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Report describes theory of vibrations in shafts supported by worn ball bearings. Purpose of theory to use strain-gauge measurements of vibrations to detect wear. Theory developed from simple model of radial motion of shaft along direction of applied lateral load. Bearing assumed to have clearance. Shaft and outer race taken to be rigid, and either outer race or shaft assumed to be stationary.
Light flashes when shaft reaches predetermined angle. Synchronization system facilitates visualization of flow in high-speed internal-combustion engines. Designed for cinematography and holographic interferometry, system synchronizes camera and light source with predetermined rotational angle of engine shaft. 10-bit resolution of absolute optical shaft encoder adapted, and 2 to tenth power combinations of 10-bit binary data computed to corresponding angle values. Pre-computed angle values programmed into EPROM's (erasable programmable read-only memories) to use as angle lookup table. Resolves shaft angle to within 0.35 degree at rotational speeds up to 73,240 revolutions per minute.
Aero-engine structures have very low inherent damping and so artificial damping is often introduced by pumping oil into annular gaps between the casings and the outer races of some or all of the rolling-element bearings supporting the rotors. The thin oil films so formed are called squeeze film dampers and they can be beneficial in reducing rotor vibration due to unbalance and keeping to reasonable limits the forces transmitted to the engine casing. However, squeeze-film dampers are notoriously non-linear and as a result can introduce into the assembly such phenomena as subharmonic oscillations, jumps and combination frequencies. The purpose of the research is to investigate such phenomena both theoretically and experimentally on a test facility reproducing the essential features of a medium-size aero engine. The forerunner of this work was published. It was concerned with the examination of a squeeze-film damper in series with housing flexibility when supporting a rotor. The structure represented to a limited extent the essentials of the projected Rolls Royce RB401 engine. That research demonstrated the ability to calculate the oil-film forces arising from the squeeze film from known motions of the bearing components and showed that the dynamics of a shaft fitted with a squeeze film bearing can be predicted reasonably accurately. An aero-engine will normally have at least two shafts and so in addition to the excitation forces which are synchronous with the rotation of one shaft, there will also be forces at other frequencies from other shafts operating on the squeeze-film damper. Theoretical and experimental work to consider severe loading of squeeze-film dampers and to include these additional effects are examined.
Many rotating machines such as compressors, turbines and pumps have long thin shafts with resulting vibration problems, and would benefit from additional damping near the center of the shaft. Magnetic dampers have the potential to be employed in these machines because they can operate in the working fluid environment unlike conventional bearings. An experimental test rig is described which was set up with a long thin shaft and several masses to represent a flexible shaft machine. An active magnetic damper was placed in three locations: near the midspan, near one end disk, and close to the bearing. With typical control parameter settings, the midspan location reduced the first mode vibration 82 percent, the disk location reduced it 75 percent and the bearing location attained a 74 percent reduction. Magnetic damper stiffness and damping values used to obtain these reductions were only a few percent of the bearing stiffness and damping values. A theoretical model of both the rotor and the damper was developed and compared to the measured results. The agreement was good.
Ball locking mechanism links input drive shaft to output shaft and disengages two shafts from each other when it locks output shaft at either of two fixed angular positions. Part of drive system turning microwave antenna 143.5 degrees between stowage and employment orientations and holds it at either orientation without back-loading drive motor and gears. Angular interval and dimensions modified for use in robotic or other actuators in which desirable to "rest" drive trains while locking actuators at fixed positions.
A finite-element model of a geared rotor system on flexible bearings was developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
This invention consists of a bearing designed to operate in a cryogenic environment and which has an inner raceway generally constructed as an annular band fitted by an interference fit to a rotating shaft. A pair of annular tension bands are fitted onto opposed sides of the band and function to firmly clamp the raceway to the shaft. This occurs because the tension bands are constructed of a material which, when cooled to approximately -335 F shrinks more than the raceway and the shaft to which it is fitted. The bands further relax somewhat at room temperature and permit the interference fit between the raceway and the shaft to be sized such that the raceway is not overly stressed.
The finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis of geared rotors by calculating the critical speeds and determining the response of any point on the shaft to mass unbalances, geometric eccentricities of gears and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.
The design of spiral bevel and hypoid gears that have a shaft extended from both sides of the cone apex (straddle design) is considered. A main difficulty of such a design is determining the length and diameter of the shaft that might be undercut by the head cutter during gear tooth generation. A method that determines the free space available for the gear shaft is proposed. The approach avoids collision between the shaft being designed and the head cutter during tooth generation. The approach is illustrated with a numerical example.
A space transport vehicle is disclosed as including a body which is arranged to be movably mounted on an elongated guide member disposed in outer space and driven therealong. A drive wheel is mounted on a drive shaft and arranged to be positioned in rolling engagement with the elongated guide carrying the vehicle. A brake member is arranged on the drive shaft for movement into and out of engagement with an adjacent surface of the drive wheel. An actuator is mounted on the body to be manually moved back and forth between spaced positions in an arc of movement. A ratchet-and-pawl mechanism is arranged to operate upon movements of the actuator in one direction between first and second positions for coupling the actuator to the drive wheel to incrementally rotate the wheel in one rotational direction and to operate upon movements of the actuator in the opposite direction for uncoupling the actuator from the wheel. The brake member is threadedly coupled to the drive shaft in order that the brake member will be operated only when the actuator is moved on beyond its first and second positions for shifting the brake member along the drive shaft and into frictional engagement with the adjacent surface on the drive wheel.
Simple inspection and measurement technique makes possible to estimate wear of balls in ball bearing, without removing bearing from shaft on which installed. To perform measurement, one observes bearing cage while turning shaft by hand to obtain integral number of cage rotations and to measure, to nearest 2 degrees, number of shaft rotations producing cage rotations. Ratio between numbers of cages and shaft rotations depends only on internal geometry of bearing and applied load. Changes in turns ratio reflect changes in internal geometry of bearing provided measurements made with similar bearing loads. By assuming all wear occurs on balls, one computes effective value for this wear from change in turns ratio.
Rotor and gear dynamics, previously treated separately, combined in one model. Geared-rotor model developed to consider coupling of torsional vibrations of gears with lateral as well as torsional vibrations of shafts. Geared-rotor system includes motor connected to one of two shafts via coupling, load at far end of other shaft, and pair of gears that couple shafts. Used in parametric studies on effects of compliances of bearings on dynamics of geared-rotor systems.
A full-scale helicopter rotor test was conducted in the NASA Ames 80- by 120-Foot Wind Tunnel with a four-bladed S-76 rotor system. This wind tunnel test generated a unique and extensive data base covering a wide range of rotor shaft angles-of-attack and rotor thrust conditions from 0 to 100 knots. Three configurations were tested: (1) empty tunnel; (2) test stand body (fuselage) and support system; and (3) fuselage and support system with rotor installed. Empty tunnel wall pressure data are evaluated as a function of tunnel speed to understand the baseline characteristics. Aerodynamic interaction effects between the fuselage and the walls of the tunnel are investigated by comparing wall, ceiling, and floor pressures for various tunnel velocities and fuselage angles-of-attack. Aerodynamic interaction effects between the rotor and the walls of the tunnel are also investigated by comparing wall, ceiling, and floor pressures for various rotor shaft angles, rotor thrust conditions, and tunnel velocities. Empty tunnel wall pressure data show good repeatability and are not affected by tunnel speed. In addition, the tunnel wall pressure profiles are not affected by the presence of the fuselage apart from a pressure shift. Results do not indicate that the tunnel wall pressure profiles are affected by the presence of the rotor. Significant changes in the wall, ceiling, and floor pressure profiles occur with changing tunnel speeds for constant rotor thrust and shaft angle conditions. Significant changes were also observed when varying rotor thrust or rotor shaft angle-of-attack. Other results indicate that dynamic rotor loads and blade motion are influenced by the presence of the tunnel walls at very low tunnel velocity and, together with the wall pressure data, provide a good indication of flow breakdown.
