Engineering PapersSearch

SEARCH · Engineering Papers

Results for “pendulum”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

A comprehensive anaytical design procedure for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions is presented. A frequency response anaysis is conducted of typical rotor blades excited by a harmonic variation of spanwise airload distributions as well as a concentrated load at the tip. The results presented included the effect of pendulum tuning on the minimization of the hub reactions. It is found that a properly designed flapping pendulum attenuates the root out-of-plane force and moment whereas the optimum designed lead-lag pendulum attenuates the root in-plane reactions. For optimum pendulum tuning the parameters to be determined are the pendulum uncoupled natural frequency, the pendulum spanwise location and its mass. It is found that the optimum pendulum frequency is in the vicinity of the excitation frequency. For the optimum pendulum a parametric study is conducted. The parameters varied include prepitch, pretwist, precone and pendulum hinge offset.

Pierce, G. A.

Dynamic characteristics of rotor blades with pendulum absorbers

The point transmission matrix for a vertical plane pendulum on a rotating blade undergoing combined flapwise bending, and chordwise bending and torsion is derived. The equilibrium equation of the pendulum is linearized for small oscillations about the steady state. A FORTRAN program was written for the case of a vertical plane pendulum attached to a uniform blade with flapwise bending degree of freedom for cantilever boundary conditions. The frequency has a singular value right at the uncoupled pendulum natural frequency and thus introduces two frequencies corresponding to the nearest natural frequency of the blade without pendulum. In both of these modes it was observed that the pendulum deflection is large. One frequency can be thought of as a coupled pendulum frequency and the other as a coupled bending and pendulum frequency.

Murthy, V. R.

Comparative Analysis of Pendulum and Flywheel Power Take-Off Mechanisms for Wave Energy Conversion

Here, this study compares three power-take-off (PTO) mechanisms for wave energy converters—a flywheel -type pitch resonator and two pendulum variants (normal and inverted)—all designed to fit within a fixed envelope. Performance is assessed via linear frequency-domain models and bi-conjugate impedance matching under a representative sea state. The inverted-pendulum PTO achieves 27.9% of the incident wave energy, versus 16.5% for the normal pendulum and 4.2% for the flywheel—that is, 6.6 × and 3.9 × improvements, respectively. These gains arise because pendulum-based systems generate higher torque for a given buoy motion and maintain impedance matching across a wider frequency band. Parametric studies of mass, pendulum arm length, spring stiffness, generator friction, and motor constant quantify the impact of key design choices on power output. By locating the pendulum pivot near the buoy's center of gravity and positioning the center of rotation below the COG, surge–pitch coupling is improved and energy transfer is further boosted.

Keow, Alicia Li Jen [Sandia National Laboratories

Control of Torsional Vibrations by Pendulum Masses

Various versions of pendulum masses have been developed abroad within the past few years by means of which resonant vibrations of rotating shafts can be eliminated at a given tuning. They are already successfully employed on radial engines in the form of pendulous counterweights. Compared with the commonly known torsional vibration dampers, the pendulum masses have the advantage of being structurally very simple, requiring no internal damping and being capable of completely eliminating certain vibrations. Unexplained, so far, remains the problem of behavior of pendulum masses in other critical zones to which they are not tuned, their dynamic behavior at some tuning other than in resonance, and their effect within a compound vibration system and at simultaneous application of several differently tuned pendulous masses. These problems are analyzed in the present report. The results constitute an enlargement of the scope of application of pendulum masses, especially for in-line engines. Among other things it is found that the natural frequency of a system can be raised by means of a correspondingly tuned pendulum mass. The formulas necessary for the design of any practical version are developed, and a pendulum mass having two different natural frequencies simultaneously is described.

Stieglitz, Albert

Two-Pendulum Model of Propellant Slosh in Europa Clipper PMD Tank

The objective of this fluids analysis is to model propellant slosh for the Europa Clipper mission using a two-pendulum model, such that controls engineers can predict slosh behavior during the mission. Propellant slosh causes shifts in center of mass and exerts forces and torques on the spacecraft which, if not adequately controlled, can lead to mission failure. The two-pendulum model provides a computationally simple model that can be used to predict slosh for the Europa Clipper tank geometry. The Europa Clipper tank is cylindrical with a domed top and bottom and includes a propellant management device (PMD). Due to the lack of experimental data in low gravity environments, computational fluid dynamics (CFD) simulation results were used as 'real' slosh behavior for two propellants at three fill fractions. Key pendulum parameters were derived that allow the pendulum model's center of mass, forces, and moments to closely match the CFD data. The parameter trends were examined as a function of tank fill fraction and compared with solutions to analytic equations that describe the frequency of slosh in tanks with simple geometries. The trends were monotonic as expected, and parameters resembled analytical predictions; any differences could be explained by the specific differences in the geometry of the tank. This paper summarizes the new method developed at Goddard Space Flight Center (GSFC) for deriving pendulum parameters for two-pendulum equivalent sloshing models. It presents the results of this method and discusses the validity of the results. This analysis is at a completed stage and will be applied in the immediate future to the evolving tank geometry as Europa Clipper moves past its preliminary design review (PDR) phase.

