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.

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.

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.

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.

The design, development, and manufacture of large wood/composite wind turbine rotors

Discusses a study conducted to determine the best development path for large wind turbine rotor design. Shape and number of blades, degrees of freedom allowed, and control strategy are considered. Manufacture and costs are also discussed. Two-bladed, stall-regulated, teetered rotors are more cost effective than three-bladed rotors. Single-bladed rotors can be even more cost-effective. No new manufacturing techniques are required. The most cost-effective rotor includes a hub constructed in wood/composite materials, bonded to the blades. There is strong incentive for the blade manufacturer to supply the complete rotor. (from author's abstract)

Characterising rotors for brushless doubly-fed machines (BDFM)

The brushless doubly fed machine (BDFM) is a robust alternative to the doubly fed induction generator (DFIG) which is widely used in wind turbines but suffers from failures associated with its brushes and sliprings. The rotor plays an important part in a BDFM, coupling the two stator fields. To date, the nested loop has been almost exclusively used in modern BDFMs, but this approach is not ideally suited to large machines in which a form wound rotor is likely to be preferable from a manufacturing point of view. This paper gives a comparative study of two rotor windings. The performance of the rotors has been predicted from theory for a frame size 160 BDFM. Actual rotors have been built, using identical rotor laminations, and tested, giving results which accord well with predictions. The results give insight into the design issues of rotors both from electrical and manufacturing viewpoints. ©2010 IEEE.

A comparison of cage and nested-loop BDFM rotors

The Brushless Double-Fed Machine (BDFM) is a type of variable speed generator or drive. Using theoretical analysis of simple BDFM rotors this paper establishes trends in how rotor structures determine the rotor's equivalent circuit resistance, leakage inductance and turns ratio. The variation in measured parameters of five prototype rotors is then analysed in light of the trends found. Both the theory and experimental results suggest a significant performance advantage in using cage+loops type rotors as opposed to the simple nested loop type more usually employed.

Effects of Boundary Layer Ingestion on the Aero-Acoustics of Transonic Fan Rotors

The use of boundary-layer-ingesting, embedded propulsion systems can result in inlet flow distortions where the interaction of the boundary layer vorticity and the inlet lip causes horseshoe vortex formation and the ingestion of streamwise vortices into the inlet. A previously-developed body-force-based fan modeling approach was used to assess the change in fan rotor shock noise generation and propagation in a boundary-layer-ingesting, serpentine inlet. This approach is employed here in a parametric study to assess the effects of inlet geometry parameters (offset-to-diameter ratio and downstream-to-upstream area ratio) on flow distortion and rotor shock noise. Mechanisms related to the vortical inlet structures were found to govern changes in the rotor shock noise generation and propagation. The vortex whose circulation is in the opposite direction to the fan rotation (counter-swirling vortex) increases incidence angles on the fan blades near the tip, enhancing noise generation. The vortex with circulation in the direction of fan rotation (co-swirling vortex) creates a region of subsonic relative flow near the blade tip radius which decreases the sound power propagated to the far-field. The parametric study revealed that the overall sound power level at the fan leading edge is set by the ingested streamwise circulation, and that for inlet designs in which the streamwise vortices are displaced away from the duct wall, the sound power at the upstream inlet plane increased by as much as 9 dB. By comparing the far-field noise results obtained to those for a conventional inlet, it is deduced that the changes in rotor shock noise are predominantly due to the ingestion of streamwise vorticity.

Effects of Boundary Layer Ingestion on the Aero-Acoustics of Transonic Fan Rotors

The use of boundary-layer-ingesting, embedded propulsion systems can result in inlet flow distortions where the interaction of the boundary layer vorticity and the inlet lip causes horseshoe vortex formation and the ingestion of streamwise vortices into the inlet. A previously-developed body-force-based fan modeling approach was used to assess the change in fan rotor shock noise generation and propagation in a boundary-layer-ingesting, serpentine inlet. This approach is employed here in a parametric study to assess the effects of inlet geometry parameters (offset-to-diameter ratio and downstream-to-upstream area ratio) on flow distortion and rotor shock noise. Mechanisms related to the vortical inlet structures were found to govern changes in the rotor shock noise generation and propagation. The vortex whose circulation is in the opposite direction to the fan rotation (counter-swirling vortex) increases incidence angles on the fan blades near the tip, enhancing noise generation. The vortex with circulation in the direction of fan rotation (co-swirling vortex) creates a region of subsonic relative flow near the blade tip radius which decreases the sound power propagated to the far-field. The parametric study revealed that the overall sound power level at the fan leading edge is set by the ingested streamwise circulation, and that for inlet designs in which the streamwise vortices are displaced away from the duct wall, the sound power at the upstream inlet plane increased by as much as 9 dB. By comparing the far-field noise results obtained to those for a conventional inlet, it is deduced that the changes in rotor shock noise are predominantly due to the ingestion of streamwise vorticity.