THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=0.The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions satisfy.Furthermore,the exact bound of a special case is given using the Chebyshev system.At the end,some numerical simulations are given to illustrate the existence of limit cycles.

Gas Temperature Distribution and Fluctuation in a Lab-Scale Fire Whirl

Fire whirls cause an increase in fire damage. This study clarified the unsteady behavior of fire whirls, considering that instantaneous changes in the temperature and flame shape of fire whirls can affect the damage to the surrounding area. Numerical simulations of a lab-scale flame that simulates a fire whirl were performed to investigate the changes in gas temperature and velocity fields under various fuel inflow velocities. The flow field was obtained by solving a continuity equation and a three-dimensional Navier-Stokes equation, and the turbulence was resolved using a large eddy simulation. A chemical equilibrium partially premixed combustion model was used, and radiation effects were considered. The time-averaged gas temperature distribution along the burner central axis revealed that the gas temperature decreased monotonically from upstream to downstream. The time-averaged velocity distribution along the burner central axis showed that the velocity decreased as one moved downstream, but the decrease was uneven. The time variation of the gas temperature demonstrated that the higher the fuel inflow velocity, especially near the burner, the greater the gas temperature flutter. Furthermore, the larger the fuel inflow velocity, the larger the flame swell and wobble. The results showed that the fuel inflow velocity affected temperature fluctuation and flame undulating movement.

WHIRL SSA:一种基于高级中间表示的优化结构

中间表示对编译器的性能、效率和可扩展性都起着决定性作用.Open64编译器采用一种树型结构的中间表示WHIRL,能表示各种高级控制流结构,但不能显式的提供数据流信息.本文基于WHIRL对SSA(Static Single Assignment)进行扩展,提出了一个新的优化结构WHIRL SSA.WHIRL SSA通过将SSA信息标注在WHIRL节点上,显式的为数据流分析提供使用-定义(UD)信息.相比于传统的数据流信息构建方法,WHIRL SSA提供了更精确、有效的数据流信息.本文讨论了WHIRL SSA的设计与实现和基于WHIRL SSA的优化.

BWDSP SIMD指令的WHIRL中间表示生成研究

WHIRL是Open64采用的一种通用的中间表示,支持多种高级语言和多种目标机。Open64的后端优化工作都是基于WHIRL设计的。BWDSP是一款支持SIMD指令的数字信号处理器,SIMD指令能够提高该处理器的指令并行性。SIMD优化也需要产生WHIRL中间表示,本文对如何产生BWDSP SIMD指令的WHIRL中间表示进行了研究,并在BWDSP的编译器OCC上得以实现。

Research on the Interannual Variability of the Great Whirl and the Related Mechanisms

Based on AVISO （archiving, validation and interpretation of satellite data in oceanography） data from 1993 to 2010, QuikSCAT （Quick Scatterometer） data from 2000 to 2008, and Argo data from 2003 to 2008, the interannual variability of the Great Whirl （GW） and related mechanisms are studied. It shows that the origin and termination times of the GW, as well as its location and intensity, have significant interarmual variability. The GW appeared earliest （latest） in 2004 （2008） and vanished ear- liest （latest） in 2006 （2001）, with the shortest （longest） duration in 2008 （2001）. Its center was most southward （northward） in 2007 （1995）, while the minimum （maximum） amplitude and area occurred in 2003 and 2002 （1997 and 2007）, respectively. The GW was weaker and disappeared earlier with its location tending to be in the southwest in 2003, while in 2005 it was stronger, van- ished later and tended to be in northeast. The abnormal years were often not the same among different characters of the GW, and were not all coincident with ENSO （El Nifio-Southern Oscillation） or IOD （Indian Ocean Dipole） events, indicating the very com- plex nature of GW variations. Mechanism investigations shows that the interannual variability of intraseasonal wind stress curl in GW region results in that of the GW. The generation of the GW is coincident with the arrival of Rossby waves at the Somali coast in spring; the intensity of the GW is also influenced by Rossby waves. The termination of the GW corresponds well to the second one of the top two peaks in the baroclinic energy conversion rate in GW region, and the intensity and the position of the GW are also closely related to the top two baroclinic energy conversion rates.

