Modal balancing of flexible rotors without test runs: An experimental investigation

In all methods of balancing flexible rotors currently in use (modal balancing and influence coefficient techniques) test masses and test runs are required for the calculation of correction masses. In the modal balancing procedure suggested by Gasch and Drechsler [1] a simple identification method is used to find the generalized unbalances without test runs. In this paper the Gasch and Drechsler balancing procedure is reported and extended to multibearing rotors with initial shaft bow. Systematic experiments done on two test rotors are described. The results show that flexible shafts mounted in ball bearings can be balanced with very good results. Even rotors in fluid film bearings, exceeding the scope of modal theory, were balanced with good results.     

Modal characteristics of a flexible beam with multiple distributed actuators

A flexible structure with surface-bonded piezoceramic patches is modelled using Timoshenko beam theory. Exact mode shapes and natural frequencies associated with the flexural motion are computed for various piezoceramic distributed actuator arrangements. The effects of patch placement and of shear on the modal characteristics are demonstrated using a cantilevered beam as an example. Perfect bonding of the piezoceramic to the beam substructure is assumed, and for the purposes of this paper only passive piezoceramic properties are considered. The modelling technique and results obtained in a closed form are intended to assist investigations into the modelling and control of active structures with surface-bonded piezoceramic actuators.     

Secondary critical speed of flexible rotors with inertia slots

Rotors of two-pole generators have longitudinal slots for the electric windings and thus have dual flexural rigidity. Second order (or twice per revolution) forced vibrations are excited by the weight of the rotor and the problem of secondary critical speed, at half of the normal critical speed, arises. To overcome this difficulty transverse saw cuts or inertia slots are made in the pole faces in order to restore equality of the flexural rigidity of the rotor. In this paper, the critical speeds of rotors with inertia slots are calculated by using the transfer matrix method. The flexural rigidity of the element used in the transfer matrix method is determined by a three-dimensional finite element method. The secondary critical speeds of asymmetric rotors with inertia slots were measured experimentally thus demonstrating the validity of the present analysis.     

Non-linear dynamics of flexible multi-bearing rotors

A general analysis has been developed to computer simulate steady state and transient vibration phenomena of complex rotor-bearing-support systems. A central feature of this analysis is a proper handling of various highly non-linear effects (most notably journal bearings) which dominate the dynamic phenoména encountered during large amplitude rotor-bearing vibrations. There are a number of potential causes of large amplitude rotor vibration, such as high rotor imbalance (e.g., loss of turbine blades at running speed), critical speed operation, journal bearing dynamic instability (oil whip), earthquakes, and shock. Failure mode analysis requires the evaluation and understanding of such potentially large dynamic forces and displacements. The paper presents development of the analysis, comparison with experiment and examples of its use in industrial applications.     

Acceleration of unbalanced flexible rotors through the critical speeds

The bending vibrational behaviour of a flexible rotor with a continuous mass distribution passing its critical speeds under a driving torque is considered. It is shown that the (non-linear) equations of motion for an actual shaft can be formally traced back to those of a Laval rotor. In this way, the results for a Laval rotor, which, in an earlier publication by the authors [1], have been presented generally for constant load torque can be applied to actual rotors. The system parameters of the Laval rotor merely have to be replaced by the generalized parameters of the respective bending modes. A special study shows that the effect of the torsional flexibility of the shaft on the bending vibrational behaviour is negligible.     

Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment

The effect of misalignment on the stability of two rotors connected by a flexible mechanical coupling subjected to angular misalignment is examined. The study performed is to understand the effect of angular misalignment on the stability of rotating machinery. The dimensionless stability criteria of the non-linear system of differential equations of two misaligned rigid rotors are derived using Liapunov's direct method. A rigid disk is attached at the middle of each rotor, where the rotor-disk assembly is mounted on two hydrodynamic bearings with four stiffness and four damping coefficients. Sets of dimensionless conditions for sufficient whirl stability of the two misaligned rotors are derived. The stability conditions are presented in graphical form for deeper understanding of the effect of the flexible mechanical coupling stiffness and angular misalignment on rotating machinery stability. The results show that an increase in angular misalignment or mechanical coupling stiffness terms leads to an increase of the model stability region.     

A theoretical introduction to the development of a unified approach to flexible rotor balancing

Several successful methods for balancing flexible rotating shafts have been developed in recent years, whose relative merits have been the subject of much debate and argument. These methods can be separated into two, seemingly distinct, groups which can be concisely identified as modal balancing and influence coefficient techniques. The present authors consider that in practice many of the differences are more apparent rather than real and that the time has arrived for an attempt to reconcile the differences and hopefully to synthesize a method which includes the best features of both methods. This paper reviews the theoretical basis for this programme. The results of a preliminary experimental exploration have been recorded elsewhere.     

