Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “differential transformation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3

Experimental Investigation of a Graphite-Composite Intertank Section for a Reusable Launch Vehicle

The use of graphite-composites as primary structure is essential for the development of a cost effective single-stage-to-orbit reusable launch vehicle (RLV). A full-scale segment of a graphite-composite intertank was designed and fabricated by an industry team and tested at NASA Langley Research Center as a part of the RLV technology development program. The intertank test component was approximately 3.0 m long by 6.7 m wide and included slightly less than a 90deg section of a cylindrical intertank. The test article was fabricated using graphite-bismaelimide composite material and consisted of a hat-stiffened skin with five ring frames. The stiffeners were secondarily bonded to the panel skin and the ring frames were mechanically attached. The test article was loaded to failure with a uniform compression load applied by 21 individually controlled hydraulic actuators. Resistance strain gages, linear variable differential transformers and video cameras were used to measure and record the test results. A linear f d t e element analysis of the test article and test fixture was performed. The test results verified the structural integrity cf the intertank test article up to the design limit load. However, the test article failed in general skin buckling between the ring frames at a load 1.08 times design limit load. This load was considerably lower than the expected failure load. The cause of premature failure is being investigated. Good correlation of the test and analysis results was obtained for loads up to the design limit load.

Sawyer, James Wayne↗

Inductive Linear-Position Sensor/Limit-Sensor Units

A new sensor provides an absolute position measurement. A schematic view of a motorized linear-translation stage that contains, at each end, an electronic unit that functions as both (1) a non-contact sensor that measures the absolute position of the stage and (2) a non-contact equivalent of a limit switch that is tripped when the stage reaches the nominal limit position. The need for such an absolute linear position-sensor/limit-sensor unit arises in the case of a linear-translation stage that is part of a larger system in which the actual stopping position of the stage (relative to the nominal limit position) must be known. Because inertia inevitably causes the stage to run somewhat past the nominal limit position, tripping of a standard limit switch or other limit sensor does not provide the required indication of the actual stopping position. This innovative sensor unit operates on an electromagnetic-induction principle similar to that of linear variable differential transformers (LVDTs)

Alhom, Dean↗

Controlling Force and Depth in Friction Stir Welding

Feedback control of the penetration force applied to a pin tool in friction stir welding has been found to be a robust and reliable means for controlling the depth of penetration of the tool. This discovery has made it possible to simplify depth control and to weld with greater repeatability, even on workpieces with long weld joints. Prior to this discovery, depths of penetration in friction stir welding were controlled by hard-tooled roller assemblies or by depth actuators controlled by feedback from such external sensors as linear variable-differential transformers or laser-based devices. These means of control are limited: A hard-tooled roller assembly confines a pin tool to a preset depth that cannot be changed easily during the welding process. A measurement by an external sensor is only an indirect indicative of the depth of penetration, and computations to correlate such a measurement with a depth of penetration are vulnerable to error. The present force-feedback approach exploits the proportionality between the depth and the force of penetration Unlike a depth measurement taken by an external sensor, a force measurement can be direct because it can be taken by a sensor coupled directly to the pin tool. The reading can be processed through a modern electronic servo control system to control an actuator to keep the applied penetration force at the desired level. In comparison with the older depth-control methods described above, this method offers greater sensitivity to plasticizing of the workpiece metal and is less sensitive to process noise, resulting in a more consistent process. In an experiment, a tapered panel was friction stir welded while controlling the force of penetration according to this method. The figure is a plot of measurements taken during the experiment, showing that force was controlled with a variation of 200 lb (890 N), resulting in control of the depth of penetration with a variation of 0.004 in. (0.1 mm).

Adams, Glynn↗

Improved Electrohydraulic Linear Actuators

A product line of improved electrohydraulic linear actuators has been developed. These actuators are designed especially for use in actuating valves in rocket-engine test facilities. They are also adaptable to many industrial uses, such as steam turbines, process control valves, dampers, motion control, etc. The advantageous features of the improved electrohydraulic linear actuators are best described with respect to shortcomings of prior electrohydraulic linear actuators that the improved ones are intended to supplant. The flow of hydraulic fluid to the two ports of the actuator cylinder is controlled by a servo valve that is controlled by a signal from a servo amplifier that, in turn, receives an analog position-command signal (a current having a value between 4 and 20 mA) from a supervisory control system of the facility. As the position command changes, the servo valve shifts, causing a greater flow of hydraulic fluid to one side of the cylinder and thereby causing the actuator piston to move to extend or retract a piston rod from the actuator body. A linear variable differential transformer (LVDT) directly linked to the piston provides a position-feedback signal, which is compared with the position-command signal in the servo amplifier. When the position-feedback and position-command signals match, the servo valve moves to its null position, in which it holds the actuator piston at a steady position.

