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At least 397 records · Page 22

Recursive forward dynamics for multiple robot arms moving a common task object

Recursive forward dynamics algorithms are developed and presented for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint angle accelerations, the contact forces, and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint angle accelerations, to the task object accelerations, and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.

Rodriguez, Guillermo↗

Antenna beamforming using optical processing

This work concerns itself with the analytical investigation into the feasibility of optical processor based beamforming for microwave array antennas. The primary focus is on systems utilizing the 20 and 30 GHz communications band and a transmit configuration exclusively to serve this band. A mathematical model is developed for computation of candidate design configurations. The model is capable of determination of the necessary design parameters required for both spatial aspects of the microwave footprint (beam) formation as well as transmitted signal quality. Computed example beams transmitted from geosynchronous orbit are presented to demonstrate network capabilities. A comprehensive device/component survey is also conducted in parallel to determine the feasibility of breadboarding a transmit processor. Recommendations are made for the configuration of such a processor and the components which would comprise such a network.

Anderson, L. P., Jr.↗

Dynamic Analyses Including Joints Of Truss Structures

Method for mathematically modeling joints to assess influences of joints on dynamic response of truss structures developed in study. Only structures with low-frequency oscillations considered; only Coulomb friction and viscous damping included in analysis. Focus of effort to obtain finite-element mathematical models of joints exhibiting load-vs.-deflection behavior similar to measured load-vs.-deflection behavior of real joints. Experiments performed to determine stiffness and damping nonlinearities typical of joint hardware. Algorithm for computing coefficients of analytical joint models based on test data developed to enable study of linear and nonlinear effects of joints on global structural response. Besides intended application to large space structures, applications in nonaerospace community include ground-based antennas and earthquake-resistant steel-framed buildings.

Belvin, W. Keith↗

An analytically linearized helicopter model with improved modeling accuracy

An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.

Jensen, Patrick T.↗

Mathematical characterization of mechanical behavior of porous frictional granular media

A new definition of loading and unloading along the yield surface of Roscoe and Burland is introduced. This is achieved by noting that the strain-hardening parameter in the plastic potential function is deduced from the yield locus equation of Roscoe and Burland. The analytical results are compared with the experimental results for plate-bearing and cone-penetrometer problems and close agreements are demonstrated. The wheel-soil interaction is studied under dynamic loading. The rate-dependent plasticity or viscoelastoplastic behavior is considered. This is accomplished by the internal (hidden) variables associated with time-dependent viscous properties directly superimposed with inelastic behavior governed by the yield criteria of Roscoe and Burland. Effects of inertia and energy dissipation are properly accounted for. Example problems are presented.

Chung, T. J.↗

Experimental and computational investigation of lift-enhancing tabs on a multi-element airfoil

An experimental and computational investigation of the effect of lift enhancing tabs on a two-element airfoil was conducted. The objective of the study was to develop an understanding of the flow physics associated with lift enhancing tabs on a multi-element airfoil. A NACA 63(sub 2)-215 ModB airfoil with a 30 percent chord Fowler flap was tested in the NASA Ames 7 by 10 foot wind tunnel. Lift enhancing tabs of various heights were tested on both the main element and the flap for a variety of flap riggings. Computations of the flow over the two-element airfoil were performed using the two-dimensional incompressible Navier-Stokes code INS2D-UP. The computer results predict all of the trends in the experimental data quite well. When the flow over the flap upper surface is attached, tabs mounted at the main element trailing edge (cove tabs) produce very little change in lift. At high flap deflections. however, the flow over the flap is separated and cove tabs produce large increases in lift and corresponding reductions in drag by eliminating the separated flow. Cove tabs permit high flap deflection angles to be achieved and reduce the sensitivity of the airfoil lift to the size of the flap gap. Tabs attached to the flap training edge (flap tabs) are effective at increasing lift without significantly increasing drag. A combination of a cove tab and a flap tab increased the airfoil lift coefficient by 11 percent relative to the highest lift tab coefficient achieved by any baseline configuration at an angle of attack of zero percent and the maximum lift coefficient was increased by more than 3 percent. A simple analytic model based on potential flow was developed to provide a more detailed understanding of how lift enhancing tabs work. The tabs were modeled by a point vortex at the training edge. Sensitivity relationships were derived which provide a mathematical basis for explaining the effects of lift enhancing tabs on a multi-element airfoil. Results of the modeling effort indicate that the dominant effects of the tabs on the pressure distribution of each element of the airfoil can be captured with a potential flow model for cases with no flow separation.

