斜齿轮柔性转子轴承系统非线性动力学分析

考虑齿侧间隙、轴承径向间隙、齿轮不平衡力,使用有限元法建立质量矩阵、刚度矩阵、阻尼矩阵并组装成整体参数矩阵,建立了适用于斜齿轮柔性转子滚动轴承系统的非线性动力学模型。采用Runge-Kutta法求解,并分析系统的动力学行为。研究了转速、转轴刚度、不平衡力对斜齿轮系统非线性动力学行为的影响规律。结果表明：随着转速的变化,系统将经历周期、拟周期、混沌等多种运动状态;随着转轴刚度的减小,混沌运动的区间减小,振幅大小发生改变;不平衡力增大后,系统混沌区间增大,混沌运动的区间也发生改变。     

Dynamic behavior of fluid‐structure coupling of hydrostatic spindle under effect of oil film slip

To better understand the dynamic characteristics of a hydrostatic spindle in fluid‐structure coupling, the impact of oil film slip on the 4 dynamic stiffness and damping coefficients of the spindle is studied. On the basis of modified Reynolds equation, which considers the microscale velocity slip effect, rotation error of the spindle is calculated. To solve the rotor axis orbit under the existence of eccentric quality, 4 dynamic stiffness and damping coefficients of the oil film, which describe the dynamics of a rotor axis orbit, are calculated by using load increment method and the pressure perturbation method. The research results show that velocity slip caused a certain impact on dynamics of bearing stiffness and damping performance. The experiment of the measuring path of the shaft verifies the correct and effect of the orbit of shaft center model.     

支点弹性、阻尼可倾瓦轴承动力特性数值仿真及试验研究

依据考虑瓦块摆动和沿几何预载荷方向微幅振动的可倾瓦轴承完全动力特性的解析模型及其对应的八参数简化动力模型,设计制备了支点弹性、阻尼特性可倾瓦轴承。该轴承通过在瓦块支点与轴承体之间设置弹性垫片,使瓦块支点支撑在弹性垫片上,弹性垫片与轴承体之间存在微小间隙并与轴颈润滑系统共享油路以实现局部挤压油膜效应。根据不同加工工艺,制备了两种形式的新型支点弹性、阻尼轴承,并通过理论计算模拟与试验分析对两种新型轴承的动力特性进行研究。结果表明,支点弹性、阻尼可倾瓦轴承能够增大转子的一临界阻尼,有效提高转子系统稳定性。     

螺旋槽气体轴承动态特性及失稳分析

针对高速动静压气体轴承气膜的复杂非线性动力学行为,以球面螺旋槽动静压气体轴承为研究对象,建立润滑分析数学模型;采用有限差分法与导数积分法进行求解,得到动态扰动压力分布及动态特性系数,并研究切向供气条件下螺旋槽参数、径向偏心率、供气压力、转速对气膜刚度阻尼系数的影响规律;建立线性稳定性计算模型,预测气膜涡动失稳转速,分析运行参数对失稳转速的影响。结果表明:气膜阻尼是一种抑制涡动的因素,气膜的稳定性取决于气膜刚度与阻尼的协同作用;气膜刚度阻尼随着槽宽比、槽深比、螺旋角的增大,整体上呈先增大后减小的趋势;刚度随转速的升高而增大,阻尼则随转速的升高而减小;径向偏心率和供气压力越大,气膜刚度和阻尼越大;在一定范围内,提高供气压力、增大径向偏心率能够提高系统失稳转速;合理地选取轴承结构参数和运行参数,能够优化轴承动态特性,保证气体轴承较高的运行稳定性。     

A New Active Tilting-Pad Bearing: Nonlinear Modeling and Feedback Control

This article introduces a new type of active fluid film bearing and its feedback control. In particular, the active adjustment of the angular velocity of the pads of a tilting-pad bearing in response to changes in the operating conditions of the rotating machine is proposed. This is motivated by the observation that there is more control authority in the pad tilting motion than in its radial translation. To this end, a dynamic model for the bearing system is first developed, inclusive of the nonlinear hydrodynamic force for the infinitely short bearing case. A model-based controller is then constructed, based on measurements of the journal position and velocity and pad tilting angles, to ensure that the journal is asymptotically regulated to the bearing center. Numerical simulations illustrate the performance of the active bearing under the proposed control in comparison with the bearing's standard passive mode of operation.     