Effect of suppressing dust by multi-direction whirling air curtain on fully mechanized mining face

A combined method of numerical simulation and field testing was adopted in this study in the interest of solving the problem of hard to control high concentrate dusts on a fully mechanized mining face. In addi- tion, the dust suppression effect of a multi-direction whirling air curtain was studied in this paper. Under the influence of the wall attachment effect, the compressed air which blows out from the two-phase or three-phase radial outlets on the generator of the air curtain can form a multi-direction whirling air curtain, which can cover the whole roadway section of a fully mechanized mining face. The traditional method of controlling dust is a forcing system with exhaust overlap which has the major disadvantage of lacking a jet effect and consequently results in poor dust control. It is difficult to form the air flow field within the range of Lp ≤ 5√S. However, due to the effect of this novel system, the radial airflow can be turned into axial airflow allowing fresh air to flow through the length of the heading. The air flow field which is good at controlling dust diffusion can be formed 12.8 m from the heading face. Furthermore, the field measurement results show that before the application of a multi-direction whirling air curtain, the dust concentration is 348.6 mg/m^3 and 271.4 mg/m^3 respectively at the roadway cross-section measurement points which are 5 m and 10 m from the heading face. However, after the application of the multi-direction whirling air curtain, the dust concentration is only 61.2 mg/m3 and 14.8 mg/m^3, respectively. Therefore, the dust control effect of a multi-direction whirling air curtain is obvious.

Simulation Research on Oil Whirl Fault in a High-speed Rotor-bearing System

Under the sliding bearing support for the rotor-bearing system, the dynamic model of a rotor-bearing system is established under the action of non-linear oil film force. The rotor-bearing system has been studied by the application of nonlinear dynamics theory, and the system＇s response was obtained by the numerical integration approach. The effects of eccentricity, speed, lubricant viscosity, radius gap, bearing length and journal radius on the system＇s response have been studied by using an amplitude-frequency curve, three-dimensional spectrum and bifurcation, which provides a theoretical basis for the diagnosis of the oil whirl fault effectively in the rotor-bearing system supported by a sliding bearing.

NONLINEAR ANALYSIS OF A CRACKED ROTOR WITH WHIRLING

Nonlinear dynamics of a cracked rotor with whirling were analyzed and were compared to a rotor without whirling. Distinct differences have been found in bifurcation, amplitude, orbit and Poincare map when carrying on this comparison. Complicated dynamics may be found when a cracked rotor has its whirling speed. The results revealed may be useful in crack-early-detection and diagnosis.

Influences of the Great Whirl on surface chlorophyll a concentration off the Somali Coast in 2017

The general features of the Great Whirl(GW)off the Somali Coast in 2017 and its influences on chlorophyll a(Chl a)concentration were studied by using satellite data and model outputs.Results show that GW,which initiated at7°N,53°E on June 13,had a lifetime of 153 d with an average amplitude of 16 cm and an average radius of 205 km.After the formation of GW,the concentration of Chl a in the interior of GW showed a downward trend throughout its life cycle,except in early July and mid-October.In early July,the Chl a blooms in the interior of GW were attributed to the combined effect of three processes.They are eddy horizontal transportation,the deepening of the mixed layer caused by the monsoon and eddy pumping,and the upward transportation of nutrients caused by eddy-induced Ekman pumping.In October,the Chl a blooms were probably due to the weakening of GW.During the period,water exchange occurred more frequently across the eddy,thus phytoplanktons were imported into the interior of GW.

Whirl Interaction of a Drill Bit with the Bore-Hole Bottom

This paper deals with the theoretic simulation of a drill bit whirling under conditions of its contact interaction with the bore-hole bottom rock plane. The bit is considered to be an absolutely rigid ellipsoidal body with uneven surface. It is attached to the lower end of a rotating elastic drill string. In the perturbed state, the bit can roll without sliding on the bore-hole bottom, performing whirling vibrations (the model of dynamic equilibrium with pure rolling when maximum cohesive force does not exceed the ultimate Coulombic friction). To describe these motions, a nonholonomic dynamic model is proposed, constitutive partial differential equations are deduced. With their use, the whirling vibrations of oblong and oblate ellipsoidal bits are analyzed, the functions of cohesive (frictional) forces are calculated. It is shown that the system of elastic drill string and ellipsoidal bit can acquire stable or unstable whirl modes with approaching critical Eulerian values by the parameters of axial force, torque and angular velocity. The analogy of the found modes of motions with ones of the Celtic stones is established. It is shown that the ellipsoidal bits can stop their whirling vibrations and change directions of their circumferential motions in the same manner as the ellipsoidal Celtic stones do. As this takes place, the trajectories of the oblate ellipsoidal bits are characterized by more complicated paths and irregularities.

