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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.
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The linearized equation of motion for the NASA/IEEE SCOLE configuration are developed. The derivation is based on the method of Lagrange and the equations are assembled into matrix second order form.
A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.
The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.
Report shows how spatial-operator algebra developed by authors used to derive linearized mathematical models of dynamics of robotic manipulators. Aspects of spatial-operator algebra also described in "Robot Control Based On Spatial-Operator Algebra" (NPO-17918), "Unified Formulation Of Dynamics Of Robot Arms" (NPO-18040), and "Spatial-Operator Algebra For Robotic Manipulators" (NPO-17770).
Linearized dynamics models for manipulators are useful in robot analysis, motion planning, and control applications. Techniques from the spatial operator algebra are used to obtain closed form operator expressions for two types of linearized dynamics models, the linearized inverse and forward dynamics models. Spatially recursive algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and coefficient matrices for the linearized inverse dynamics model are developed first. Subsequently, operator factorization and inversion identities are used to develop corresponding closed-form expressions for the linearized forward dynamics model (LFDM). Once again, these are used to develop algorithms of O(n) and O(n-squared) complexity for the computation of the perturbation vector and the coefficient matrices. The algorithms for the LFDM do not require the explicit computation of the mass matrix nor its numerical inversion and are also of lower complexity than the conventional O(n-cubed) algorithms.
A linearized model for rotorcraft dynamics has been developed through the use of symbolic automatic equation generation techniques. The dynamic model has been formulated in a unique way such that it can be used to analyze a variety of rotor/body coupling problems including a rotor mounted on a flexible shaft with a number of modes as well as free flight stability and control characteristics. Direct comparison of the time response to longitudinaol, lateral and directional control inputs at various trim conditions shows that the linear model yields good to very good correlation with flight test. In particular it is also shown that a dynamic inflow model is essential to obtain good time response correlation especially for the hover trim condition and also that at translational flight trim conditions the main rotor wake interaction with the tail rotor and fixed tail surfaces is a significant contributor to the response. A relatively simple model for the downwash and sidewash at tail surfaces based on flat vortex wake theory is shown to produce good agreement. Finaly, the influence of rotor flap and lag dynamics on automatic control systems feedback gain limitations is investigated with the model.
An efficient method for the load analysis of Shuttle-payload systems with linear or nonlinear attachment interfaces is presented which allows the kinematics of the interface degrees of freedom at a given time to be evaluated without calculating the combined system modal representation of the Space Shuttle and its payload. For the case of a nonlinear dynamic model, an iterative procedure is employed to converge the nonlinear terms of the equations of motion to reliable values. Results are presented for a Shuttle abort landing event.
Pulsation properties of star models with linear density distribution, considering radial, adiabatic contraction and dynamical stability
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power, and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.
The linear model of the Stirling system developed by NASA Glenn Research Center (GRC) has been extended to include a user-specified heat input. Previously developed linear models were limited to the Stirling convertor and electrical load. They represented the thermodynamic cycle with pressure factors that remained constant. The numerical values of the pressure factors were generated by linearizing GRC s non-linear System Dynamic Model (SDM) of the convertor at a chosen operating point. The pressure factors were fixed for that operating point, thus, the model lost accuracy if a transition to a different operating point were simulated. Although the previous linear model was used in developing controllers that manipulated current, voltage, and piston position, it could not be used in the development of control algorithms that regulated hot-end temperature. This basic model was extended to include the thermal dynamics associated with a hot-end temperature that varies over time in response to external changes as well as to changes in the Stirling cycle. The linear model described herein includes not only dynamics of the piston, displacer, gas, and electrical circuit, but also the transient effects of the heater head thermal inertia. The linear version algebraically couples two separate linear dynamic models, one model of the Stirling convertor and one model of the thermal system, through the pressure factors. The thermal system model includes heat flow of heat transfer fluid, insulation loss, and temperature drops from the heat source to the Stirling convertor expansion space. The linear model was compared to a nonlinear model, and performance was very similar. The resulting linear model can be implemented in a variety of computing environments, and is suitable for analysis with classical and state space controls analysis techniques.
