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.

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.

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.

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.

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.

Modal parameter determination and chatter prediction for blade whirling: a comparative study based on symmetric and asymmetric FRF

Whirling has been adopted for the cost-effective machining of blade-shape components in addition to traditional end milling and flank milling processes.To satisfy the requirements of rotary forming in the blade whirling process,the workpiece must be clamped at both ends in suspension and rotated slowly during machining,which complicates the dynamics.This study aims to identify the dynamic characteristics within the blade whirling operation and present strategies for stability prediction.In this study,the dynamic characteristics of a whirling system are modeled by assuming symmetric and asymmetric parameters.Theoretical prediction frequency response function(FRF)results are compared with experimental results.Moreover,semi-discretization stability lobe diagrams(SLDs)obtained using the dynamic parameters of these models are investigated experimentally.The results show that the asymmetric model is more suitable for describing the whirling system,whereas the symmetric model presents limitations associated with the frequency range and location of measuring points.Finally,a set of airfoil propeller blade whirling operations is conducted to verify the prediction accuracy.

On physical models in V.I.Gulyayev's three papers on drill string whirling and torsional vibrations

This paper introduces physical models of drill string whirling and torsional vibrations and analyses the physical models in V.I.Gulyayev's three papers on drill string whirling and torsional vibrations:“V.I.Gulyayev,L.V.Shevchuk,Drill string bit whirl simulation with the use of frictional and nonholonomic models,Journal of Vibration and Acoustics 138(1)(2016)011021”,“V.I.Gulyayev,L.V.Shevchuk,Nonholonomic dynamics of drill string bit whirling in a deep bore-hole,J Multi-body Dynamics 227(3)(2013)234–244”and“V.I.Gulyayev,SN Hudoliy,O.V.Glushakova,Simulation of torsion relaxation auto-oscillations of drill string bit with viscous and coulombic friction moment models,J Multi-body Dynamics 225(2011)139–152”.This work finds that the physical models described in these three papers are clearly incorrect.

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。

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.

Wind-induced instabilities and monitoring of wind turbine

This paper presents real-time monitoring data and analysis results of the non-stationary vibrations of an operational wind turbine. The advanced time-frequency spectrum analysis reveals varied non-stationary vibrations with timevarying frequencies, which are correlated with certain system natural modes characterized by finite element analysis. Under the effects of strong wind load, the wind turbine system exhibits certain resonances due to blade passing excitations. The system also exhibits certain instabilities due to the coupling of the tower bending modes and blade flapwise mode with blade passing excitations under the variation of wind speed. An analytical model is used to elaborate the non-stationary and instability phenomena observed in experimental results. The properties of the nonlinear instabilities are evaluated by using Lyapunov exponent estimation.

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.

面向多簇架构DSP的树匹配向量化算法

BWDSP是针对高性能计算设计的一款新型的处理器,采用多簇超长指令字体系结构和SIMD架构,有丰富的指令集.为充分利用BWDSP提供的向量化资源,迫切需要提出一种向量化算法.本文在open64基础上研究并实现了面向多簇超长指令字(VLIW)DSP的SIMD编译优化算法.算法基于OPEN64的中间语言WHIRL,能够充分地利用BWDSP丰富的硬件资源和向量化指令.最终实验结果表明,对于能够合成双字和单字的循环程序,该优化算法能够平均取得6倍和4倍的加速比.

Diagnosis and Treatment of the Vibration Fault of a Gas Turbine 6300kW

A gas turbine in a certain gas company didn't work normally because of its strong vibration.Although this turbine had been balanced repeatedly at low speed, the vibration amplitude and unbalance weight of the machine changed irregularly. The causes and characteristics of the vibration are discussed. According to the change of the critical speed and the characteristics of vibration, it is found that the vibration is caused by weakness of the tight force on the central rod of the rotor and the oil whirl of the back bearing of the compressor. After clearing these faults and balancing the rotor of the compressor at high speed, the turbine worksnormally again.

Rotordynamic forces generated by discharge-to-suction leakage flows in centrifugal pumps

In order to investigate the flow-induced vibration in the shroud passage of centrifugal pump and predict rotordynamic forces of centrifugal pump rotor system, an analysis of rotordynamic forces arising from shrouded centrifugal pump is presented. CFD techniques were utilized to analyze the full three-dimensional viscous, primary/secondary flow field in a centrifugal pump impeller to determine rotordynamic forces. Multiple quasisteady solutions of an eccentric three-dimensional model at different whirl frequency ratios yielded the rotordynamic forces. The skew-symmetric stiffness, damping, and mass matrices were obtained by second-order leastsquares analysis. Simulation of the coupled primary/secondary flow field was conducted, and the complex flow characteristics in the flow field of a shroud passage were achieved including the mean velocity and pressure, as well as the eddy in a large scale of flow field due to viscosity. The rotordynainic force coefficients were calculated, and the resuhs were in good agreement with those of experiment except for the direct inertial coefficient without the consideration of whirling forces from the impeller primary flow passage.

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.

APPLICATION OF MECHANIZED MATHEMATICS TO ROTOR DYNAMICS

Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing model and Muszynska's dynamic model, the dynamical behavior of rotor-beating system and its stability of motion are investigated. As example, the concept of Wu characteristic set and Maple software, whirl parameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At the same time, stability of zero solution of Jeftcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration.

Dynamic Stability Study of Static Gas Bearing for Small Cryogenic Turbo-Expander

An experimental method is presented to analyze the dynamic stability of the gas bearing for small cryogenic turbo-expanders. The rotation imbalance response and the shape of the rotor orbit were obtained for different speeds up to 110,000 rpm, and the critical speed of the rotor-bearing system was determined by a Bode diagram. An FFT signal analytical method was applied to identify the resonance frequency, and the waterfall plot was presented. During the whole process of speeding up to the designed speed of 110,000 rpm, the rotor-bearing works stably with no whirl instability, which is validated in a waterfall plot. Also, the tested rotor-bearing model was analyzed theoretically. It was proved that the experimental results were highly consistent with those of theoretical calculations. Thus the experimental method proposed here to analyze the dynamic stability of the gas bearing is feasible.

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.