Ashby, Dale↗

Extravehicular Mobility Unit Penetration Probability from Micrometeoroids and Orbital Debris: Revised Analytical Model and Potential Space Suit Improvements

The NASA Extravehicular Mobility Unit (EMU) micrometeoroid and orbital debris protection ability has recently been assessed against an updated, higher threat space environment model. The new environment was analyzed in conjunction with a revised EMU solid model using a NASA computer code. Results showed that the EMU exceeds the required mathematical Probability of having No Penetrations (PNP) of any suit pressure bladder over the remaining life of the program (2,700 projected hours of 2 person spacewalks). The success probability was calculated to be 0.94, versus a requirement of >0.91, for the current spacesuit s outer protective garment. In parallel to the probability assessment, potential improvements to the current spacesuit s outer protective garment were built and impact tested. A NASA light gas gun was used to launch projectiles at test items, at speeds of approximately 7 km per second. Test results showed that substantial garment improvements could be made, with mild material enhancements and moderate assembly development. The spacesuit s PNP would improve marginally with the tested enhancements, if they were available for immediate incorporation. This paper discusses the results of the model assessment process and test program. These findings add confidence to the continued use of the existing NASA EMU during International Space Station (ISS) assembly and Shuttle Operations. They provide a viable avenue for improved hypervelocity impact protection for the EMU, or for future space suits.

Chase, Thomas D.↗

Heat storage capability of a rolling cylinder using Glauber's salt

The rolling cylinder phase change heat storage concept was developed to the point where a prototype design is completed and a cost analysis is prepared. A series of experimental and analytical tasks are defined to establish the thermal, mechanical, and materials behavior of rolling cylinder devices. These tasks include: analyses of internal and external heat transfer; performance and lifetime testing of the phase change materials; corrosion evaluation; development of a mathematical model; and design of a prototype and associated test equipment.

Herrick, C. S.↗

Calculation of sensitivity derivatives in thermal problems by finite differences

The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.

Haftka, R. T.↗

Diffusion in Melts and Magmas

Diffusion results from random motion of particles and entities. Diffusion in melts and magmas is due to thermally excited random motion of atoms, ions, and clusters, and plays a critical role in magmatic and volcanic processes. In melts and magmas, diffusion is one of the two mechanisms of mass transfer; the other being bulk flow (referred to as convection or advection). When both are present, diffusion refers to the dispersive motion relative to the mean bulk flow in a given reference frame (Richter et al. 1998). Diffusion plays critical roles in controlling magma mixing (Watson 1982; Koyaguchi 1985, 1989; Lesher 1994; Huber et al. 2009; Guo and Zhang 2020), mineral growth and dissolution rates in magmas (e.g., Watson 1982; Harrison and Watson 1983; Zhang et al. 1989; Newcombe et al. 2014; Macris et al. 2018), bubble growth and dissolution rate in magmas (Sparks 1978; Proussevitch and Sahagian 1998; Liu and Zhang 2000; Zhang 2013), and elemental and isotope fractionation during mineral 2 growth and dissolution (Jambon 1980; Richter et al. 1999, 2003; Watson and Muller 2009; Chopra et al. 2012; Watkins et al. 2014, 2017; Holycross et al. 2016, 2018). As a result, diffusion also plays an essential role in explosive volcanic eruptions and magma crystallization. Furthermore, diffusion has important applications in geospeedometry (Lasaga 1983, 1998; Zhang 1994, 2008; Trail et al. 2016; Zhang and Xu 2016). Experimental investigation of diffusion in geologically relevant silicate melts began to flourish in the 1970’s when micro-analytical measurements of diffusion profiles became available. In addition to the vast number of papers published since then, numerous books and reviews are available for diffusion in silicate melts. Hofmann et al. (1974) edited a book titled “Geochemical Transport and Kinetics” published by Carnegie Institution of Washington. This was the first landmark book summarizing the field. Lasaga and Kirkpatrick (1981) edited a book “Kinetics of Geochemical Processes” as volume 8 of the Reviews in Mineralogy (later becoming Reviews in Mineralogy and Geochemistry) series. Zhang and Cherniak (2010) edited “Diffusion in Minerals and Melts” as volume 72 of Reviews of Mineralogy and Geochemistry series, in which one chapter focused on diffusion theory, five chapters on diffusion in silicate melts (Behrens 2010; Lesher 2010; Liang 2010; Zhang and Ni 2010; Zhang et al. 2010), and other chapters were on experimental, analytical, and computational methods, and diffusion in minerals. Several textbooks covered the principles and applications of diffusion theories (Kirkaldy and Young 1987; Shewmon 1989; Cussler 1997; Lasaga 1998; Zhang 2008; Vrentas and Vrentas 2016), and two classic books covered the mathematics of diffusion (Carslaw and Jaeger 1959; Crank 1975). In preparing for this review chapter, we thought carefully about what to cover for this vast field, and decided to briefly go through the fundamentals of diffusion (more complete review can be found in Chakraborty 1995; Zhang 2008, 2010) and solutions to often-encountered 3 diffusion problems, and then focus on post-2010 diffusion studies on silicate melts and magmas. Here, melts refer to (mostly natural) silicate liquid, and magmas refer to crystal-bearing and/or bubble-bearing melts in which the continuous phase is the melt. There is a large body of work on diffusion in glasses, especially in the materials science literature, which is not covered in this review.