An analytical and computerized study of the steady state and transient response of a phosphoric acid fuel cell (PAFC) system was completed. Parametric studies and sensitivity analyses of the PAFC system's operation were accomplished. Four non-linear dynamic models of the fuel cell stack, reformer, shift converters, and heat exchangers were developed based on nonhomogeneous non-linear partial differential equations, which include the material, component, energy balance, and electrochemical kinetic features. Due to a lack of experimental data for the dynamic response of the components only the steady state results were compared with data from other sources, indicating reasonably good agreement. A steady state simulation of the entire system was developed using, nonlinear ordinary differential equations. The finite difference method and trial-and-error procedures were used to obtain a solution. Using the model, a PAFC system, that was developed under NASA Grant, NCC3-17, was improved through the optimization of the heat exchanger network. Three types of cooling configurations for cell plates were evaluated to obtain the best current density and temperature distributions. The steady state solutions were used as the initial conditions in the dynamic model. The transient response of a simplified PAFC system, which included all of the major components, subjected to a load change was obtained. Due to the length of the computation time for the transient response calculations, analysis on a real-time computer was not possible. A simulation of the real-time calculations was developed on a batch type computer. The transient response characteristics are needed for the optimization of the design and control of the whole PAFC system. All of the models, procedures and simulations were programmed in Fortran and run on IBM 370 computers at Cleveland State University and the NASA Lewis Research Center.
The long-standing problem of understanding the evolution of the global magnetic fields that drive solar activity through different temporal scales is becoming more tractable because, in addition to 400 years of sunspot records, we now have almost 4 solar cycles of magnetic field observations. These observations allow us to discern physical connections between dynamo model variables and observations using data assimilation analysis. In particular, the Ensemble Kalman Filter approach takes into account uncertainties in both observations and modeling and allows us to make reliable forecasts of solar cycle activity by using a relatively simple non-linear dynamical model of the solar dynamo. To expand this approach for more complex 2D and 3D dynamo modeling, it is necessary to decompose the observed synoptic magnetograms into poloidal and toroidal field components. In this presentation I will present initial results on magnetogram decomposition and assimilation of magnetogram data into dynamo modeling.
The long-standing problem of understanding the evolution of the global magnetic fields that drive solar activity through different temporal scales is becoming more tractable because, in addition to 400 years of sunspot records, we now have almost 4 solar cycles of magnetic field observations. These observations allow us to discern physical connections between dynamo model variables and observations using data assimilation analysis. In particular, the Ensemble Kalman Filter approach takes into account uncertainties in both observations and modeling and allows us to make reliable forecasts of solar cycle activity cycles by using a relatively simple non-linear dynamical model of the solar dynamo. To expand this approach for more complex 2D and 3D dynamo modeling, it is necessary to decompose the observed synoptic magnetograms into poloidal and toroidal field components. In this presentation I will present initial results on magnetogram decomposition and assimilation of magnetogram data into dynamo modeling.
A digital computer program, DYGABCD, was developed that generates linearized, dynamic models of simulated turbofan and turbojet engines. DYGABCD is based on an earlier computer program, DYNGEN, that is capable of calculating simulated nonlinear steady-state and transient performance of one- and two-spool turbojet engines or two- and three-spool turbofan engines. Most control design techniques require linear system descriptions. For multiple-input/multiple-output systems such as turbine engines, state space matrix descriptions of the system are often desirable. DYGABCD computes the state space matrices commonly referred to as the A, B, C, and D matrices required for a linear system description. The report discusses the analytical approach and provides a users manual, FORTRAN listings, and a sample case.
Active magnetic radial bearings are constructed with a combination of permanent magnets to provide bias forces and electromagnets to generate control forces for the reduction of cost and the operating energy consumption. Ring-shaped permanent magnets with axial magnetization are attached to a shaft and share their magnet stators with the electromagnets. The magnet cores are made of solid iron for simplicity. A simplified magnetic circuit of the combined magnet system is analyzed with linear circuit theory by approximating the characteristics of permanent magnets with a linear relation. A linearized dynamical model of the control force is presented with the first-order approximation of the effects of eddy currents. Frequency responses of the rotor motion to disturbance inputs and the motion for impulsive forces are tested in the non-rotating state. The frequency responses are compared with numerical results. The decay of rotor speed due to magnetic braking is examined. The experimental results and the presented linearized model are similar to those of the all-electromagnetic design.
Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.
Stability and control characteristics of a high-performance aircraft have been examined over a wide range of maneuvering flight conditions, in order to identify general rules for the design of departure-preventing control systems. This has been accomplished using fully coupled linear dynamic models which account for nonzero mean values of aerodynamic angles and angular rates. Stability augmentation systems derived from optimal control theory are shown to maintain stable, well-damped aircraft dynamics over a wide range of maneuvering flight conditions. This design approach generates cross-feeds and control interconnects (as well as conventional feedback terms) for improved aircraft stability.