Hamtil, James↗

Operational Experience with the Electromagnetic Position Sensor (EPS) for the NASA 6-inch MSBS

A Magnetic Suspension and Balance System (MSBS), originally developed in 1969, has been recommissioned at NASA Langley and is being used to explore dynamic test techniques for planetary entry capsules. A critical component of this system is the Electromagnetic Position Sensor (EPS) which provides non-contact position measurement for control of the actively suspended model. The sensor’s operation is similar to a Linear Variable Differential Transformer (LVDT). However the EPS has a much larger gap and smaller core than traditional LVDTs and therefore it requires specialized driving and processing circuitry. This paper describes the history of this sensor system, its mechanical and electrical design, and the efforts to improve signal conditioning circuitry.

T. D. Schott↗

Computer transformation of partial differential equations into any coordinate system

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Sullivan, R. D.↗

Unsteady subsonic and supersonic potential aerodynamics for complex configurations

A recently developed general theory for unsteady compressible potential fluid dynamics for complex-configuration aircraft is reviewed. The method is based on a combination of the following techniques: Green's function method (to transform the differential equation into an integral differential-delay equation), finite element method (to transform the equation into a set of differential-delay equations in time), and the Laplace transform method (to transform the differential-delay equations into algebraic equations).

Morino, L.↗

Similarity analysis of differential equations by Lie group.

Methods for transforming partial differential equations into forms more suitable for analysis and solution are investigated. The idea of Lie's infinitesimal contact transformation group is introduced to develop a systematic method which involves mostly algebraic manipulations. A thorough presentation of the application of this general method to the problem of similarity analysis in a broader sense - namely, the similarity between partial and ordinary differential equations, boundary value and initial value problems, and nonlinear and linear equations - is given with new and very general methods evolved for deriving the possible groups of transformations.

Na, T. Y.↗

Analysis and design of steady transonic flow over airfoils by the method of parametric differentiation

The results reported here are based on applying the method of parametric differentiation (MPD) to transform the nonlinear differential equation governing small-disturbance transonic flow to a linear equation. Implicit approximate factorization and monotone methods were used to accelerate convergence of the linear problem by an order of magnitude over successive line over-relaxation. The relative merits of using MPD are discussed in comparison to conventional small-disturbance applications. Several MPD analyses are performed on an array of airfoils. A design procedure utilizing MPD is discussed and demonstrated for two nonlifting cases.

Halt, D. W.↗

Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Driskell, C. N., Jr.↗

Theoretical Investigation of Thermo-Mechanical Behavior of Carbon Nanotube-Based Composites Using the Integral Transform Method

This project uses the integral transform technique to model the problem of nanotube behavior as an axially symmetric system of shells. Assuming that the nanotube behavior can be described by the equations of elasticity, we seek a stress function x which satisfies the biharmonic equation: del(exp 4) chi = [partial deriv(r(exp 2)) + partial deriv(r) + partial deriv(z(exp 2))] chi = 0. The method of integral transformations is used to transform the differential equation. The symmetry with respect to the z-axis indicates that we only need to consider the sine transform of the stress function: X(bar)(r,zeta) = integral(from 0 to infinity) chi(r,z)sin(zeta,z) dz.

Pawloski, Janice S.↗

The Compton-getting effect.

Transformation of differential mean and current densities and anisotropy of cosmic ray particles and photons observed in frames of reference relative to each other with isotropic flux

Axford, W. I.↗

A Preliminary Assessment of LANDSAT-4 Thematic Mapper Data

The geometric errors for image to map rectification of one Thematic Mapper (TM) scene of an area near Windsor, Ontario were studied. The scene had been produced on computer compatible tape by NASA and contained radiometric and system corrections for geometric distortions. The geometric properties of TM photographic imagery permitted very good fitting to map detail using simple scaling techniques to localized areas and, using simple scaling, the overall geometry remained with 500 meters or 0.4 mm at the image scale of 1:1,141,600. An affine transformation, permitting differential scaling, slightly improves the fit to about 400 meters or 0.35 mm at image scale. The imagery shows promise of having the needed additional resolution and spectral discrimination to provide map revision information in urban-rural areas where the MSS sensor is considered inadequate. The late-season prairie image, however, did not hold such promise, and judgement must be reserved until images are acquired at other seasons in this particular geographic area.

Goodenough, D. G.↗