Equations of Motion for a Generic Multibody Tilt-rotor Aircraft
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Topics addressed include: transient dynamics; transient finite element method; transient analysis in impact and crash dynamic studies; multibody computer codes; dynamic analysis of space structures; multibody mechanics and manipulators; spatial and coplanar linkage systems; flexible body simulation; multibody dynamics; dynamical systems; and nonlinear characteristics of joints.
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
The present conference on the dynamics and control methods of multibody robotic systems applicable to outer space applications first gives attention to such topics in multibody dynamics and control as the substructure synthesis approach to flexible multibody system control, an elastic finite-element kinematic analysis of a multirigid body, computational methods for high speed vehicles on flexible guideways, and multiarm coordination and control. Attention is then given to such issues in space manipulator dynamics and control methods as the global navigation of a free-flying space robot, dynamic singularities in the control of free-floating space manipulators, experimental results for compact space robot actuator control, and a 17-degree-of-freedom dexterous manipulator.
This research project has as its main goal the development of methods for selecting the damping characteristics of components of a large structure or multibody system, in such a way as to produce some desired system damping characteristics. The main need for such an analytical device is in the simulation of the dynamics of multibody systems consisting, at least partially, of flexible components. The reason for this need is that all existing simulation codes for multibody systems require component-by-component characterization of complex systems, whereas requirements (including damping) often appear at the overall system level. The main goal was met in large part by the development of a method that will in fact synthesize component damping matrices from a given system damping matrix. The restrictions to the method are that the desired system damping matrix must be diagonal (which is almost always the case) and that interbody connections must be by simple hinges. In addition to the technical outcome, this project contributed positively to the educational and research infrastructure of Tuskegee University - a Historically Black Institution.
A Workstation has been designed and constructed for rapidly simulating motions of rigid and elastic multibody systems. We examine the Workstation from the point of view of analysts who use the machine in an industrial setting. Two aspects of the device distinguish it from other simulation programs. First, one uses a series of windows and menus on a computer terminal, together with a keyboard and mouse, to provide a mathematical and geometrical description of the system under consideration. The second hallmark is a facility for animating simulation results. An assessment of the amount of effort required to numerically describe a system to the Workstation is made by comparing the process to that used with other multibody software. The apparatus for displaying results as a motion picture is critiqued as well. In an effort to establish confidence in the algorithms that derive, encode, and solve equations of motion, simulation results from the Workstation are compared to answers obtained with other multibody programs. Our study includes measurements of computational speed.
Pong is a new software tool developed at the NASA Johnson Space Center that advances interference-based geometric contact dynamics based on 3D graphics models. The Pong software consists of three parts: a set of scripts to extract geometric data from 3D graphics models, a contact dynamics engine that provides collision detection and force calculations based on the extracted geometric data, and a set of scripts for visualizing the dynamics response with the 3D graphics models. The contact dynamics engine can be linked with an external multibody dynamics engine to provide an integrated multibody contact dynamics simulation. This paper provides a detailed overview of Pong including the overall approach and modeling capabilities, which encompasses force generation from contact primitives and friction to computational performance. Two specific Pong-based examples of International Space Station applications are discussed, and the related verification and validation using this new tool are also addressed.
Ocean observation buoys require relatively small amounts of power, yet traditionally necessitate costly resupply trips for battery replacement. With the offshore location of the buoys and small power requirements, wave energy may be an effective solution for providing consistent and reliable power to support the buoy instrumentation. The US National Science Foundation Ocean Observatories Initiative (OOI) includes arrays of point absorber-like buoy systems used for ocean observation that have been deployed at multiple locations including the Southern Mid-Atlantic Bight. A study is currently underway to design a pitch resonator wave energy converter to supplement existing renewable energy generation for powering observation instrumentation. This paper details field measurements from surface moorings of the OOI Coastal Pioneer Array, which informs the subsequent development of a numerical model for the moored observation system. The model is developed in Wave Energy Converter Simulator (WEC-Sim), which leverages the Simscape multibody solver within the MATLAB/Simulink framework and linear potential flow theory to simulate the hydrodynamic interactions and multibody dynamics in 6 degrees of freedom. Multiple tuning variables are considered to produce a model for the system that matches well with empirical data (about 8% error). In conclusion, the WEC-Sim model will serve as a platform for integrating the pitch resonator wave energy converter concept and deployment preparation (detailed design including power take-off and control systems, response evaluation, etc.).