基于二次型全局最优控制算法的汽轮发电机组轴系扭振主动控制模拟

把线性定常二次型全局最优控制算法与大型汽轮发电机组轴系扭振理论相结合,以减少轴系扭振能和控制源能量为优化目标,提出了大型汽轮发电机组轴系扭振的线性定常二次型全局最优控制理论,构造了汽轮发电机组轴系扭振主动控制的状态空间方程。阐述了求解离散黎卡提矩阵代数方程的非递推解法,提出利用求解哈密特矩阵特征值问题来确定二次型最优控制反馈矩阵的方法。为了考查扭振主动控制效果,编制了适用于离散系统扭振主动控制的仿真计算程序,利用所编程序对一台200 MW汽轮发电机组轴系进行了扭振主动控制模拟计算,并进行了扭振主动控制的时域特性分析。分析结果表明,采用线性定常二次型全局最优控制理论对汽轮发电机组轴系扭振进行主动控制,不但有很好的减振效果,而且所需控制力矩较小。     

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor.     

Fixed-Geometry,Hydrodynamic Bearing with Enhanced Stability Characteristics

This article presents the results of a successful bearing optimization study aimed at identifying a fixed-geometry, hydro-dynamic journal bearing that does not suffer from the low load instability typical of this class of bearings. This goal was met through optimization of a fairly simple objective function based on the rigid rotor whirl-speed ratio, using a constrained, nonlinear algorithm based on sequential quadratic programming. In the interests of reducing computational time, a two-dimensional isoviscous formulation of the Reynolds equation was used for this work. The equation was solved using a finite element approach.

This article includes a discussion of the optimization approach, the finite element solution approach, the resulting bearing design, and its performance characteristics. It concludes with an application example comparing the optimized bearing's predicted performance to a tilting-pad bearing's predicted performance for a centrifugal compressor-like rotor. The mismatch between shaft and bearing stiffness due to the rigid rotor optimization makes the optimized bearing less desirable from an unbalance response point of view. However, the optimized bearing is shown to have very good stability characteristics, which compare favorably to a tilting-pad bearing.     

具有迟滞和蠕变特性压电作动器的模糊自适应逆控制方法

针对具有迟滞和蠕变特性的压电作动器非线性模型,提出了一种前馈控制和反馈控制相结合的自适应模糊逆控制方案。在前馈控制器中压电作动器的迟滞和蠕变非线性特性的逆模型由自适应模糊逻辑系统近似;在反馈控制器中比例控制器用来调节压电作动器的输出误差。该方法可以实时补偿压电作动器的迟滞和蠕变特性,减少作动器跟踪误差。仿真计算结果表明了该方法的有效性。     

Robust rotor dynamics for high-speed air bearing spindles

For ultra-precision machining machine tool components need to operate outside critical frequencies of the machining system to avoid insufficient surface finish caused by vibrations. This particularly applies to tooling spindles as those are generally the component of a machine tool with low stiffness and damping values. Surface finish and shape of a machined part rely directly on the overall accuracy in motion of the tooling spindle over the entire machining parameter and speed range. Thus spindle designs for an operation outside critical frequencies combined with high stiffness and damping values are crucial for ultra-precision machining.For sufficient stiffness properties bearing gaps of gas bearings have to have a size of only a few microns and show a distinct sensitivity on temperature and for journal bearings also on speed. This again means that bearing properties change with temperature and speed. Considering a spindle system comprising a rigid shaft rotating in a radial/axial bearing system with changing stiffness and damping properties leads to a resonance speed map with changing rigid mode resonance speeds.This paper treats the influence of shaft speed and temperature on bearing gaps from which rigid mode resonance speeds for a shaft spinning in a bearing system are derived. The quoted influence of centrifugal load and temperature on bearing stiffness, damping and load capacity can be applied to any kind of gas bearing. Therefore the calculation of bearing stiffness, damping or load capacity is not treated in detail. The reader will be shown that there are simple design rules for air bearing systems and shafts of high-speed tooling spindles to avoid critical speeds through the entire speed range. Finally, methods of how to prove the initial design goals and how to verify dynamics of high-speed spindles in production will be presented to the reader. It will also be shown that there are production high-speed spindles available which do not include any critical speed within their speed range and thus show robust rotor dynamics with extremely low errors in motion.Procedures in design, validation and application treated in this paper shall give the reader not only design guidelines for spindles to avoid critical spindle speeds within its speed range, but also recommendations for machine tool builders and end-users for a machine operation taking machine and rotor dynamics into account. As the knowledge for this paper is predominantly based on the experience and work of the author himself only a few references are used. However presented testing results entirely confirm the approach presented in this paper.     

