Quasi-optimum three-axis control of a space vehicle.
Quasi-optimum three-axis attitude control law for minimum time of rigid body, noting gyroscopic cross axis coupling
ATTITUDE CONTROL↗
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Blade loss transient dynamics analysis with flexible bladed disk
The transient dynamic response of a flexible bladed disk on a flexible rotor in a two rotor system is formulated by modal synthesis and a Lagrangian approach. Only the nonequilibrated one diameter flexible mode is considered for the flexible bladed disk, while the two flexible rotors are represented by their normal modes. The flexible bladed disk motion is modeled as a combination of two one diameter standing waves, and is coupled inertially and gyroscopically to the flexible rotors. Application to a two rotor model shows that a flexible bladed disk on one rotor can be driven into resonance by an unbalance in the other rotor, and at a frequency equal to the difference in the rotor speeds.
Gallardo, V. C.↗
The dynamics of a flexible bladed disc on a flexible rotor in a two-rotor system
This paper describes the development of the analysis of the transient dynamic response of a bladed disk on a flexible rotor. The rotating flexible bladed disk is considered as a module in a complete turbine engine structure. The analysis of the flexible bladed disk (FBD) module is developed for the non-equilibrated one-diameter axial mode. The FBD motion is considered as a sum of two standing axial waves constrained to the rotor. The FBD is coupled inertially and gyroscopically to its rotor support, and indirectly through connecting elements, to the adjacent rotor and/or other supporting structures. Incorporated in the basic Turbine Engine Transient Response Analysis program (TETRA), the FBD module is demonstrated with a two-rotor model where the FBD can be excited into resonance by an unbalance in the adjacent rotor and at a frequency equal to the differential rotor speed. The FBD module also allows the analysis of two flexible bladed disks in the same rotor.
Gallardo, V. C.↗
Some Recent Studies in Structural Dynamics of Rotor Aircraft
This paper presents a summary of four recent studies relating to the structural-dynamics problems of rotor-powered aircraft. The first study concerns the measurement by means of dynamic models of the forces and moments at the hubs of various rotor configurations. The results of this study show that the periodic components of the forces and moments are highly dependent on both the rotor configuration and the flight condition. The second study treats the problem of resonance amplifications of rotor-blade stress and shows that by using multiple flapping hinges or flex-joints it is possible to control the natural frequencies of the rotor blade so that conditions of resonance between the frequencies of the aerodynamic input forces and the natural frequencies of the lower blade modes are avoided for all rotor speeds. Two studies of the stability of rotor aircraft axe also discussed. One of these involves the mechanical instability or ground resonance of rotorcraft wherein the rotor support in each of two mutually perpendicular directions in the rotor plane is represented as a multiple-degree-of-freedom system in contrast to the system having a "single" degree of freedom normally used in helicopter analysis. The consideration of the rotor support system as a two-degree-of-freedom system predicts additional unstable ranges of rotor speed not predicted by former analyses. The other instability treated is propeller whirl for which the significant motions are the pitching and yawing motions of the propeller disk which are coupled together by gyroscopic forces. The effect of the significant variables on the instability is presented and shows that the speed at which the instability occurs can be increased by increasing the relative stiffness of the propeller in the pitch and yaw directions or by increasing the effective structural damping of the nacelle.
George W Brooks↗
Comparison of On-Orbit Performance of Rate Sensing Gyroscopes
This work presents results from the study of a large volume of spacecraft flight data pertaining to gyroscope performance. We have examined long and short term trends of gyroscope biase of first, an exact solution for the time-dependence of the attitude part of the state error covariance, averaged over the three spacecraft axes, is given. This solution is more complete than the usual cubic polynomial for the variance in that it includes coupling among the three gyroscope axes and includes an important term arising from the initial correlations. Second, several continuous 24-hour spans of gyroscope data are examined to verify the short-term statistical model. This analysis demonstrates that in-flight data can be used to determine the strength of the white noise driving the random walk of the gyroscope bias. This may be useful for postlaunch improvement to the noise model and for diagnosing the health of the gyroscope. Third, the long-term trends in gyroscope biases show a nearly linear systematic variation over time scales of years. This has been found on three different missions. While the random walk model is adequate as a basis for onboard Kalman filters or for state estimation using relatively short time spans, these trends indicate that some applications could benefit by accounting for the secular changes in the biases. One example is a new gyroscope calibration method that is under development that allows for multi-epoch bias solutions.
Sedlak, Joseph↗
Can a macroscopic gyroscope feel torsion
We demonstrate that for a large class of Lagrangian-based torsion theories a macroscopic gyroscope is insensitive to the torsion field: there can be no coupling of the torsion to the gyroscope's angular momentum of rotation. To detect torsion a polarized system with a net elementary particle spin is needed. These conclusions are evident from the conservation laws, which form the basis for deriving the equations of motion.
