Axially Loaded Timoshenko Rotors From A Prestressed Continuum Approach

We consider an axially loaded Timoshenko rotor rotating at a constant speed and derive its governing equations from a continuum viewpoint. The primary aim of this paper is to understand the source and role of gyroscopic terms, when the rotor is viewed not as a Timoshenko beam but as a genuine 3D continuum. We offer the primary insight that macroscopically observed gyroscopic terms may also, quite equivalently, be viewed as external manifestations of internally existing spin-induced prestresses at the continuum level. To demonstrate this idea with an analytical example (the Timoshenko rotor), we have studied the reliable equations of Choi et al. (Journal of Vibration and Acoustics, 114, 1992, 249-259). Using a straightforward application of our insight in the framework of nonlinear elasticity, we obtain equations that exactly match Choi et al. for the case with no axial load. For the case of axial preload, our straightforward formulation leads to a slightly different set of equations that have negligible numerical consequence for solid rotors. However, we offer a macroscopic, intuitive, justification for modifying our formulation so as to obtain the exact equations of Choi et al. with the axial load included.

Natural Frequencies And Transient Responses Of 3-Phase Rotating Machine Windings

The analysis of transient electrical stresses in the insulation of high voltage rotating machines is rendered difficult because of the existence of capacitive and inductive couplings between phases. The Published theories ignore many of the couplings between phases to obtain the solution. A new procedure is proposed here to determine the transient voltage distribution on rotating machine windings. All the significicant capacitive and inductive couplings between different sections in a phase and between different sections in different phases have been considered in this analysis. The experimental results show good correlation with those computed.

Non-linear dynamic analysis of rotors by finite element method

Non-linear natural vibration characteristics and the dynamic response of hingeless and fully articulated rotors of rectangular cross-section are studied by using the finite element method. In the formulation of response problems, the global variables are augmented with appropriate additional variables, facilitating direct determination of sub-harmonic response. Numerical results are given showing the effect of the geometric non-linearity on the first three natural frequencies. Response analysis of typical rotors indicates a possibility of substantial sub-harmonic response especially in the fully articulated rotors widely adopted in helicopters.

Finite element analysis of rotors

A finite element formulation for the natural vibration analysis of tapered and pretwisted rotors has been presented. Numerical results for natural frequencies for various values of the geometric parameters and rotational speeds, have been computed for the case of rotors with and without pretwist. A Galerkin solution for the fundamental has also been worked out and has been used to provide a comparison for the finite element results. Charts for rapid estimation of the fundamental frequency parameter of tapered rotors, have been included.

A Five-Level Inverter Scheme for a Four-Pole Induction Motor Drive by Feeding the Identical Voltage-Profile Windings From Both Sides

This paper presents a five-level inverter scheme with four two-level inverters for a four-pole induction motor (IM) drive. In a conventional three-phase four-pole IM, there exists two identical voltage-profile winding coil groups per phase around the armature, which are connected in series and spatially apart by two pole pitches. In this paper, these two identical voltage-profile pole-pair winding coils in each phase of the IM are disconnected and fed from four two-level inverters from four sides of the windings with one-fourth dc-link voltage as compared to a conventional five-level neutral-point-clamped inverter. The scheme presented in this paper does not require any special design modification for the induction machine. For this paper, a four-pole IM drive is used, and the scheme can be easily extended to IMs with more than four poles. The proposed scheme is experimentally verified on a four-pole 5-hp IM drive.

Response, loads and stability of rotors with interconnected blades

An isolated rotor with blades interconnected through viscoelastic elements is analyzed for response, loads and stability in moment trim under forward flight conditions. A conceptual model of a multibladed rotor with rigid flap and lag motions is considered, Although the interconnecting elements are placed in the In-plane direction, considerable coupling between the flap-lag motions of the blades can occur in certain ranges of interblade element stiffness. Interblade coupling can yield significant changes in the response, loads and stability which are dependent on the interblade element and rotor parameters.

Influence of Phase Connection and Terminal Conditions on Natural Frequencies of Three-Phase Transformer Windings

With the increasing use of extra high-voltage transmission in power system expansion, the manufacturers of power apparatus and the electric utilities are studying the nature of overvoltages in power systems due to lightning and, in particular, switching operations. For such analyses, knowledge of the natural frequencies of the windings of transformers under a wide variety of conditions is important. The work reported by the author in a previous paper is extended and equivalent circuits have been developed to represent several sets of terminal conditions. These equivalent circuits can be used to determine the natural frequencies and transient voltages in the windings. Comparison of the measured and the computed results obtained with a model transformer indicates that they are in good agreement. Hence, this method of analysis provides a satisfactory procedure for the estimation of natural frequencies and transient voltages in transformer windings.