Rotary release mechanism includes fusible rotary link made of alloy that melts at relatively low temperature of 60 degrees C. When solid, link couples driving shaft to driven shaft. When necessary, link melted to temporarily decouple two shafts. Upon cooling below melting temperature link hardens, so it once again couples two shafts. Release mechanism extremely compact alternative to pyrotechnic release device. Basic concept applied to such other mechanisms as pin pullers, pin pushers, electrical-disconnection mechanisms, and clutches.
To investigate the effects of ovariectomy and the simultaneous administration of prostaglandin E2 (PGE2) on rat tibial shaft cortical bone histomorphometry, thirty-five 3 month-old female Sprague-Dawley rats were either ovariectomized (OVX), or sham ovariectomy (sham-OVX). The OVX rats were divided into three groups and treated with 0, 1 and 6 mg PGE2/kg/day for 90 days. The double fluorescent labeled undecalcified tibial shaft cross sections (proximal to the tibiofibular junction) of all the subjects were used for histomorphometry analysis. No differences in cross-sectional area and cortical bone area were found between sham-OVX and OVX controls, but OVX increased marrow area, intracortical porosity area and endocortical eroded perimeter. Periosteal and endocortical bone formation rates decreased with aging yet OVX prevented these changes. These OVX-induced increases in marrow area and endocortical eroded perimeter were prevented by 1 mg PGE2/kg/day treatment and added bone to periosteal and endocortical surfaces and to the marrow cavity. At the 6 mg/kg/day dose level, PGE2-treated OVX rats increased total tissue area, cortical bone area, marrow trabmular bone area, minimal cortical width and intracortical porosity area, and decreased marrow area compared to basal, sham-OVX and OVX controls. In addition, periosteal bone formation was elevated in the 6 mg PGE2/kg/day-treated OVX rats compared to OVX controls. Endocortical eroded perimeter increased from basal and sham-OVX control levels, but decreased from OVX control levels in the 6 mg PGE2/kg/day-treated OVX rats. Our study confirmed that ovariectomy does not cause osteopenia in tibial shaft cortical bone in rats, but it does stimulate endocortical bone resorption and enlarges marrow area. The new findings from the present study demonstrate that PGE2 prevents the OVX-induced increases in endocortical bone resorption and marrow area and adds additional bone to periosteal and endocortical surfaces and to marrow cavity to increase total bone mass in the tibial shaft of OVX rats when given immediately following ovafiectomy.
The effective use of active magnetic bearings for vibration control in turbomachinery depends on an understanding of the forces available from a magnetic bearing actuator. The purpose of this project was to characterize the forces as functions shaft position. Both numerical and experimental studies were done to determine the characteristics of the forces exerted on a stationary shaft by a magnetic bearing actuator. The numerical studies were based on finite element computations and included both linear and nonlinear magnetization functions. Measurements of the force versus position of a nonrotating shaft were made using two separate measurement rigs, one based on strain gage measurement of forces, the other based on deflections of a calibrated beam. The general trends of the measured principal forces agree with the predictions of the theory while the magnitudes of forces are somewhat smaller than those predicted. Other aspects of theory are not confirmed by the measurements. The measured forces in the normal direction are larger than those predicted by theory when the rotor has a normal eccentricity. Over the ranges of position examined, the data indicate an approximately linear relationship between the normal eccentricity of the shaft and the ratio of normal to principal force. The constant of proportionality seems to be larger at lower currents, but for all cases examined its value is between 0.14 and 0.17. The nonlinear theory predicts the existence of normal forces, but has not predicted such a large constant of proportionality for the ratio. The type of coupling illustrated by these measurements would not tend to cause whirl, because the coupling coefficients have the same sign, unlike the case of a fluid film bearing, where the normal stiffness coefficients often have opposite signs. They might, however, tend to cause other self-excited behavior. This possibility must be considered when designing magnetic bearings for flexible rotor applications, such as gas turbines and other turbomachinery.
