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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Dynamics of a split torque helicopter transmission

Split torque designs, proposed as alternatives to traditional planetary designs for helicopter main rotor transmissions, can save weight and be more reliable than traditional designs. This report presents the results of an analytical study of the system dynamics and performance of a split torque gearbox that uses a balance beam mechanism for load sharing. The Lagrange method was applied to develop a system of equations of motion. The mathematical model includes time-varying gear mesh stiffness, friction, and manufacturing errors. Cornell's method for calculating the stiffness of spur gear teeth was extended and applied to helical gears. The phenomenon of sidebands spaced at shaft frequencies about gear mesh fundamental frequencies was simulated by modeling total composite gear errors as sinusoid functions. Although the gearbox has symmetric geometry, the loads and motions of the two power paths differ. Friction must be considered to properly evaluate the balance beam mechanism. For the design studied, the balance beam is not an effective device for load sharing unless the coefficient of friction is less than 0.003. The complete system stiffness as represented by the stiffness matrix used in this analysis must be considered to precisely determine the optimal tooth indexing position.

Krantz, Timothy L.↗
NASA NTRS2004

Using Redundancy To Reduce Errors in Magnetometer Readings

A method of reducing errors in noisy magnetic-field measurements involves exploitation of redundancy in the readings of multiple magnetometers in a cluster. By "redundancy"is meant that the readings are not entirely independent of each other because the relationships among the magnetic-field components that one seeks to measure are governed by the fundamental laws of electromagnetism as expressed by Maxwell's equations. Assuming that the magnetometers are located outside a magnetic material, that the magnetic field is steady or quasi-steady, and that there are no electric currents flowing in or near the magnetometers, the applicable Maxwell 's equations are delta x B = 0 and delta(raised dot) B = 0, where B is the magnetic-flux-density vector. By suitable algebraic manipulation, these equations can be shown to impose three independent constraints on the values of the components of B at the various magnetometer positions. In general, the problem of reducing the errors in noisy measurements is one of finding a set of corrected values that minimize an error function. In the present method, the error function is formulated as (1) the sum of squares of the differences between the corrected and noisy measurement values plus (2) a sum of three terms, each comprising the product of a Lagrange multiplier and one of the three constraints. The partial derivatives of the error function with respect to the corrected magnetic-field component values and the Lagrange multipliers are set equal to zero, leading to a set of equations that can be put into matrix.vector form. The matrix can be inverted to solve for a vector that comprises the corrected magnetic-field component values and the Lagrange multipliers.

Kulikov, Igor↗
NASA NTRS1993

Shape optimization governed by the Euler equations using an adjoint method

A numerical approach for the treatment of optimal shape problems governed by the Euler equations is discussed. Focus is on flows with embedded shocks. A very simple problem is considered: the design of a quasi-one-dimensional Laval nozzle. A cost function and a set of Lagrange multipliers are introduced to achieve the minimum. The nature of the resulting costate equations is discussed. A theoretical difficulty that arises for cases with embedded shocks is pointed out and solved. Finally, some results are given to illustrate the effectiveness of the method.

Iollo, Angelo↗
NASA NTRS1972

Analytic partial derivatives for estimating low-thrust parameters.

Analytic partial derivatives for estimating orbital low-thrust parameters via differential correction are developed and compared with two different numerical methods. The formulation is independent of the particular thrust model used and is applicable to all physically possible elliptic orbits. The starting point for the development is the set of variational equations of the elliptic orbital elements in the form due to Lagrange. The first time derivatives of the elements are transformed to derivatives with respect to the space variable, true anomaly, and integrated to first order in closed form in a straightforward general perturbations approach, with one exception: particular attention is given to the mean anomaly as influenced by thrust perturbations in the semimajor axis so that the complete first-order effect is included. The partials of the elements are then taken with respect to any given thrust parameter. Two comparisons are made with numerical methods for computing these thrust partials: numerical quotients and numerical integration of the variational equations for thrust.

Cunningham, G. W.↗
NASA NTRS1985

Formulation and application of Russell's method

It is shown that the numerical technique of Russell's momentum approach can be derived by using Hamilton's principle and Vance's numerical scheme. It results in a set of first order differnce equations for solving the angular velocities. The numerical examples show that the method is reliable. The algorithm is modified next to perform the analysis of N-body systems with closed loop topology. To increase the formulation flexibility, the equations of motion are represented by using Cartesian coordinates and Lagrange multipliers. The algorithm consists of two parts, Vance's scheme and an unconstrained minimization. The Vance's scheme is used to find the angular velocities, and the unconstrained minimization is applied to provide the correct angular displacements. The proposed scheme is further extended to find the design sensitivity of an N-body system with closed loop configuration, and to carry out the design optimization as well. The numerical example of a small-scaled mechanical system is presented to verify the proposed formulation.

