Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

A vibration analysis of a high-speed rotor-bearing system using the finite element is presented. Models were developed to study the effect of rotor mass and stiffness, support bearing stiffness, and bearing pedestal stiffness on rotor critical speeds. Bearing stiffnesses were obtained from a previously-developed computer program. Pedestal stiffnesses were obtained from a plane-stress finite element analysis. A rotor model which incorporated these bearing and pedestal stiffnesses was then analyzed using a three-dimensional finite element analysis to determine its critical speeds. Results of this analysis are compared to experimentally obtained data and discussed. Recommendations for future analyses, experimental developments, and rotor configurations are given. / Master of Science

No description available.

A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh. / Ph. D.

Helicopters are versatile vehicles that can vertically take off and land, hover, and perform maneuver at very low forward speeds. These characteristics make them unique for a number of civilian and military applications. However, the radial and azimuthal variation of dynamic pressure causes rotors to experience adverse phenomena such as transonic shocks and 3-D dynamic stall. Adverse interactions such as blade vortex interaction and rotor-airframe interaction may also occur. These phenomena contribute to noise and vibrations. Finally, in the event of an engine failure, rotorcraft tends to descend at high vertical velocities causing structural damage and loss of lives. A variety of techniques have been proposed for reducing the noise and vibrations. These techniques include on-board control (OBC) devices, individual blade control (IBC), and higher harmonic control (HHC). Addition of these devices adds to the weight, cost, and complexity of the rotor system, and reduces the reliability of operations. Simpler OBC concepts will greatly alleviate these drawbacks and enhance the operating envelope of vehicles. In this study, the use of Gurney flaps is explored as an OBC concept using a physics based approach. A three dimensional Navier-Stokes solver developed by the present investigator is coupled to an existing free wake model of the wake structure. The method is further enhanced for modeling of Blade-Vortex-Interactions (BVI). Loose coupling with an existing comprehensive structural dynamics analysis solver (DYMORE) is implemented for the purpose of rotor trim and modeling of aeroelastic effects. Results are presented for Gurney flaps as an OBC concept for improvements in autorotation, rotor vibration reduction, and BVI characteristics. As a representative rotor, the HART-II model rotor is used. It is found that the Gurney flap increases propulsive force in the driving region while the drag force is increased in the driven region. It is concluded that the deployable Gurney flap may improve autorotation characteristics if deployed only over the driving region. Although the net effect of the increased propulsive and drag force results in a faster descent rate when the trim state is maintained for identical thrust, it is found that permanently deployed Gurney flaps with fixed control settings may be useful in flare operations before landing by increasing thrust and lowering the descent rate. The potential of deployable Gurney flap is demonstrated for rotor vibration reduction. The 4P harmonic of the vertical vibratory load is reduced by 80% or more, while maintaining the trim state. The 4P and 8P harmonic loads are successfully suppressed simultaneously using individually controlled multi-segmented flaps. Finally, simulations aimed at BVI avoidance using deployable Gurney flaps are also presented.

Rotating blades, which are the most critical components of any turbo-machinery, need to be designed to withstand forced vibrations due to accidental tip rub impact against inner surface of casing. These vibrations are typically dependent on operating conditions and geometric parameters. In the current study, a rotor test rig with a maximum tip speed capability of 144 km/hr has been developed for studying the dynamic behavior of representative jet engine compressor blades actuated by the closure of clearance between the tip of a given rotating blade and a sector of the inner lining of the casing. Ten different blade profiles are chosen in the present research. The blades are obtained by lofting NACA GOE123 airfoil cross-section along different stacking axes. Rotor test rigs which simulate transient dynamic events require high frequency data acquisition systems like slip ring arrangement or telemetric transmission. While slip rings introduce noise into the signal, the telemetric transmission works out to be rather expensive. To circumvent the stated shortcomings of data acquisition systems, a novel rotor-mounted data acquisition system has been implemented here which captures dynamic strains in vibrating blades during operation. The current data acquisition system can store data for duration of five seconds with a sampling rate of 35 kHz. It has been calibrated with four standard tests, and provides a simple and efficient mode of data capturing. Three blades with airfoil sections (a flat beam-type blade of uniform rectangular cross-section, a blade with twisted cross-sections stacked along a straight line, and a blade similar to the latter but with a curved stacking axis) are tested under controlled rub conditions at four different speeds. The maximum test speed is restricted to 800 rpm for reasons of safety although the set-up is designed to operate up to a maximum speed of 2000 rpm. For each of the rotor speeds, a blade is tested for three to four different stagger angles in the range of 0o-30o. By plotting the RMS values of measured dynamic responses with respect to stagger angle for a given rotor speed, it has been observed, perhaps for the first time in published literature, that a stagger angle of around 20o yields the maximum RMS value of strain response. A major objective of the current study has been to utilize the data generated in the tip rub impact tests for validating a predictive numerical model of the test set-up using explicit finite element analysis. To this end, a finite element model of the rotor rig inclusive of a rotor with two blades and the static frame structure is developed and analyzed using an explicit LS-DYNA solver. This model is calibrated with the test results of the three blade designs described above. In particular, it has been shown that the frequency contents of the measured dynamic strain responses agree quite well with frequencies obtained from the numerically computed responses. It has been found in the experimental responses that a given blade vibrates with two main frequencies: one corresponding to the first natural frequency of the rotor-blade system during the tip-rubbing phase (which lasts until the blade tip is in contact with the rub element which is a sector of the circular casing), and another corresponding to the first natural frequency of the blade when it vibrates freely without its tip being in contact with the rub-liner of the casing. A shortcoming of the current modeling approach is its inability to realistically represent the damping behaviors observed in the tests. For reasons of computational efficiency and consistent with the fact that there was no perceptible damage in the tested blades, an elastic constitutive behavior is specified for the blades, while the sacrificial PVC rub-liner is assumed to behave elasto-plastically. A limited study has also been carried out by assigning an elasto-plastic constitutive model to one of the blades previously represented with elastic properties only, and although incipient yielding is observed in a highly localized region at the tip of a blade (which can also be a numerical artifact), the responses under the two material behavior considerations (i.e. elastic and elasto-plastic) are found to be nearly same. Finally, this validated modeling approach is applied to the study of blades of ten distinct geometric profiles (including the three configurations already considered) at a speed of 800 rpm and the resonant speed of a given blade. Comparisons are made between the relevant responses (such as time-histories of root strain, shaft torque, blade axial displacement, bearing load and rub force) of nine blades with airfoil cross-sections (leaving aside the results for the first blade of rectangular cross-section which is only of academic interest). Based on this study, of all the blade designs, it has been found that the curve-stacked airfoils exhibit better ‘Rub-tolerant’ behavior. Both experimental and simulation results have predominantly proven the fact that adding curvature to a straight stacked blade through curve-stacked or bow result in reducing the rub induced vibration. While sweep and bow provide some aerodynamic advantages, they are not much helpful in containing the vibrations to a sustainable extent.