The effects of two types of flow non-uniformity on stall inception behavior were assessed with linearized stability analyses of two compressor flow models. Response to rotating tip clearance asymmetries induced by a whirling rotor shaft or rotor height variations were investigated with a two-dimensional flow model. A 3-D compressor model was also developed to study the stability of both full-span and part-span rotating stall modes in annular geometries with radial flow variations. The studies focussed on (1) understanding what compressor designs were sensitive to these types of circumferential and spanwise flow non-uniformities, and (2) situations where 2-D stability theories were inadequate because of 3-D flow effects. Rotating tip clearance non-uniformity caused the greatest performance loss for shafts whirling at the rotating stall frequency. A whirling shaft displacement of 1 percent chord caused the stalling mass flow to rise by as much as 10 percent and the peak pressure rise to decrease by 6 percent. These changes were an order of magnitude larger than for equivalent-sized stationary or rotor-locked clearance asymmetries. Spanwise flow non-uniformity always destabilized the compressor, so that 2-D models over-predicted that stall margin compared to 3-D theory. The difference increased for compressors with larger spanwise variations of characteristic slope and reduced characteristic curvature near the peak. Differences between 2-D and 3-D stall point predictions were generally unacceptable (2 - 4 percent of flow coefficient) for single-stage configurations, but were less than 1 percent for multistage compressors. 2-D analyses predicted the wrong stall mode for specific cases of radial inlet flow distortion, mismatching and annulus area contraction, where higher-order radial modes led to stall. The stability behavior of flows with circumferential or radial non-uniformity was unified through a single stability criterion. The stall point for both cases was set by the integral around the annulus of the pressure rise characteristic slope, weighted by the amplitude of the mode shape. For the case of steady circumferential variations, this criterion reduced to the integrated mean slope (IMS) condition associated with steady inlet distortions. The rotating tip clearance asymmetry model was also used to demonstrate the feasibility of actively controlling the shaft position to suppress rotating stall. In axisymmetric mean flow, this method only stabilized the first harmonic mode, increasing the operating range until surge or higher harmonic modes became unstable.
Although noninterference optical instrumentation has been previously used to monitor and measure rotor blade vibrations, it has not been used at the NASA Glenn Research Center for the determination of damping. This article describes such a measurement in Glenn's Spin Rig facility. The optical system was chosen because installation of the slip rig for this particular configuration was not feasible, ruling out strain gauge instrumentation. The shaft in this facility was suspended with two radial magnetic bearings, and the excitation was supplied to the bearings by a signal generator. For the first mode, the direction of excitation force was always perpendicular to the blade as described by Morrison. The preceding graph shows blade displacements, as measured by an optical probe during a frequency sweep designed to locate the first mode resonance. The resonance determines the frequency at which the shaft is excited. Because the sampling rate was fixed to only once per revolution with these transducers, and the first mode frequency was much larger than the rotational frequency, the data in this figure were undersampled with an apparent frequency that was only 1 Hz at the beginning of the sweep, about 14 Hz at the maximum amplitude, and about 20 Hz at the end of the sweep. The true excitation frequency varied during the sweep from 320 to 340 Hz, and the resonance occurred at 334 Hz. Damping is determined by applying a frequency burst to the shaft. Upon cessation of the burst, the blade undergoes free decay. The apparent damping is then obtained by a least squares fit of the theoretical cosine decay function through the experimental points. The following graph illustrates this procedure. Because of frequency aliasing, the apparent measured damping must be divided by the ratio of the true resonant frequency to the apparent measured frequency to obtain the true damping. Note that the contribution of the shaft vibration to the blade vibration could be neglected because it was shown that it is an order of magnitude smaller and that its decay is an order of magnitude faster.