Stoeger, W. R.↗
Gyroscopic stimulation of the semicircular canals during sensory deprivation.
A static object revolving at a constant velocity is stationary with respect to that environment. When the object is rotated outside the plane of spin, a gyroscopic or cross-coupled acceleration is produced orthogonal to the two planes of rotation. In this situation, a man feels himself moving in a direction other than that which his visual or proprioceptive sensors perceive. The conflict in spatial orientation is the cross-coupled acceleration imposed on the semicircular canals. This perceptual conflict and the thresholds involved were studied by partial isolation of the physiological stimuli through sensory deprivation. Subjects weighted to neutral buoyancy were submerged in 94 F water in the dark. The subjects were then rotated while being revolved about a displaced axis. Thresholds for detection of angular acceleration were higher than those reported in the literature for detection of acceleration of a single plane. This discrepancy may be attributable to the length of time the stimuli are imposed to each of the canals and the cupular response periods.
Newsom, B. D.↗
Small Body Hopper Mobility Concepts
A propellant-saving hopper mobility system was studied that could help facilitate the exploration of small bodies such as Phobos for long-duration human missions. The NASA Evolvable Mars Campaign (EMC) has proposed a mission to the moons of Mars as a transitional step for eventual Mars surface exploration. While a Mars transit habitat would be parked in High-Mars Orbit (HMO), crew members would visit the surface of Phobos multiple times for up to 14 days duration (up to 50 days at a time with logistics support). This paper describes a small body surface mobility concept that is capable of transporting a small, two-person Pressurized Exploration Vehicle (PEV) cabin to various sites of interest in the low-gravity environment. Using stored kinetic energy between bounces, a propellant-saving hopper mobility system can release the energy to vector the vehicle away from the surface in a specified direction. Alternatively, the stored energy can be retained for later use while the vehicle is stationary in respect to the surface. The hopper actuation was modeled using a variety of launch velocities, and the hopper mobility was evaluated using NASA Exploration Systems Simulations (NExSyS) for transit between surface sites of interest. A hopper system with linear electromagnetic motors and mechanical spring actuators coupled with Control Moment Gyroscope (CMG) for attitude control will use renewable electrical power, resulting in a significant propellant savings.
Phobos↗
A rate gyroscope based on interaction of sonic waves.
Rate gyroscope based on sonic wave interaction with solid media emphasizing angular rate sensitivity and cross coupling effects
CROSS COUPLING↗
Coupling Dynamics in Aircraft: A Historical Perspective
Coupling dynamics can produce either adverse or beneficial stability and controllability, depending on the characteristics of the aircraft. This report presents archival anecdotes and analyses of coupling problems experienced by the X-series, Century series, and Space Shuttle aircraft. The three catastrophic sequential coupling modes of the X-2 airplane and the two simultaneous unstable modes of the X-15 and Space Shuttle aircraft are discussed. In addition, the most complex of the coupling interactions, inertia roll coupling, is discussed for the X-2, X-3, F-100A, and YF-102 aircraft. The mechanics of gyroscopics, centrifugal effect, and resonance in coupling dynamics are described. The coupling modes discussed are interacting multiple degrees of freedom of inertial and aerodynamic forces and moments. The aircraft are assumed to be rigid bodies. Structural couplings are not addressed. Various solutions for coupling instabilities are discussed.
Day, Richard E.↗
Non-Hermitian Gyroscopes: Can Exceptional Points Increase Sensor Precision
We show that exceptional points in conservatively coupled systems can increase the quantum-limited precision of laser gyroscopes as a result of gain saturation, but that this requires recovery of the beat note by interference with an auxiliary mode, with consequences for the quantum and classical noise that depend on the particular recovery scheme.
David D Smith↗
Computer program for calculating critical speeds of rotating shafts
Shaft may include bearings, couplings, extra masses, and disks for gyroscopic effect. Shaft deflection is taken into account and provision is made in program for sections of shaft that are tapered. Plotter produces drawing of shaft with superimposed deflection curves at critical speeds together with all pertinent information related to shaft.
Trivisonno, R. J.↗
SQUID readout and ultra-low magnetic fields for Gravity Probe-B (GP-B)
The superconducting readout system to be used for resolving 0.001 arcsec changes in the gyroscope spin direction in the Relativity Gyroscope (GP-B) experiment is described. This system couples the London magnetic moment flux of the spinning gyro to a low noise superconducting quantum interference device (SQUID) detector. Resolution limits and noise performance of the detection system are discussed, and improvements obtained and expected with advanced SQUIDs are presented. Also described is the novel use of superconducting magnetic shielding techniques to obtain a 250 dB attenuation of the earth's magnetic field at the location of the gyroscopes. In this approach, expanded superconducting foil shields are coupled with fixed cylindrical superconducting shields and special geometric considerations to obtain the extremely high attenuation factor required. With these shielding techniques, it appears that the 0.5-Gauss earth field (which appears to the gyroscopes as an ac field at the satellite roll rate) can be reduced to the 10 to the -13th G level required by the experiment. Recent results concerning improvements in the performance of the superconducting foil techniques obtained with the use of a new computer-controlled cooling system are presented.