The goal of this two-year grant is to provide access to the PI to dusty plasma experimental facilities at the DOE-funded Collaborative Research Facility Magnetized Plasma Research Laboratory, Auburn University to become a user of that facility, to obtain experimental data to support another ongoing grant DE-SC0021146 (an Early Career Award to the PI that is focused on modeling of dusty plasma thermodynamics and transport processes), to generate experimental data for funding proposals, and to provide exposure to University of Memphis students to advanced experimental techniques. The following technical accomplishments were made: 1. Development of a novel Bidirectional Electrode Control Arms Assembly (BECAA) for producing perfect 2D grain layers for complex plasma experimentation. BECAA uses movable electrode arms to tilt or move the electrode in a RF discharge from outside the chamber, allowing for the manipulation of grain clouds without needing to change the plasma parameters or gas pressure. This work addresses a longstanding gap in the literature for a method to produce clusters of selectable number of grains and that are perfectly two dimensional as opposed to being only quasi-2D. 2. Experimental investigation of the structural properties of finite-N clusters with N=2 to 50. Individual particle behavior in clusters could vary from grain to grain and this study measured systematically produced clusters for two different grain sizes. Analysis (funded by another grant DE-SC0021146) is currently underway to quantify the differences between grains that are found on the surface vs. the interior of clusters, the shell structure, and the decay of correlations in position, velocity, and kinetic energy. 3. An experimental method to measure the structural entropy of clusters was developed by observing the self-induced structural transitions between various possible arrangements. In a series of heating and cooling cycles, the number of times each possible arrangement was attained was experimentally observed and used to compute the probability of existence of that arrangement, and subsequently the configurational entropy of the cluster. Analysis (funded by another grant DE-SC0021146) is currently underway to produce the entropy of clusters as a function of the number of grains and use the same to compute thermodynamic state variables for 2D complex plasma/grain clusters. 4. A preliminary experimental study of multibody collisions between N grains (N=2 – 10) was conducted. The clusters were produced using the BECAA technique and velocities were imparted to the grains using manipulation laser pulses. Analysis (funded by another grant DE-SC0021146) is currently underway to develop a theoretical framework to describe multibody collisions analogous to classical two-body interactions.
A wind tunnel experiment involving single, double, and triple combinations of mutually interfering generic, unfinned aircraft stores has been conducted. Each combination of stores was tested at Mach numbers from 0.60 to 1.20 and at angles of attack from 0 to 25 deg for the single store and from 0 to 6 deg for the double and triple store configurations. Extensive axial and circumferential pressure and flow visualization data at each store location were obtained. Euler solutions for each configuration at 0 deg incidence have been generated and compared with experimental data. This comparison indicates an Euler flow solver can yield accurate predictions of the location and magnitude of multibody interference provided an appropriate grid is used and the viscous effects associated with these configurations remain small. The data indicate multibody interference in the transonic region increases as the freestream Mach number approaches 1 from either direction, and subsides as the Mach number moves away from sonic conditions. This interference is characterized by a large, localized reduction in pressure on the inboard surfaces of the bodies which results in forces that draw the configuration closer together.
Demands for nonlinear time history simulations of large, flexible multibody dynamic systems has created a need for efficient interfaces between finite-element modeling programs and time-history simulations. One such interface, TREEFLX, an interface between NASTRAN and TREETOPS, a nonlinear dynamics and controls time history simulation for multibody structures, is presented and demonstrated via example using the proposed Space Station Mobile Remote Manipulator System (MRMS). The ability to run all three programs (NASTRAN, TREEFLX and TREETOPS), in addition to other programs used for controller design and model reduction (such as DMATLAB and TREESEL, both described), under a UNIX Workstation environment demonstrates the flexibility engineers now have in designing, developing and testing control systems for dynamically complex systems.