Frequency Analysis of Drill Bit Whirlings on Uneven Bottoms of Deep Bore-holes

An incipient stage of a rotating drill string bit whirl motion proceeding on a well bottom surface is studied on the basis of kinematic （nonholonomic） models of mechanic interaction between the contacting uneven bodies. The bit is considered to be an absolutely rigid spherical or ellipsoidal body, the well bottom surface can be plane or spherical. It is assumed that the system coaxiality is disturbed through small initial curvature of the drill string, imperfections of the bit and bore-well geometry or the system mass debalance. Linearized equations of the bit whirling are deducted, the frequencies of periodic motions are calculated, and their modes are constructed for different geometric parameters of the spherical and ellipsoidal bits. It is demonstrated that, depending on the system properties, the bit motion can acquire the regimes of forward and backward whMings or to transit to the state of stationary spinning relative to an immovable center of velocities. The most unfavorable and atypical whirling modes are characteristic for oblate eilipsoidal bits and curvilinear surfaces of the well bottom.

Structural stability estimation of whirling unit

Whirling is a cutting process in which a series of cutting edges on whirling ring remove material by turning over a rotating workpiece. In this study static and dynamic stability of whirling unit was estimated by using ADAMS and NASTRAN softwares. Each maximum force acting on the bearing attached to the spindle assembly and the cutting tool attached to the whirling ring with the rotating speed of 6 000 r/min was 235 N and 902 N respectively. The maximum stress of 0.74 MPa on the base frame is far smaller than the yield strength of 282 MPa. The calculated natural frequency of 148 Hz of the system is far from the frequency of the driving speed of 6 000 r/min. The experimentally obtained maximum cutting force of 792 N is smaller than that of calculated value. And the experimentally obtained natural frequency of 118 Hz is beyond the driving speed of 6000 r/min. From above results it can be judged that the whirling system is statically and dynamically stable.

螺旋桨发动机安装系统动力学设计技术综述

随着螺旋桨发动机安装系统国产化研制进程的加快,需要开展相关的安装系统技术研究,而动力学设计是其中的重要组成部分。本文对比分析了不同结构形式安装系统的动态性能特点,进一步从军民用标准规范和工程实践经验出发,归纳了安装系统动力学设计的技术要求,梳理了安装系统动力学设计技术的发展历程和国内外现状,指出国内外差距主要体现在设计理念、关键技术和应用实践经验等方面。在此基础上,展望了螺旋桨发动机安装系统动力学设计技术的发展趋势,为当前及未来螺旋桨发动机安装系统的设计技术研究提供了参考。

特深井钻柱动力学特性模拟与分析

随着钻井深度不断增加,钻柱运动所涉及的力学问题变得更加复杂,钻柱动力学特性模拟及分析可为安全优质高效钻井提供支撑。为了探求特深井钻柱的运动特性,将钻柱运动的控制方程采用Newmark法对时间离散后,运用SOR节点迭代法,对每一时间步的钻柱整体构形进行求解,实现了总长超9000 m的钻柱动力学特性模拟,不仅给出了钻柱4个典型位置的涡动轨迹、涡动速度和横向加速度,还分析了钻柱的粘滑特性。分析结果表明,上部钻柱的涡动及粘滑现象不明显;随着位置下移,出现不规则涡动及不充分粘滑现象;近钻头位置的钻柱会出现较剧烈涡动,也会出现粘滑振动;中性点位置处钻柱的涡动最为剧烈、碰摩严重,可能给钻柱带来安全隐患。研究结果为特深井安全钻井提供了理论依据。

Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

基于空间耦合传输方法的FBG传感器转子涡动测温误差及其影响因素研究

针对电机转子涡动对光纤光栅温度监测系统精度产生的影响,采用光纤光栅(FBG)的传输矩阵理论和自聚集透镜的耦合损耗理论,建立了涡动条件下FBG扫描光谱模型,结合相关试验,研究了扫描光谱的畸变规律及系统测温误差的影响因素。结果表明:涡动导致扫描光谱反射峰发生偏移、3 dB带宽减小,通过协调涡动频率和解调仪扫描频率,使准直器间耦合损耗周期达到FBG光谱扫描时间的10倍以上(q>10)是保证较低测温误差的关键;同时,质心法对剧烈涡动条件下扫描光谱的寻峰效果明显优于高斯曲线拟合法。随着转子端面处的径向位移幅值或轴线偏角幅值的增大,系统的测温误差先缓慢地增大、后剧烈地增大;随着椭圆形轴心运动轨迹轴比的增大,测温误差先剧烈地增大、后缓慢地增大至稳定。当转子径向位移幅值小于200μm、轴线偏角幅值小于0.167°时,在轴比等于3、q值等于10条件下,15次采样试验反映出质心法和高斯曲线拟合法分别令系统的测温误差从2.9℃降低至0.6℃和1.1℃,为监测系统的应用与测温精度的预估提供了依据。