弓张式超磁致伸缩材料换能器的设计与分析

为了提高超磁致伸缩换能器的作动行程,以获得足够大的发音强度,并使之满足发音装置体积小、装配零件少的要求,结合超磁致伸缩材料（GMM）的优良特性,提出一种基于三角放大原理的弓张式GMM换能器。该换能器以GMM棒作为驱动元件,通过固定弓张结构的一端,将双向输出转变为单向输出,同时利用柔性铰链结构,进一步增大换能器的位移输出。通过分析换能器的工作原理,计算得到其理论放大倍数为2.73,与所建立的有限元仿真模型计算得到的放大倍数2.8相近。制作了试验样机并搭建了相应的试验系统,得到在1 kHz范围内换能器最大输出位移为15.5 m,与仿真结果14.058 m相近。提出的弓张结构实现了换能器的位移放大,相应的分析方法也较好地反映了换能器的输出特性。     

Natural frequencies of a shaft with periodically placed rotors and bearings

Flexural and torsional natural frequencies of a shaft with periodically placed rotors and bearings are investigated by using a “wave approach”. By a judicious choice of parameters, it is possible to obtain ranges of operating speed that are free from both flexural and torsional resonances. Suggestions for widening such speed ranges are included.     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

弓张式超磁致伸缩材料换能器的设计与分析

为了提高超磁致伸缩换能器的作动行程,以获得足够大的发音强度,并使之满足发音装置体积小、装配零件少的要求,结合超磁致伸缩材料（GMM）的优良特性,提出一种基于三角放大原理的弓张式GMM换能器。该换能器以GMM棒作为驱动元件,通过固定弓张结构的一端,将双向输出转变为单向输出,同时利用柔性铰链结构,进一步增大换能器的位移输出。通过分析换能器的工作原理,计算得到其理论放大倍数为2.73,与所建立的有限元仿真模型计算得到的放大倍数2.8相近。制作了试验样机并搭建了相应的试验系统,得到在1 kHz范围内换能器最大输出位移为15.5 m,与仿真结果14.058 m相近。提出的弓张结构实现了换能器的位移放大,相应的分析方法也较好地反映了换能器的输出特性。     

Dynamics of load balancing with constraints

In this paper, we consider a centralized strategy for scheduling charging patterns of electrical vehicles and other batteries in power grids. We formulate it as a load balancing problem with constraints, which tries to distribute the charging loads both spatially and temporally. We show that a variant of herding system can be applied to load balancing.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

A review of upstream and bow shock energetic-particle measurements

Summary Measurements of energetic electrons and protons frequently observed in the interplanetary medium upstream from the bow shock are reviewed. Bursts of electrons with energy 0.5 to 100 keV and duration 1 to 100s (termed “spikes”) appear when the spacecraft is on a field line which is tangent to the bow shock surface. The electrons move upstream in a thin, curved sheet lying nearly along the interplanetary-magnetic-field direction. The thinness of the electron sheet shows that the electrons are accelerated only in a small region about the curve of tangency of the interplanetary magnetic field and the bow shock surface. The upstream ions, on the other hand, occupy a much larger spatial region. Some of the upstream ions, particularly those at the energies above 100 keV, may have magnetospheric origin. The mechanism of the ion acceleration is still not known nor is it ruled out that acceleration in the upstream region may take place. A variety of plasma waves is excited by the upstream particles.

---

Riassunto Si riesaminato misurazioni di elettroni e protoni energetici frequentemente osservati nel mezzo interplanetario a monte dell'onda d'urto. Esplosioni di elettroni con energia da 0.5 a 100 keV e durata da 1 a 100 s (chiamate ?spikes?) appaiono quando la navicella spaziale è su una linea di campo che è tangente alla superficie dell'onda d'urto. Gli elettroni si spostano a monte in uno strato sottile e curvo che giace quasi lungo la direzione del campo magnetico interplanetario. La sottigliezza dello strato elettronico mostra che gli elettroni sono accelerati solo in una piccola regione intorno alla curva di tangenza fra il campo magnetico interplanetario e la superficie dell'onda d'urto. Gli ioni a monte, d'altra parte, occupano una regione di spazio molto più ampia. Alcuni di questi ioni a monte, particolarmente quelli a energia superiori a 100 keV, possono avere origine magnetosferica. Il meccanismo di accelerazione degli ioni non è ancora noto, nè è escluso che nella regione a monte possano verificarsi accelerazioni. Una certa varietà di onde di plasma è eccitata dalle particelle a monte.

---

Резюме Анализируются свойства энергетичных энектронов и протонов, наблюденных в межпланетной среде и (по крайней мере в течение многих часов) ускоренных либо в, либо вдоль поверхности ударных волн. Наблюдались усиления потоков электронов с энергией от 0.5 до 100 кэВ с малой длительностяю (от секунд до минуты), когда космический аппарат находится на линии магнитного поля, которая касается ударной волны сжатия. Эти всплески обычно имеют место, когда интенсивность протонов сходных энергий либо увеличивается, либо уменьшается; а также во времена, когда протонный поток остается, по существу, постоянным в течение многих минут или даже часов. Эти волны возбуждаются в межпланетной среде частицами больших энергий.

     

Fluorescent molecular rotors with specific hydrophilic functions: Glucosamine and inositol derivatives

New fluorescent molecular rotors having hydrophilic functional groups (such as a sugar or an inositol group) were synthesized. The aim was to obtain impermeant and uncharged probes, with a defined orientation within a model membrane bilayer or in a cell membrane. Their fluorescence properties, which are dependent on solvent polarity and viscosity, were successfully applied to characterize organized media: for example, the CMC of surfactants and the transition temperature of DPPC liposomes were evaluated.