Natural Frequencies of 3-Pkase Transformer Windings

Natural frequencies and surge response of the windings of 3-phase transformers have been determined in the past by neglecting the capacitive and inductive couplings between the phase windings. This paper shows that these assumptions are not valid and presents a new method of formulating equivalent networks of 3-phase transformer windings for the various winding connections and terminal conditions. By utilizing these equivalent networks the natural frequencies and surge response of the windings can be determined. Tests made on a model transformer showed good correlation with calculated results.

Partition function for hindered, one-and multi-dimensional rotors

Writing the hindered rotor (hr) partition function as the trace of (rho) over cap = e(-beta(H) over cap hr), we approximate it by the sum of contributions from a set of points in position space. The contribution of the density matrix from each point is approximated by performing a local harmonic expansion around it. The highlight of this method is that it can be easily extended to multidimensional systems. Local harmonic expansion leads to a breakdown of the method a low temperatures. In order to calculate the partition function at low temperatures, we suggest a matrix multiplication procedure. The results obtained using these methods closely agree with the exact partition function at all temperature ranges. Our method bypasses the evaluation of eigenvalues and eigenfunctions and evaluates the density matrix for internal rotation directly. We also suggest a procedure to account for the antisymmetry of the total wavefunction in the same. (C) 2012 Elsevier B.V. All rights reserved.

Stability Of Large Damped Flexible Spacecraft With Stored Angular Momentum

Vibrational stability of large flexible structurally damped spacecraft carrying internal angular momentum and undergoing large rigid body rotations is analysed modeling the systems as elastic continua. Initially, analytical solutions to the motion of rigid gyrostats under torque-free conditions are developed. The solutions to the gyrostats modeled as axisymmetric and triaxial spacecraft carrying three and two constant speed momentum wheels, respectively, with spin axes aligned with body principal axes are shown to be complicated. These represent extensions of solutions for simpler cases existing in the literature. Using these solutions and modal analysis, the vibrational equations are reduced to linear ordinary differential equations. Equations with periodically varying coefficients are analysed applying Floquet theory. Study of a few typical beam- and plate-like spacecraft configurations indicate that the introduction of a single reaction wheel into an axisymmetric satellite does not alter the stability criterion. However, introduction of constant speed rotors deteriorates vibrational stability. Effects of structural damping and vehicle inertia ratio are also studied.

A New Three-Phase Current Source Inverter with Flexible PWM Capability

A new three-phase current source inverter topology is presented, consisting of three single-phase bridge inverters connected in series and feeding the isolated windings of a standard three-phase induction motor. Because a current zero in one phase now does not affect the others, it enables the implementation of a wide range of current PWM patterns for the reduction and selective elimination of torque pulsations. Furthermore, this system allows for very fast control of the fundamental load current through the use of sinusoidal PWM, a method that was not possible to implement on existing inverter topologies.

Fast Accurate Transient Stability Simulations

The paper describes a Simultaneous Implicit (SI) approach for transient stability simulations based on an iterative technique using traingularised admittance matrix [1]. The reduced saliency of generator in the subtransient state is taken advantage of to speed up the algorithm. Accordingly, generator differential equations, except rotor swing, contain voltage proportional to fluxes in the main field, dampers and a hypothetical winding representing deep flowing eddy currents, as state variables. The simulation results are validated by comparison with two independent methods viz. Runge-Kutta simulation for a simplified system and a method based on modelling damper windings using conventional induction motor theory.

Modified current source inverter fed induction motor drive with reduced torque pulsations

A new technique for reducing the torque pulsations in a conventional current source inverter fed induction motor drive is presented. This does not attempt to improve the current waveforms, but modifies the airgap MMF directly. This is based on the use of a motor with two sets of balanced phase windings, with a 30 electrical degree phase difference between them, and each set being fed from a conventional current source inverter. The two inverters are further connected in series so that they can operate from the same current source. As a consequence of this arrangement, the voltage rating of the components of each inverter is reduced, along with reduced torque ripple. This scheme has been experimentally verified and compared with the performance of a conventional scheme.

Use of Multiblade Coordinates for Helicopter Flap-Lag Stability with Dynamic Inflow

Rotor flap-lag stability in forward flight is studied with and without dynamic inflow feedback via a multiblade coordinate transformation (MCT). The algebra of MCT is found to be so involved that it requires checking the final equations by independent means. Accordingly, an assessment of three derivation methods is given. Numerical results are presented for three- and four-bladed rotors up to an advance ratio of 0.5. While the constant-coefficient approximation under trimmed conditions is satisfactory for low-frequency modes, it is not satisfactory for high-frequency modes or for untrimmed conditions. The advantages of multiblade coordinates are pronounced when the blades are coupled by dynamic inflow.