转子运动条件下光纤光栅的扫描光谱特性及测温误差研究

针对基于空间耦合传输方法的电机转子温度监测系统,采用光纤光栅的传输矩阵理论和自聚集透镜的耦合传输理论,建立了转子运动条件下光纤光栅(fiber Bragg grating,FBG)的扫描光谱模型,首先研究了扫描光谱的畸变规律及各算法的寻峰效果,结果表明:转子的涡动导致FBG扫描光谱的反射峰发生偏移,3 dB带宽减小,随着耦合损耗与原始反射峰之间的相位差发生变化,中心波长的最大扫描误差以类似正弦函数的规律发生变化,新反射峰位置由耦合损耗变化速率、FBG原始反射率及其变化速率之间的限定关系决定。协调解调仪扫描速率与转子涡动频率之间的数值关系是减轻光谱畸变的主要方法;此外,相比于半峰法和多种拟合型算法,质心法通过提取畸变光谱的重心也明显地减小了中心波长的扫描误差。然后,通过理论和试验研究了转子涡动频率与解调仪扫描频率对系统测温误差产生的影响,结果表明:随着耦合损耗周期与光谱扫描时间之比(q值)的增加,系统的最大测温误差先剧烈地减小、然后缓慢减小至稳定,令q>10是确保系统的测温误差及其波动较小的最低条件;对于转速小于200 000 r/min的转子(涡动频率小于1 667 Hz),当转子径向振动的幅值小于200μm、轴心轨迹的轴比小于3、轴心线偏转的角度小于0.1°时,采用扫描频率大于760 Hz的解调仪和质心寻峰法可以保证涡动引起的测温误差小于0.3℃,为转子测温系统的实际应用及测温误差的预估提供了依据。

Characteristics of dry friction backward whirl—A self-excited oscillation in rotor-to-stator contact systems

In this paper,the response characteristics of dry friction backward whirl of a general rotor/stator model,which accounts for both the dynamics of the rotor and the stator as well as the friction and the deformation at the contact surfaces,are investigated.The existence boundaries and the whirl frequencies of the dry friction backward whirl are determined analytically.It is found that there are two or three existence boundaries of the dry friction backward whirl that usually form two existence regions,either standing completely separately,or overlapping each other partly,or one containing the other completely,depending upon the system parameters.The whirl frequencies in the two existence regions are quite different and may jump between the lower and the higher values with the variation of the rotating speed.The results have been found to have good correspondence in the related rotor/stator rubbing experiments.

离心空压机波箔气体轴承设计及实验研究

针对功率26 kW、主轴径22 mm的氢燃料电池离心空压机,设计波箔动压气体轴承;在搭建的实验台上进行轴承静动态特性实验和耐久性实验,得到轴承滞回曲线和静态刚度曲线,以及空压机轴系升降速振动三维频谱图、30 000~95 000 r/min下的时域图。实验结果表明:研发的波箔动压气体轴承静态刚度与轴承位移具有非线性特性;空压机启停100 000余次后,平箔表面仅有轻微磨损,波箔高度几乎无变化,表明轴承具有良好的耐久性;转子振动以基频为主,全转速范围内主振幅为1μm左右,无明显低频和高频振动;两级气浮轴承离心空压机实验最高工作转速可达95 000 r/min,并且表现出良好的热力性能。

聚焦于碰摩诱导的非规则形貌套管磨损分析

由于钻磨铣作业管柱刚度低且受力情况复杂,发生涡动时不可避免会碰摩套管,诱导套管产生不连续、随机的磨损,降低井筒安全性。为研究碰摩磨损对套管安全性的影响规律,基于转子动力学理论建立了钻磨铣作业钻柱有限元动力学模型,得到钻柱涡动轨迹及钻柱涡动诱发的套管碰摩特征;同时建立了碰摩磨损体积计算模型,考察转速、钻压对碰摩诱导的套管磨损的影响规律;将碰摩磨损缺陷引入套管模型,采用应力集中比值分析碰摩磨损缺陷对套管承载性能的影响规律。研究结果表明:钻磨铣作业期间钻柱对套管的碰摩主要发生在下部钻具组合处,表现为不连续性碰摩和连续性碰摩2种形式;转速、钻压与碰摩磨损程度呈正相关关系;碰摩磨损缺陷的偏磨率、开口大小及数量会对套管承载性能产生不同的影响。研究结果可为由碰摩诱导产生的套管磨损分析及井筒完整性评价提供理论依据。