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At least 235 records · Page 13

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NASA NTRS1990

On the numerical solution of the dynamically loaded hydrodynamic lubrication of the point contact problem

The transient analysis of hydrodynamic lubrication of a point-contact is presented. A body-fitted coordinate system is introduced to transform the physical domain to a rectangular computational domain, enabling the use of the Newton-Raphson method for determining pressures and locating the cavitation boundary, where the Reynolds boundary condition is specified. In order to obtain the transient solution, an explicit Euler method is used to effect a time march. The transient dynamic load is a sinusoidal function of time with frequency, fractional loading, and mean load as parameters. Results include the variation of the minimum film thickness and phase-lag with time as functions of excitation frequency. The results are compared with the analytic solution to the transient step bearing problem with the same dynamic loading function. The similarities of the results suggest an approximate model of the point contact minimum film thickness solution.

Lim, Sang G.↗

NASA NTRS1989

Iterative procedures for space shuttle main engine performance models

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented.

Santi, L. Michael↗

NASA NTRS1991

Analysis and design of a six-degree-of-freedom Stewart platform-based robotic wrist

The kinematic analysis and implementation of a six degree of freedom robotic wrist which is mounted to a general open-kinetic chain manipulator to serve as a restbed for studying precision robotic assembly in space is discussed. The wrist design is based on the Stewart Platform mechanism and consists mainly of two platforms and six linear actuators driven by DC motors. Position feedback is achieved by linear displacement transducers mounted along the actuators and force feedback is obtained by a 6 degree of freedom force sensor mounted between the gripper and the payload platform. The robot wrist inverse kinematics which computes the required actuator lengths corresponding to Cartesian variables has a closed-form solution. The forward kinematics is solved iteratively using the Newton-Ralphson method which simultaneously provides a modified Jacobian Matrix which relates length velocities to Cartesian translational velocities and time rates of change of roll-pitch-yaw angles. Results of computer simulation conducted to evaluate the efficiency of the forward kinematics and Modified Jacobian Matrix are discussed.

Nguyen, Charles C.↗

NASA NTRS1990

Modeling of flow systems for implementation under KATE

The modeling of flow systems is a task currently being investigated at Kennedy Space Center in parallel with the development of the KATE artificial intelligence system used for monitoring diagnosis and control. Various aspects of the modeling issues are focussed on with particular emphasis on a water system scheduled for demonstration within the KATE environment in September of this year. LISP procedures were written to solve the continuity equations for three internal pressure nodes using Newton's method for simultaneous nonlinear equations.

Whitlow, Jonathan E.↗

NASA NTRS1991

A system-approach to the elastohydrodynamic lubrication point-contact problem

The classical EHL (elastohydrodynamic lubrication) point contact problem is solved using a new system-approach, similar to that introduced by Houpert and Hamrock for the line-contact problem. Introducing a body-fitted coordinate system, the troublesome free-boundary is transformed to a fixed domain. The Newton-Raphson method can then be used to determine the pressure distribution and the cavitation boundary subject to the Reynolds boundary condition. This method provides an efficient and rigorous way of solving the EHL point contact problem with the aid of a supercomputer and a promising method to deal with the transient EHL point contact problem. A typical pressure distribution and film thickness profile are presented and the minimum film thicknesses are compared with the solution of Hamrock and Dowson. The details of the cavitation boundaries for various operating parameters are discussed.

Lim, Sang Gyu↗

NASA NTRS1991

Experimental study of trajectory planning and control of a high precision robot manipulator

The kinematic and trajectory planning is presented for a 6 DOF end-effector whose design was based on the Stewart Platform mechanism. The end-effector was used as a testbed for studying robotic assembly of NASA hardware with passive compliance. Vector analysis was employed to derive a closed-form solution for the end-effector inverse kinematic transformation. A computationally efficient numerical solution was obtained for the end-effector forward kinematic transformation using Newton-Raphson method. Three trajectory planning schemes, two for fine motion and one for gross motion, were developed for the end-effector. Experiments conducted to evaluate the performance of the trajectory planning schemes showed excellent tracking quality with minimal errors. Current activities focus on implementing the developed trajectory planning schemes on mating and demating space-rated connectors and using the compliant platform to acquire forces/torques applied on the end-effector during the assembly task.