Lockhart, James M.↗
Modal analysis of turborotors using planar modes - Theory
The generalized dynamic equations of motion have been obtained by the direct stiffness method for multimass flexible rotor bearing systems including the effects of gyroscopic moments, disk skew, and rotor acceleration. A set of undamped critical speed mode shapes calculated from the average horizontal and vertical bearing stiffness is used to transform the equations of motion into a set of coupled modal equations of motion. The modal equations are coupled by the generalized bearing coefficients and the gyroscopic moments. An analysis using only undamped critical speeds or decoupled modal analysis assuming proportional damping may lead to erroneous results. This paper presents a rapid method of calculating rotor resonance speeds with their corresponding amplification factors, stability and unbalance response of turborotors. Examples of the application of this modal approach are presented and results are compared to those of other methods such as matrix transfer analysis.
Gunter, E. J.↗
A methodology for modeling the mechanical interaction between a reaction wheel and a flexible structure
This paper presents a modeling methodology used to predict the performance of a flexible structure, such as a space telescope, in the presence of an on-board vibrational disturbance source, such as a reaction wheel assembly (RWA). Both decoupled and coupled analysis methods are presented. The decoupled method relies on blocked RWA disturbances, measured with the RWA hardmounted to a rigid surface. The coupled method corrects the blocked RWA disturbance boundary conditions using "force filters," which depend on estimates of the interface accelerances of the RWA and space-craft. Both methods were validated on the Micro-Precision Interferometer testbed at the Jet Propulsion Laboratory. Experimental results are encouraging, indicating that both methods provide sufficient accuracy compared to measured values; however, the coupled method provides the best results when the gyroscopic nature of the spinning RWA is captured in the RWA accelerance model. Additionally, the RWA disturbance cross spectral density terms are found to be influential.
vibration↗
Dispersive Elements for Enhanced Laser Gyroscopy and Cavity Stabilization
We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the modulation to determine the conditions for cavity self-stabilization and enhanced gyroscopic sensitivity. We find an enhancement in the sensitivity of a laser gyroscope to rotation for normal dispersion, while anomalous dispersion can be used to self-stabilize an optical cavity. Our results indicate that atomic media, even coherent superpositions in multilevel atoms, are of limited use for these applications, because the amplitude and phase filters work against one another, i.e., decreasing the modulation frequency increases its amplitude and vice-versa. On the other hand, for optical resonators the dispersion reversal associated with critical coupling enables the amplitude and phase filters to work together. We find that for over-coupled resonators, the absorption and normal dispersion on-resonance increase the contrast and frequency of the beat-note, respectively, resulting in a substantial enhancement of the gyroscopic response. Under-coupled resonators can be used to stabilize the frequency of a laser cavity, but result in a concomitant increase in amplitude fluctuations. As a more ideal solution we propose the use of a variety of coupled-resonator-induced transparency that is accompanied by anomalous dispersion.
Smith, David D.↗
FORTRAN 4 computer program for calculating critical speeds of rotating shafts
A FORTRAN 4 computer program, written for the IBM DCS 7094/7044 computer, that calculates the critical speeds of rotating shafts is described. The shaft may include bearings, couplings, extra masses (nonshaft mass), and disks for the gyroscopic effect. Shear deflection is also taken into account, and provision is made in the program for sections of the shaft that are tapered. The boundary conditions at the ends of the shaft can be fixed (deflection and slope equal to zero) or free (shear and moment equal to zero). The fixed end condition enables the program to calculate the natural frequencies of cantilever beams. Instead of using the lumped-parameter method, the program uses continuous integration of the differential equations of beam flexure across different shaft sections. The advantages of this method over the usual lumped-parameter method are less data preparation and better approximation of the distribution of the mass of the shaft. A main feature of the program is the nature of the output. The Calcomp plotter is used to produce a drawing of the shaft with superimposed deflection curves at the critical speeds, together with all pertinent information related to the shaft.
Trivisonno, R. J.↗
Ring-laser gyroscope system using dispersive element(s)
A ring-laser gyroscope system includes a ring-laser gyroscope (RLG) and at least one dispersive element optically coupled to the RLG's ring-shaped optical path. Each dispersive element has a resonant frequency that is approximately equal to the RLG's lasing frequency. A group index of refraction defined collectively by the dispersive element(s) has (i) a real portion that is greater than zero and less than one, and (ii) an imaginary portion that is less than zero.
Smith, David D.↗