Dynamic stiffness and damping coefficients of aerodynamic tilting-pad journal bearings

The dynamic gas–film forces of aerodynamic bearing often can be characterized by eight linear stiffness and damping coefficients. How to theoretically predict these coefficients is a very difficult issue for tilting-pad gas bearing design because of its structural complexity. The current study presents a novel and universal theoretical analysis method for calculating the dynamic stiffness and damping coefficients of aerodynamic tilting-pad bearing. The gas–film pressure within the bearing is expressed in the form of dimensionless compressible gas-lubricated Reynolds equation, which is solved by means of the finite element method. With the assumption that the journal and the pads are disturbed with the same frequency, the dynamic coefficients of tilting-pad gas bearing are computed by using the partial derivative method and the equivalent coefficient method. Finally, the investigations are conducted about the effects of bearing number, perturbation frequency of the journal and the pads, eccentricity ratios, preload and length-to-diameter ratio of the bearing on the dynamic coefficients of aerodynamic tilting-pad journal bearing. The numerical results indicate that the dynamic stiffness and damping coefficients of tilting-pad gas bearing are closely related with these factors. The proposed analytical method provides a valuable means of predicting dynamic performances of tilting-pad gas bearing. The solution can be used for the purpose of prediction of dynamic behavior of the rotor systems supported by aerodynamic tilting-pad bearings.     

带钢冷轧闭环反馈控制最优化算法程序开发

基于多变量最优化控制的带钢闭环反馈控制模型能够充分利用弯辊和轧辊倾斜等平直度控制机构对板形偏差进行控制。闭环反馈控制的目的是使带钢实测板形与目标板形一致,闭环反馈最优化算法程序能充分利用输入信息,全面考虑多个执行机构对板形的作用,避免各控制之间的相互影响,它是该模型准确计算板形调节量的关键。为了实现自主建立带钢冷轧生产线,对某厂1 700 mm四机架四辊冷连轧机第四机架闭环反馈控制进行深入研究,根据对偶法采用C语言开发出基于多变量最优化闭环反馈计算程序并将其嵌入到可编程逻辑控制器(Programmable logic controller,PLC)中,开发出自主的基于多变量最优化闭环反馈控制模块。由该模块计算的闭环反馈平直度执行机构调节量与采用Matlab工具箱Quadprog函数计算结果一致,计算精度高。     

磁悬浮轴承非定向差动控制方式研究

提出非定向差动控制方式,通过独立控制各差动磁极对,提高参与控制的最少差动磁极对数量,以提高磁悬浮轴承的承载能力。以16极径向磁悬浮轴承为例,详细介绍了非定向差动控制方式与常规差动控制方式,对比了两种控制方式的等效刚度和等效阻尼、复刚度和复阻尼、名义承载力等支承性能。通过高速旋转试验验证两种控制方式下系统的控制性能。理论分析结果表明,采用非定向差动控制方式时,磁悬浮轴承的承载能力提高了8.24%,最大承载力提高了30.657%。试验结果表明,采用非定向差动控制方式时,系统具有更好的控制效果。     

Vibration from a shaft-bearing-plate system due to an axial excitation of helical gears