Nguyen, Charles C.↗

NASA NTRS1991

A study of space-rated connectors using a robotic end-effector

The fabrication and testing of a pair of robot fingers designed to grasp two types of Orbital Replacement Unit (ORU) interfaces, the H Handle type and the Micro Square type are discussed. A closed-form solution is given for the force inverse kinematics. A numerical solution using the Newton-Raphson Method for force forward kinematics is given. Mathematical expressions are derived to compute forces/torques applied to the finger. Suggestions are given for improving finger fabrication. The results of numerous experiments conducted to study the characteristics and feasibility of the fingers are given. The first part of the study was devoted to obtaining data on the forces applied by the finger to the interfaces under various translational and rotational misalignments; the second part was devoted to determining the maximum allowed capture angles that would insure successful mating; and the third part was devoted to the processing and interpretation of the forces/torque data.

Nguyen, Charles C.↗

NASA NTRS1991

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Hoyniak, Daniel↗

NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗

NASA NTRS1992

A computational algorithm for crack determination: The multiple crack case

An algorithm for recovering a collection of linear cracks in a homogeneous electrical conductor from boundary measurements of voltages induced by specified current fluxes is developed. The technique is a variation of Newton's method and is based on taking weighted averages of the boundary data. The method also adaptively changes the applied current flux at each iteration to maintain maximum sensitivity to the estimated locations of the cracks.

Bryan, Kurt↗

NASA NTRS1992

A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers

Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.

Watson, Brian C.↗

NASA NTRS1992

A system-approach to the elastohydrodynamic lubrication point-contact problem

Lim, Sang G.↗

NASA NTRS1992

On options for interdisciplinary analysis and design optimization

The interdisciplinary optimization of engineering systems is discussed from the standpoint of the computational alternatives available to the designer. The analysis of such systems typically requires the solution of coupled systems of nonlinear algebraic equations. The solution procedure is necessarily iterative in nature. It is shown that the system can be solved by fixed point iteration, by Newton's method, or by a combination of the two. However, the need for sensitivity analysis may affect the choice of analysis solution method. Similarly, the optimization of the system can be formulated in several ways that are discussed in the paper. It is shown that the effect of the topology of the interaction between disciplines is a key factor in the choice of analysis, sensitivity and optimization methods. Several examples are presented to illustrate the discussion.

Haftka, R. T.↗

NASA NTRS1992

Improving the efficiency of aerodynamic shape optimization procedures

The computational efficiency of an aerodynamic shape optimization procedure which is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newton's method in lieu of an alternating direction implicit (ADI) methodology to calculate the highly converged flow solutions which are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. A substantial factor of 8 decrease in computational time for the optimization process was achieved by implementing both of the design improvements.

Burgreen, Greg W.↗

NASA NTRS1993

Reconstruction of multiple cracks from experimental electrostatic boundary measurements

An algorithm for recovering a collection of linear cracks in a homogeneous electrical conductor from boundary measurements of voltages induced by specified current fluxes is described. The technique is a variation of Newton's method and is based on taking weighted averages of the boundary data. An apparatus that was constructed specifically for generating laboratory data on which to test the algorithm is also described. The algorithm is applied to a number of different test cases and the results are discussed.

Bryan, Kurt↗

NASA NTRS1994

Steady potential solver for unsteady aerodynamic analyses

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Hoyniak, Dan↗

NASA NTRS1995

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Mei, Chuh↗

NASA NTRS1994

Improving the efficiency of aerodynamic shape optimization

The computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid-point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newton's method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. Practically identical optimization results are obtained that are independent of the method used to represent the surface. A substantial factor of 8 decrease in computational time for the optimization process is achieved by implementing both of the design procedure improvements.

Burgreen, Greg W.↗