Hou, J. W.↗
NASA NTRS1984

The ADS general-purpose optimization program

The mathematical statement of the general nonlinear optimization problem is given as follows: find the vector of design variables, X, that will minimize f(X) subject to G sub J (x) + or - 0 j=1,m H sub K hk(X) = 0 k=1,l X Lower I approx less than X sub I approx. less than X U over I i = 1,N. The vector of design variables, X, includes all those variables which may be changed by the ADS program in order to arrive at the optimum design. The objective function F(X) to be minimized may be weight, cost or some other performance measure. If the objective is to be maximized, this is accomplished by minimizing -F(X). The inequality constraints include limits on stress, deformation, aeroelastic response or controllability, as examples, and may be nonlinear implicit functions of the design variables, X. The equality constraints h sub k(X) represent conditions that must be satisfied precisely for the design to be acceptable. Equality constraints are not fully operational in version 1.0 of the ADS program, although they are available in the Augmented Lagrange Multiplier method. The side constraints given by the last equation are used to directly limit the region of search for the optimum. The ADS program will never consider a design which is not within these limits.

Vanderplaats, G. N.↗
NASA NTRS1991

Elimination of secular terms from the differential equations for the elements of perturbed two-body motion

In 1961, Sperling linearized and regularized the differential equations of motion of the two-body problem by changing the independent variable from time to fictitious time by Sundman's transformation (r = dt/ds) and by embedding the two-body energy integral and the Laplace vector. In 1968, Burdet developed a perturbation theory which was uniformly valid for all types of orbits using a variation of parameters approach on the elements which appeared in Sperling's equations for the two-body solution. In 1973, Bond and Hanssen improved Burdet's set of differential equations by embedding the total energy (which is a constant when the potential function is explicitly dependent upon time.) The Jacobian constant was used as an element to replace the total energy in a reformulation of the differential equations of motion. In the process, another element which is proportional to a component of the angular momentum was introduced. Recently trajectories computed during numerical studies of atmospheric entry from circular orbits and low thrust beginning in near-circular orbits exhibited numerical instability when solved by the method of Bond and Gottlieb (1989) for long time intervals. It was found that this instability was due to secular terms which appear on the righthand sides of the differential equations of some of the elements. In this paper, this instability is removed by the introduction of another vector integral called the delta integral (which replaces the Laplace Vector) and another scalar integral which removes the secular terms. The introduction of these integrals requires a new derivation of the differential equations for most of the elements. For this rederivation, the Lagrange method of variation of parameters is used, making the development more concise. Numerical examples of this improvement are presented.

Bond, Victor R.↗
NASA NTRS1994

Radiation from advanced solid rocket motor plumes

The overall objective of this study was to develop an understanding of solid rocket motor (SRM) plumes in sufficient detail to accurately explain the majority of plume radiation test data. Improved flowfield and radiation analysis codes were developed to accurately and efficiently account for all the factors which effect radiation heating from rocket plumes. These codes were verified by comparing predicted plume behavior with measured NASA/MSFC ASRM test data. Upon conducting a thorough review of the current state-of-the-art of SRM plume flowfield and radiation prediction methodology and the pertinent data base, the following analyses were developed for future design use. The NOZZRAD code was developed for preliminary base heating design and Al2O3 particle optical property data evaluation using a generalized two-flux solution to the radiative transfer equation. The IDARAD code was developed for rapid evaluation of plume radiation effects using the spherical harmonics method of differential approximation to the radiative transfer equation. The FDNS CFD code with fully coupled Euler-Lagrange particle tracking was validated by comparison to predictions made with the industry standard RAMP code for SRM nozzle flowfield analysis. The FDNS code provides the ability to analyze not only rocket nozzle flow, but also axisymmetric and three-dimensional plume flowfields with state-of-the-art CFD methodology. Procedures for conducting meaningful thermo-vision camera studies were developed.

Farmer, Richard C.↗
NASA NTRS1977

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

Vinh, N. X.↗
NASA NTRS1984

Hybrid Semiloof elements for plates and shells based upon a modified Hu-Washizu principle

Hybrid SemiLoof elements for plates and shells are developed based upon modified Hu-Washizu principle. In the new version of the assumed stress hybrid formulation the equilibrium equations are satisfied through the introduction of internal displacement parameters as Lagrange multipliers. The inversion of the resulting H-matrices is simplified particularly when the stresses are expressed in terms of natural coordinates. A 24-DOF triangular element and a 32-DOF quadrilateral element based on shallow shell theory are derived and evaluated.

Pian, T. H. H.↗
NASA NTRS1990

Randomly Sampled-Data Control Systems

The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions.