Propellant Slosh

Extension and Validation of the Pendulum Model for Longitudinal Solar Prominence Oscillations

Context. Longitudinal oscillations in prominences are common phenomena on the Sun. These oscillations can be used to infer the geometry and intensity of the filament magnetic field. Previous theoretical studies of longitudinal oscillations made two simplifying assumptions: uniform gravity and semicircular dips on the supporting flux tubes. However, the gravity is not uniform and realistic dips are not semicircular. Aims. Our aim is to understand the effects of including the nonuniform solar gravity on longitudinal oscillations and explore the validity of the pendulum model with different flux-tube geometries. Methods. We first derived the equation describing the motion of the plasma along the flux tube including the effects of nonuniform gravity, yielding corrections to the original pendulum model. We also computed the full numerical solutions for the normal modes and compared them with the new pendulum approximation. Results. We find that the nonuniform gravity introduces a significant modification in the pendulum model. We also found a cut-off period; i.e., the longitudinal oscillations cannot have a period longer than 167 min. In addition, considering different tube geometries, the period depends almost exclusively on the radius of curvature at the bottom of the dip. Conclusions. We conclude that nonuniform gravity significantly modifies the pendulum model. These corrections are important for prominence seismology, because the inferred values of the radius of curvature and minimum magnetic-field strength differ substantially from those of the old model. However, we find that the corrected pendulum model is quite robust and is still valid for noncircular dips.

Sun: corona

Pendulum Motion in Main Parachute Clusters

The coupled dynamics of a cluster of parachutes to a payload are notoriously difficult to predict. Often the payload is designed to be insensitive to the range of attitude and rates that might occur, but spacecraft generally do not have the mass and volume budgeted for this robust of a design. The National Aeronautics and Space Administration (NASA) Orion Capsule Parachute Assembly System (CPAS) implements a cluster of three mains for landing. During testing of the Engineering Development Unit (EDU) design, it was discovered that with a cluster of two mains (a fault tolerance required for human rating) the capsule coupled to the parachute cluster could get into a limit cycle pendulum motion which would exceed the spacecraft landing capability. This pendulum phenomenon could not be predicted with the existing models and simulations. A three phased effort has been undertaken to understand the consequence of the pendulum motion observed, and explore potential design changes that would mitigate this phenomenon. This paper will review the early analysis that was performed of the pendulum motion observed during EDU testing, summarize the analysis ongoing to understand the root cause of the pendulum phenomenon, and discuss the modeling and testing that is being pursued to identify design changes that would mitigate the risk.

Ray, Eric S.

Nonlinear Analysis of a Two-Parachute System Undergoing Pendulum Motion

Motion resembling that of a pendulum undergoing large-amplitude limit cycle oscillation was observed during a series of flight tests of an unoccupied Orion Capsule Parachute Assembly System (CPAS) comprised of two parachutes and a capsule payload. Large excursions away from vertical by the capsule could cause it to strike the ground or ocean at a large angle with respect to vertical, or at a large horizontal speed. These conditions are undesirable because they would endanger the occupants of the capsule in an actual mission. A simplified planar dynamics model in conjunction with a nonlinear normal force coefficient vs. angle of attack model serves as the basis of an analytical investigation of the fundamental dynamics of this pendulum motion. Output error methodology from system identification theory was used to identify the parameters of the nonlinear aerodynamics model. The identified model yielded excellent comparison with portions of flight test data where the pendulum motion occurred. Due to the inherent nonlinear nature of the pendulum motion limit cycle, traditional nonlinear analysis techniques were applied to gain further insight into the system. Lyapunov’s direct method provided mathematical proof in the absolute stability of the pendulum mode. Describing Function method was used to predict the amplitude and frequency of the limit cycle oscillation. Finally, phase plane analysis allowed easy visualization on the size and shape of the limit cycle with respect to variations in key aerodynamic parameters.

Pei, Jing

Vibration analysis of rotor blades with pendulum absorbers

A comprehensive vibration analysis of rotor blades with spherical pendulum absorbers is presented. Linearized equations of motion for small oscillations about the steady-state deflection of a spherical pendulum on elastic rotor blades undergoing coupled flapwise bending, chordwise bending, and torsional vibrations are obtained. A transmission matrix formulation is given to determine the natural vibrational characteristics of rotor blades with spherical or simple flapping pendulum absorbers. The natural frequencies and mode shapes of a hingeless rotor blade with a spherical pendulum are computed.

