicate magnitude and direction of total mass unbalance of the rotorrespectively Analysis of the motion equations by using the averaging method yields that the rotor willdo a special side oscillation when an auxiliary system maks the rotor spin about its pole axis which isorientating toward the local vertical. The radical mass unbalance can be obtained by building a properdisplacement sensor to sense the amplitude of the side oscillation. Necessary analysis of the motionequaions also shows that when the rotor spins at a small angular velocity and the rotary axis is per-pendicular to the vertical, the p     

人工心脏泵磁悬浮转子质量不平衡及磁耦合研究

结合建模与实验，分析了人工心脏泵转子质量不平衡及磁耦合对转子稳定悬浮的影响，依据转子动力学理论推导出了五自由度转子运动方程。由运动方程知，转子前后端的质量耦合可消去，转子同自由度前后端同时控制优于分开控制。运用转子自由振动及陀螺力方程分析了动不平衡对转子偏心的影响，结果表明：建模时增加动不平衡矩阵可有效减小偏心；为减小涡动，转子径向采样周期应与转速相适应，不宜过快。采用有限元方法给出了磁极不同工作方式时的磁力线分布，结果表明同时控制互相垂直方向的磁极有利于减小磁耦合。实验测量了转子在平衡位置的各向位移，并计算出静态时X方向的偏心相对误差为0．28％，Y方向的偏心相对误差为0．42％。