Han, Kuoruey↗
NASA NTRS1988

The use of the articulated total body model as a robot dynamics simulation tool

The Articulated Total Body (ATB) model is a computer sumulation program which was originally developed for the study of aircrew member dynamics during ejection from high-speed aircraft. This model is totally three-dimensional and is based on the rigid body dynamics of coupled systems which use Euler's equations of motion with constraint relations of the type employed in the Lagrange method. In this paper the use of the ATB model as a robot dynamics simulation tool is discussed and various simulations are demonstrated. For this purpose the ATB model has been modified to allow for the application of torques at the joints as functions of state variables of the system. Specifically, the motion of a robotic arm with six revolute articulations with joint torques prescribed as functions of angular displacement and angular velocity are demonstrated. The simulation procedures developed in this work may serve as valuable tools for analyzing robotic mechanisms, dynamic effects, joint load transmissions, feed-back control algorithms employed in the actuator control and end-effector trajectories.

Obergfell, Louise A.↗
NASA NTRSDate not supplied

Using DSCOVR EPIC as an Additional Calibration Reference to Radiometrically Scale the Geo Imagers for the NASA CERES Project

The NASA CERES project provides climate-quality observed TOA and calculated surface fluxes to the climate community. The CERES instruments are mounted on the Aqua, Terra, NPP, and NOAA-20 low earth orbiting (LEO) satellites, where they are used alongside the VIIRS and MODIS based cloud properties necessary for converting CERES radiance observations into fluxes. The CERES SYN1deg product provides the regional hourly fluxes in between the Terra and Aqua/NOAA-20-CERES observations based on geostationary imager (GEO) radiances. The GEO radiances are radiometrically scaled to the MODIS or VIIRS calibration references. The GEO and MODIS inter-calibration events are limited by the Aqua-MODIS or VIIRS local equator crossing time of 1:30 PM. The DSCOVR satellite orbits the Lagrange-1 (L1) point about 1.5 million kilometers from Earth, and the Earth Polychromatic Imaging Camera (EPIC) instrument onboard DSCOVR has a constant view of the sunlit side of the Earth while taking images ranging from the UV to the NIR throughout the day. While the EPIC sensor has no onboard calibration systems, multiple inter-calibration studies have indicated that EPIC is radiometrically stable, which allows it to potentially be used as a transfer radiometer between imagers. This study will assess the viability of using EPIC as a consistent and stable calibration source for GEO imagers. EPIC will be inter-calibrated with Himawari-8 that has been radiometrically scaled with Aqua. The Himawari-8 based EPIC calibration gains will be verified by the EPIC calibration gains determined directly from Aqua-MODIS matches. The EPIC calibration gains based on Himawari-8 will be stratified by local time to determine any diurnal dependence of the GEO/EPIC calibration strategy.

C O Haney↗
NASA NTRS1990

Explicit-implicit staggered procedure for multibody dynamics analysis

An explicit-implicit staggered time-integration procedure is presented for the solution of multibody dynamical equations involving large rotations and constraints. The algorithms adopts a two-stage modification of the central difference algorithm for integrating the translational coordinates and the angular velocity vector, and the midpoint implicit algorithm to solve the kinematical relation in terms of the Euler parameters for updating the angular orientations. The Lagrange multipliers to enforce the system constraints are obtained by implicitly integrating a parabolically regularized differential equation for the multipliers. The performance of the present procedure has been evaluated to applying the procedure to solve several sample problems. The results indicate that the procedure is robust in dealing with a variety of constraints and spatial kinematic motions, hence it is recommended for applications to general multibody dynamics analyses.

Park, K. C.↗
NASA NTRS1970

Spatially homogeneous world models

Einstein field equations for spatially homogeneous spaces, considering rotating matter model in regularized Euler-Lagrange form

Ozsvath, I.↗
NASA NTRS1973

A new technique for calculating reentry base heating

The laminar base flow field of a two-dimensional reentry body has been studied by Telenin's method. The flow domain was divided into strips along the x-axis, and the flow variations were represented by Lagrange interpolation polynomials in the transformed vertical coordinate. The complete Navier-Stokes equations were used in the near wake region, and the boundary layer equations were applied elsewhere. The boundary conditions consisted of the flat plate thermal boundary layer in the forebody region and the near wake profile in the downstream region. The resulting two-point boundary value problem of 33 ordinary differential equations was then solved by the multiple shooting method. The detailed flow field and thermal environment in the base region are presented in the form of temperature contours, Mach number contours, velocity vectors, pressure distributions, and heat transfer coefficients on the base surface. The maximum heating rate was found on the centerline, and the two-dimensional stagnation point flow solution was adquate to estimate the maximum heating rate so long as the local Reynolds number could be obtained.

Meng, J. C. S.↗