Murthy, V. R.

Inverting the Pendulum Using Fuzzy Control (Center Director's Discretionary Fund (Project 93-02)

A single pendulum was simulated in software and then built on a rotary base. A fuzzy controller was used to show its advantages as a nonlinear controller since bringing the pendulum inverted is extremely nonlinear. The controller was implemented in a Motorola 6811 microcontroller. A double pendulum was simulated and fuzzy control was used to hold it in a vertical position. The double pendulum was not built into hardware for lack of time. This project was for training and to show advantages of fuzzy control.

Kissel, R. R.

Robust Control Algorithm for a Two Cart System and an Inverted Pendulum

The Rectilinear Control System can be used to simulate a launch vehicle during liftoff. Several control schemes have been developed that can control different dynamic models of the rectilinear plant. A robust control algorithm was developed that can control a pendulum to maintain an inverted position. A fluid slosh tank will be attached to the pendulum in order to test robustness in the presence of unknown slosh characteristics. The rectilinear plant consists of a DC motor and three carts mounted in series. Each cart s weight can be adjusted with brass masses and the carts can be coupled with springs. The pendulum is mounted on the first cart and an adjustable air damper can be attached to the third cart if desired. Each cart and the pendulum have a quadrature encoder to determine position. Full state feedback was implemented in order to develop the control algorithm along with a state estimator to determine the velocity states of the system. A MATLAB program was used to convert the state space matrices from continuous time to discrete time. This program also used a desired phase margin and damping ratio to determine the feedback gain matrix that would be used in the LabVIEW program. This experiment will allow engineers to gain a better understanding of liquid propellant slosh dynamics, therefore enabling them to develop more robust control algorithms for launch vehicle systems

Wilson, Chris L.

Orion Multi-Purpose Crew Vehicle Solving and Mitigating the Two Main Cluster Pendulum Problem

The Orion Multi-purpose Crew Vehicle (MPCV) Orion spacecraft will return humans from beyond earth's orbit, including Mars and will be required to land 20,000 pounds of mass safely in the ocean. The parachute system nominally lands under 3 main parachutes, but the system is designed to be fault tolerant and land under 2 main parachutes. During several of the parachute development tests, it was observed that a pendulum, or swinging, motion could develop while the Crew Module (CM) was descending under two parachutes. This pendulum effect had not been previously predicted by modeling. Landing impact analysis showed that the landing loads would double in some places across the spacecraft. The CM structural design limits would be exceeded upon landing if this pendulum motion were to occur. The Orion descent and landing team was faced with potentially millions of dollars in structural modifications and a severe mass increase. A multidisciplinary team was formed to determine root cause, model the pendulum motion, study alternate canopy planforms and assess alternate operational vehicle controls & operations providing mitigation options resulting in a reliability level deemed safe for human spaceflight. The problem and solution is a balance of risk to a known solution versus a chance to improve the landing performance for the next human-rated spacecraft.

Ali, Yasmin

Design and analysis of a torsion braid pendulum displacement transducer

The dynamic properties at various temperatures of braids impregnated with polymer can be measured by using the braid as the suspension of a torsion pendulum. This report describes the electronic and mechanical design of a torsional braid pendulum displacement transducer which is an advance in the state of the art. The transducer uses a unique optical design consisting of refracting quartz windows used in conjunction with a differential photocell to produce a null signal. The release mechanism for initiating free torsional oscillation of the pendulum has also been improved. Analysis of the precision and accuracy of the transducer indicated that the maximum relative error in measuring torsional amplitude was approximately 0. A serious problem inherent in all instruments which use a torsional suspension was analyzed: misalignment of the physical and torsional axes of the torsional member which results in modulation of the amplitude of the free oscillation.

Rind, E.

Helicopter vibration suppression using simple pendulum absorbers on the rotor blade

A design procedure is presented for the installation of simple pendulums on the blades of a helicopter rotor to suppress the root reactions. The procedure consists of a frequency response analysis for a hingeless rotor blade excited by a harmonic variation of spanwise airload distributions during forward flight, as well as a concentrated load at the tip. The structural modeling of the blade provides for elastic degrees of freedom in flap and lead-lag bending plus torsion. Simple flap and lead-lag pendulums are considered individually. Using a rational order scheme, the general nonlinear equations of motion are linearized. A quasi-steady aerodynamic representation is used in the formation of the airloads. The solution of the system equations derives from their representation as a transfer matrix. The results include the effect of pendulum tuning on the minimization of the hub reactions.

Hamouda, M.-N. H.

