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System of computer programs uses linear theories to evaluate static and dynamic stability, trim state, inertial, and aerodynamic loading, and elastic deformations of aircraft configurations at subsonic and supersonic speeds. Primary emphasis is on analysis of stability and control characteristics of flexible aircraft. System also solves simple rigid aerodynamic problems.
A general version of Lagrange's equations, including auxiliary nonholonomic, rheonomic conditions of constraint, is used in the dynamic simulation and stability analysis of interconnected flexible bodies. Modeling of the nonlinear flexible/rigid dynamic coupling effects, the interaction forces/torques, and the elastic deformation effects is discussed. A digital computer program is developed to obtain time-domain solution for the nonlinear response of systems represented as a collection of individual bodies, numerical linearization of system-governing equations, time-domain solution for the perturbation response about a nominal state, and a frequency-domain stability analysis corresponding to the linearization. The digital simulation code is employed to study the dynamic behavior of a typical satellite and a spacecraft with deployable experiment booms.
Many sealing configurations incorporate the geometry of line contact on bluff, slablike bodies. When sliding speed is sufficiently high along or across the line of contact, instabilities may arise from interactions of thermal expansion, elastic deformation and frictional heating. These lead to concentrated contact with elevated temperatures and pressures. Previous studies have been largely restricted to two-dimensional models of such contact. The present study shows how those earlier results must be modified to apply to the more realistic geometry, and show also that the principal features of the interactions are the same in both geometries.
A simple and straightforward method for calculating the elastic deformation at the center of contact between two solids with different radii of curvature is proposed instead of the conventional contact deformation analysis for ball bearings, gears, and cams, which usually involves tedious iterative procedures or the use of design charts. Ellipticity of the contact is approximated from a least-squares power fit. Simplified expressions are derived which allow rapid calculation of deformation from the material properties and geometry of the contacting elements.
Parabolic concentrators used in solar-energy systems are constructed from many flat rectangular mirrors. Each mirror is elastically deformed in one dimension. Several such mirrors placed adjacent to each other along parabolic curve form inexpensive mirror suitable for solar application.
A comparison of program estimates of wing weight, material distribution. structural loads and elastic deformations with actual Northrop F-5A/B data is presented. Correlation coefficients obtained using data from a number of existing aircraft were computed for use in vehicle synthesis to estimate wing weights. The modifications necessary to adapt the WADES code for use in the ACSYNT program are described. Basic program flow and overlay structure is outlined. An example of the convergence of the procedure in estimating wing weights during the synthesis of a vehicle to satisfy F-5 mission requirements is given. A description of inputs required for use of the WADES program is included.
A theoretical investigation of three dimensional relativistic klystron action is described. The relativistic axisymmetric equations of motion are derived from the time-dependent Lagrangian function for a charged particle in electromagnetic fields. An analytical expression of the fringing RF electric and magnetic fields within and in the vicinity of the interaction gap and the space-charge forces between axially and radially elastic deformable rings of charges are both included in the formulation. This makes an accurate computation of electron motion through the tunnel of the cavities and the drift tube spaces possible. Method of analysis is based on Lagrangian formulation. Bunching is computed using a disk model of electron stream in which the electron stream is divided into axisymmetric disks of equal charge and each disk is assumed to consist of a number of concentric rings of equal charges. The Individual representative groups of electrons are followed through the interaction gaps and drift tube spaces. Induced currents and voltages in interacting cavities are calculated by invoking the Shockley-Ramo theorem.
A numerical solution of an elastohydrodynamically lubricated (EHL) line contact between two long, rough-surface cylinders that considers the frictional heating of asperities was obtained. Pressure distribution, temperature distribution, film thickness and EHL load for given speeds, lubricant properties, material properties of surfaces, and surface roughness parameters were theoretically solved by simultaneous solution of the elasticity equation and the Reynolds equation for two partially lubricated rough surfaces. The pressure due to asperity contact was calculated by assuming a Gaussian distribution of surface irregularities. The elastic deformation used for film thickness computation was found from the two kinds of pressure by plane strain analysis. The temperature rise in the contact zone was calculated by using the Blok-Jaeger flash temperature model. The effects of surface roughness on EHL load for various slide-role ratios, surface roughness parameters, surface patterns, and temperature parameters was studied. It was found that the maximum temperature rise in most cases occurred in the inlet zone, and that the minimum film thickness decreased and the maximum temperature increased as the surface roughness was increased.
NASA is currently developing a low mass antenna which derives its reflector surface quality from the application of electrostatic forces to form a thin membrane into the desired concave reflector surface. The shuttle-deployed antenna would have a diameter of 100 m and an RMS surface smoothness of 10 to 1 mm for operation at 1 to 10 GHz. Surface quality measurements have been made on a highly deformable elastic membrane, pressurized by electrostatic forces. Included are the effects of the perimeter boundary, splicing of the membrane, the long-scale smoothness of commercial membranes, and the spatial controllability of the membrane using voltage adjustments to alter the electrostatic forces. The electrostatic membrane was found to operate well in an open-loop sense, showing a high degree of position stability and negligible power consumption in dry air. Visco-electric creep was not evident, but the polymer membrane did expand and contract considerably due to its hygroscopic expansion coefficient. A residual roughness of about 0.75 mm existed with the polymer used in these tests; this error is attributed to seams and membrane anisotropy where the material is stiffer in one direction.