Present research centers on the development of advanced computational methods for transient simulation analyses. Aircraft, launch vehicles and space structure components are potential applications, but primary focus is presently on large space structures. There are both in-house and out-of-house activities. The in-house activity centers around the development of a multibody simulation tool for truss-like structures called LATDYN for Large Angle Transient DYNamics. Multibody analysis involves articulation of structural components as well as robotic maneuvers. These items are necessary for construction (erection or deployment) of large space structures in orbit and the carrying out of certain operations on board the space station. Thus, part of the in-house activity involves the development of methods which treat the changing mass, stiffness and constraints associated with articulating systems. The out-of-house activity involves subcycling, development of large deformation/motion beam formulation, constraint stabilization and direct time integration transient algorithms in parallel computing.
The efforts of Mechanical Dynamics, Inc. in obtaining a general formulation for flexible bodies in a multibody setting are discussed. The efforts being supported by MDI, both in house and externally are summarized. The feasibility of using lumped mass approaches to modeling flexibility in a multibody dynamics context is examined. The kinematics and kinetics for a simple system consisting of two rigid bodies connected together by an elastic beam are developed in detail. Accuracy, efficiency and ease of use using this approach are some of the issues that are then looked at. The formulation is then generalized to a superelement containing several nodes and connecting several bodies. Superelement kinematics and kinetics equations are developed. The feasibility and effectiveness of the method is illustrated by the use of some examples illustrating phenomena common in the context of spacecraft motions.
The development of a new capability for the time-domain simulation of multibody dynamic systems and its application to the study of a large angle rotational maneuvers of the Space Station is described. The effort was divided into three sequential tasks, which required significant advancements of the state-of-the art to accomplish. These were: (1) the development of an explicit mathematical model via symbol manipulation of a flexible, multibody dynamic system; (2) the development of a methodology for balancing the computational load of an explicit mathematical model for concurrent processing; and (3) the implementation and successful simulation of the above on a prototype Custom Architectured Parallel Processing System (CAPPS) containing eight processors. The throughput rate achieved by the CAPPS operating at only 70 percent efficiency, was 3.9 times greater than that obtained sequentially by the IBM 3090 supercomputer simulating the same problem. More significantly, analysis of the results leads to the conclusion that the relative cost effectiveness of concurrent vs. sequential digital computation will grow substantially as the computational load is increased. This is a welcomed development in an era when very complex and cumbersome mathematical models of large space vehicles must be used as substitutes for full scale testing which has become impractical.
Digital control systems for applications such as aircraft avionics and multibody systems must maintain adequate control integrity in adverse as well as nominal operating conditions. For example, control systems for advanced aircraft, and especially those with relaxed static stability, will be critical to flight and will, therefore, have very high reliability specifications which must be met regardless of operating conditions. In addition, multibody systems such as robotic manipulators performing critical functions must have control systems capable of robust performance in any operating environment in order to complete the assigned task reliably. Severe operating conditions for electronic control systems can result from electromagnetic disturbances caused by lightning, high energy radio frequency (HERF) transmitters, and nuclear electromagnetic pulses (NEMP). For this reason, techniques must be developed to evaluate the integrity of the control system in adverse operating environments. The most difficult and illusive perturbations to computer-based control systems that can be caused by an electromagnetic environment (EME) are functional error modes that involve no component damage. These error modes are collectively known as upset, can occur simultaneously in all of the channels of a redundant control system, and are software dependent. Upset studies performed to date have not addressed the assessment of fault tolerant systems and do not involve the evaluation of a control system operating in a closed-loop with the plant. A methodology for performing a real-time simulation of the closed-loop dynamics of a fault tolerant control system with a simulated plant operating in an electromagnetically harsh environment is presented. In particular, considerations for performing upset tests on the controller are discussed. Some of these considerations are the generation and coupling of analog signals representative of electromagnetic disturbances to a control system under test, analog data acquisition, and digital data acquisition from fault tolerant systems. In addition, a case study of an upset test methodology for a fault tolerant electromagnetic aircraft engine control system is presented.