Frequency Shift During Mass Properties Testing Using Compound Pendulum Method

During mass properties testing on the X-48B Blended Wing Body aircraft (The Boeing Company, Chicago, Illinois) at the National Aeronautics and Space Administration Dryden Flight Research Center, Edwards, California, large inertia measurement errors were observed in results from compound pendulum swings when compared to analytical models. By comparing periods of oscillations as measured from an average over the test period versus the period of each oscillation, it was noticed that the frequency of oscillation was shifting significantly throughout the test. This phenomenon was only noticed during compound pendulum swings, and not during bifilar pendulum swings. The frequency shift was only visible upon extensive data analysis of the frequency for each oscillation, and did not appear in averaged frequency data over the test period. Multiple test articles, test techniques, and hardware setups were used in attempts to eliminate or identify the cause of the frequency shift. Plotting the frequency of oscillation revealed a region of minimal shift that corresponded to a larger amplitude range. This region of minimal shift provided the most accurate results compared to a known test article; however, the amplitudes that produce accurate inertia measurements are amplitudes larger than those generally accepted in mass properties testing. This paper examines two case studies of the frequency shift, using mass properties testing performed on a dummy test article, and on the X-48B Blended Wing Body aircraft.

Wolfe, David

Anomalous Thrust Production from an RF Test Device Measured on a Low-Thrust Torsion Pendulum

This paper describes the eight-day August 2013 test campaign designed to investigate and demonstrate viability of using classical magnetoplasmadynamics to obtain a propulsive momentum transfer via the quantum vacuum virtual plasma. This paper will not address the physics of the quantum vacuum plasma thruster, but instead will describe the test integration, test operations, and the results obtained from the test campaign. Approximately 30-50 micro-Newtons of thrust were recorded from an electric propulsion test article consisting primarily of a radio frequency (RF) resonant cavity excited at approximately 935 megahertz. Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure. Several different test configurations were used, including two different test articles as well as a reversal of the test article orientation. In addition, the test article was replaced by an RF load to verify that the force was not being generated by effects not associated with the test article. The two test articles were designed by Cannae LLC of Doylestown, Pennsylvania. The torsion pendulum was designed, built, and operated by Eagleworks Laboratories at the NASA Johnson Space Center of Houston, Texas. Approximately six days of test integration were required, followed by two days of test operations, during which, technical issues were discovered and resolved. Integration of the two test articles and their supporting equipment was performed in an iterative fashion between the test bench and the vacuum chamber. In other words, the test article was tested on the bench, then moved to the chamber, then moved back as needed to resolve issues. Manual frequency control was required throughout the test. Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article). Test data gathered includes torsion pendulum displacement measurements which are used to calculate generated force, still imagery in the visible spectrum to document the physical configuration, still imagery in the infrared spectrum to characterize the thermal environment, and video imagery. Post-test data includes static and animated graphics produced during RF resonant cavity characterization using the COMSOL Multiphysics® software application. Excerpts from all of the above are included and discussed in this paper. Lessons learned from test integration and operations include identification of the need to replace manual control of the resonant cavity target frequency with an automated frequency control capability. Future test plans include the development of an automatic frequency control circuit. Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma. Future test plans include independent verification and validation at other test facilities.

Brady, David

Linear Analysis of a Two-Parachute System Undergoing Pendulum Motion

Motion resembling that of a pendulum undergoing large-amplitude oscillation was ob- served during a series of flight tests of an unoccupied Orion Capsule Parachute Assembly System (CPAS) drop-test vehicle. Large excursions away from vertical by the capsule could cause it to strike the ground or ocean at a large angle with respect to vertical, with an undesirable attitude with respect to heading, or with a large horizontal or vertical speed. These conditions are to be avoided because they would endanger the occupants of the capsule in an actual mission. Pendulum motion is intimately related to a parachute’s aerodynamic normal force coefficient, which is a nonlinear function of angle of attack. An analytical investigation of the dynamics of pendulum motion is undertaken with the aid of a simplified model of the physical system and the assumption that the normal force coefficient is a linear function of angle of attack in the neighborhood of a value corresponding to stable equilibrium. The analysis leads to a simple relationship for the location of a pivot point, which provides insights that are consistent with previous studies.

Roithmayr, Carlos M.

Machine Learning for Dynamical Modeling of a Flexible Inverted Pendulum System

The inverted pendulum system, a canonical example of an unstable mechanical system, is often used to model the control problems encountered in the flight of rockets in the initial stages of launch, when the airspeed is too small for aerodynamic stability. A system with a flexible pendulum is a variant that more accurately simulates rocket flight nonlinearities (particularly, the flex modes of the rocket). To increase NASA capability of modeling dynamical systems for which closed form solutions are not clear or easily developed, this project aims to provide a machine learning approach that produces a learned dynamical model of the PENNY robot (a rover with a flexible inverted pendulum) from operational data. The developed approach can then be generalized to other complex dynamical systems, including but not limited to rockets and other robotic systems.

M. A. DuPuis