Youxue Zhang↗

Model verification of large structural systems

A methodology was formulated, and a general computer code implemented for processing sinusoidal vibration test data to simultaneously make adjustments to a prior mathematical model of a large structural system, and resolve measured response data to obtain a set of orthogonal modes representative of the test model. The derivation of estimator equations is shown along with example problems. A method for improving the prior analytic model is included.

Lee, L. T.↗

Large Deformation Behavior of Long Shallow Cylindrical Composite Panels

An exact solution is presented for the large deformation response of a simply supported orthotropic cylindrical panel subjected to a uniform line load along a cylinder generator. The cross section of the cylinder is circular and deformations up to the fully snapped through position are investigated. The orthotropic axes are parallel to the generator and circumferential directions. The governing equations are derived using laminated plate theory, nonlinear strain-displacement relations, and applying variational principles. The response is investigated for the case of a panel loaded exactly at midspan and for a panel with the load offset from midspan. The mathematical formulation is one dimensional in the circumferential coordinate. Solutions are obtained in closed-form. An experimental apparatus was designed to load the panels. Experimental results of displacement controlled tests performed on graphite-epoxy curved panels are compared with analytical predictions.

Carper, Douglas M.↗

Curvilinear Displacement Transfer Functions for Deformed Shape Predictions of Curved Structures Using Distributed Surface Strains

Curvilinear Displacement Transfer Functions were formulated for deformed shape predictions of different curved structures using surface strains. The embedded curved beam (depth-wise cross section of a curved structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. The discrete approach enabled piecewise integrations of a curvature-strain differential equation for the embedded curved beam to yield closed-form Curvilinear Displacement Transfer Functions, which are written in terms of embedded curved-beam geometrical parameters and surface strains. By inputting the surface strain data, the Curvilinear Displacement Transfer Functions can transform surface strains into deflections along each embedded curved beam for mapping out the overall structural deformed shapes. The finite-element method was used to analytically generate the surface strains of the curved beams. The deformed shape prediction accuracies were then determined by comparing the theoretical deflections with the finite-element-generated deflections, which were used as yardsticks. By introducing the correction factors in simple mathematical forms, the Curvilinear Displacement Transfer Functions can be quite accurate for shape predictions of different curved-beam structures ranging from limit case of straight beam up to semicircular curved beam.

Ko, William L.↗

Earth-moon system: Dynamics and parameter estimation

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Breedlove, W. J., Jr.↗

Theory of motion of Jupiter's Galilean satellites

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

Lieske, J. H.↗

Parameter identification applied to analytic hingeless rotor modeling

It is known that dynamic rotor inflow has a substantial effect on rotor dynamic loads. Despite the complexity of the unsteady flow problem, simple analytical models can be made useful by identifying their parameters from transient response tests without performing flow measurements. Two analytical inflow models are studied: the first is based on an equivalent blade Lock number, the second is based on a time delayed unsteady momentum inflow. In preparation for the experimental data analysis, identifications from simulated test data and an eigenvalue analysis are performed. The experimental results show that the first analytical inflow model is accurate for rotor advance ratios of 0.4 and above. For lower advance ratios, the second inflow model provides better accuracy. Prediction studies with experimental data not used for the identification are performed to determine the accuracy of the mathematical models.

Banerjee, D.↗

Boundary-layer model of pattern formation in solidification

A model of pattern formation in crystal growth is proposed, and its analytic properties are investigated. The principal dynamical variables in this model are the curvature of the solidification front and the thickness (or heat content) of a thermal boundary layer, both taken to be functions of position along the interface. This model is mathematically much more tractable than the realistic, fully nonlocal version of the free-boundary problem, and still recaptures many of the features that seem essential for studying dendritic behavior, for example. Preliminary numerical solutions produce snowflakelike patterns similar to those seen in nature.

Ben-Jacob, E.↗