In this paper, a simplified model is studied to predict analytically the vibration from the helical gear system due to an axial excitation of helical gears. The simplified model describes gear, shaft, bearing, and housing. In order to obtain the axial force of helical gears, the mesh stiffness is calculated in the load deflection relation. The axial force is obtained from the solution of the equation of motion, using the mesh stiffness. It is used as a longitudinal excitation of the shaft, which in turn drives the gear housing through the bearing. In this study, the shaft is modeled as a rod, while the bearing is modeled as a parallel spring and damper only supporting longitudinal forces. The gear housing is modeled as a clamped circular plate with viscous damping. For the modeling of this system, transfer matrices for the rod and bearing are used, using a spectral method with four pole parameters. The model is validated by finite element analysis. Using the model, parameter studies are carried out. As a result, the linearized dynamic shaft force due to the gear excitation in the frequency domain was proposed. Out-of-plan displacement from the forced vibrating circular plate and the renewed mode normalization constant of the circular plate were also proposed. In order to control the axial vibration of the helical gear system, the plate was more important than the shaft and the bearing. Finally, the effect of the dominant design parameters for the gear system can be investigated by this model.     

Vibration analysis on the rolling element bearing-rotor system of an air blower

Air blowers are widely used in industry. The vibration of the rolling bearing-rotor is a key factor in the blower’s performance because it significantly influences the security and working life of the whole system. In previous research on the vibration characteristics of the air blower, the supporting rolling element bearing was always simplified as a particle on a shaft with radial stiffness and damping coefficient. Such simplification neglects the effects of the bearing structure on the vibration performance of the rotor system. In this paper, a numerical model of the bending stiffness of the tapered roller bearing was established through mechanics and deformation analysis. On the base of the model, a new TMM (transfer matrix method) for bearing-rotor system was established; the new TMM considers the influences of the bearing structure on the vibration of the rotor system. Furthermore, modal analysis on an air blower rotor system was carried out by using the new TMM, and the mode shape, critical speed and unbalance response of the air blower system were obtained. The same blower rotor was also analyzed by FEM to verify the validation of the new TMM, showing that the new method proposed in this paper for vibration characteristics calculation of an air blower is credible.     

径向磁悬浮轴承参数不确定控制的研究

研究了基于状态空间算法的径向磁悬浮轴承参数不确定H∞ 控制 ,将磁悬浮轴承的位移和速度变量直接反馈 ,设计了H∞ 状态反馈控制器 ,解决了轴向重载磁悬浮轴承系统中的关联不确定性问题。仿真结果表明 ,在所考虑的参数不确定范围内控制系统具有鲁棒稳定性。     

Identifying Bearing Rotor-Dynamic Coefficients Using an Extended Kalman Filter

An extended Kalman filter is developed to estimate the linearized direct and indirect stiffness and damping force coefficients for bearings in rotor-dynamic applications from noisy measurements of the shaft displacement in response to imbalance and impact excitation. The bearing properties are modeled as stochastic random variables using a Gauss-Markov model. Noise terms are introduced into the system model to account for all of the estimation error, including modeling errors and uncertainties and the propagation of measurement errors into the parameter estimates. The system model contains two user-defined parameters that can be tuned to improve the filter's performance; these parameters correspond to the covariance of the system and measurement noise variables. The filter is also strongly influenced by the initial values of the states and the error covariance matrix. The filter is demonstrated using numerically simulated data for a rotor-bearing system with two identical bearings, which reduces the number of unknown linear dynamic coefficients to eight. The filter estimates the direct damping coefficients and all four stiffness coefficients correlated well with actual values, whereas the estimates the cross-coupled damping coefficients were the least accurate.     

多列组合角接触球轴承刚度和位移量

以滚动轴承动力学分析和滚道控制理论为基础,提出了应用Powell优化算法和Newton-Raphson算法相结合的方式计算非线性方程组,给出了预紧力和转速的多列组合角接触球轴承组合刚度相应程序。对7016A5轴承DBD组合的研究结果表明:预紧力和转速与单个轴承和轴承的组合刚度及位移量呈现非线性关系。轴承的组合轴向刚度小于单个轴承的轴向刚度,其径向刚度大于单个轴承的径向刚度。为实现预定的轴承动态性能,单双侧轴承内圈的间隙量须大于两侧轴承位移量之和。