A numerical solution of an elastohydrodynamic lubrication (EHL) contact between two long rough surface cylinders is obtained. A simultaneous solution of an elasticity equation and the Reynolds equation for two partially lubricated rough surfaces is used to obtain a theoretical solution of pressure distribution, elastohydrodynamic load and film thicknesses for given speeds. A theoretical solution is also found for lubricants with pressure dependent viscosity, material properties of cylinders, and surface roughness parameters. Elastic deformation is found from hydrodynamic and contact pressure using plane strain analysis, and results indicate that for a constant central film thickness, increasing the surface roughness decreases the EHL load and there is little variation in minimum film thicknesses as the surface roughness is increased.
Method of installing support tubes allows retrofitting of vibrationreducing elements. Tubes deform elastically as inserted and expand partially as gap becomes wider. Force-fit tubes eliminate fatigue problem.
A method for computation of reflective dihedral symmetry in symmetrical structures under nonsymmetric loads is described. The method makes it possible to confine the analysis to a half, a quarter, or an octagonal segment. The symmetry of elastic deformation is discussed, and antisymmetrical deformation is distinguished from nonsymmetrical deformation. Modes of deformation considered are axial, bending, membrane, and torsional deformation. Examples of one and two dimensional elements are presented and extended to three dimensional elements. The method of setting up a problem within NASTRAN is discussed. The technique is applied to a thick structure having quarter symmetry which was modeled with polyhedra and subjected to five distinct loads having varying degrees of symmetry.
The vertical gust response of the helicopter rotor in cruising flight is studied analytically by means of the local momentum theory (LMT) and experimentally in a wind tunnel utilizing a gust generator. By introducing the unsteady aerodynamic effects into the LMT and by considering the elastic deformation of the rotor blade, the vibratory characteristics of flapping blades and of the rotor forces can be obtained. Since the LMT makes it possible to calculate the instantaneous load distribution along the rotor blade in desired azimuthal or timewise intervals, the effects of gradual penetration of the rotor into the gust can be studied and the Fourier analysis or power spectrum analysis of the rotor response applied to any kind of gust input. Some results obtained analytically are verified by the experimental tests performed in the wind tunnel which generates step, sinusoidal and random vertical gusts by the motion of a series of cascaded vanes upstream of the rotor.
The effects of the elastic deformation of the wind tunnel wall held to a streamline-like shape were simulated numerically. The wall itself is simulated by a finite element model and is allowed to deform under the pressure loading developing in the wind tunnel with an airfoil model present. A modified version of the transonic analysis program, TSFOIL, is then used to determine the resulting flow field with the effects of the deformed wall included, the shape of the wall and the flow field. Once a result from a particular operating condition was obtained, the pressure distribution on the airfoil in the wind tunnel model is compared with solutions generated by TSFOIL in the free air mode.
A number of lubricated machine elements are subjected to cyclic variations of load and speed, particularly in reciprocating machinery. It is well known that squeeze-film action plays an important role in preserving satisfactory lubricating films in many cases in which the entraining velocities fall to zero during each cycle, as in the reciprocating seal and synovial joints. The essential features of combined 'entraining' and 'normal' motion are described for both hydrodynamic and elastohydrodynamic conditions. It is shown that very small squeeze-film velocities (W), or order (h(sub o)/l)U, can lead to substantial hydrodynamic action. A brief review of previous studies of squeeze-film lubrication between spheres or cylinders and a plane is followed by reference to a recent analysis of ankle joint lubrication. It is then shown that elastohydrodynamic lubrication might be encountered in the conjunction between a piston ring and cylinder liner and that in such cases combined entraining and squeeze-film action is important. Analysis of a 2-stroke Diesel engine shows that variations in squeeze-film velocity throughout the conjunction, associated with time rates of change of elastic deformation, must be considered in a full elastohydrodynamic lubrication analysis.
The understanding of hydrodynamic lubrication began with the classical experiments of Tower and Petrov. Reynolds used a reduced form of the Navier-Stokes equations and the continuity equation to generate a second order differential equation for the pressure in the narrow, converging gap of a bearing contact. Such a pressure enables a load to be transmitted between the surfaces with very low friction since the surfaces are completely separated by a film of fluid. In such a situation it is the physical properties of the lubricant, notably the dynamic viscosity, that dictate the behavior of the contact. The understanding of boundary lubrication is normally attributed to Hardy and Doubleday. In boundary lubrication it is the physical and chemical properties of thin films of molecular proportions and the surfaces to which they are attached that determine contact behavior. The lubricant viscosity is not an influential parameter. Research is devoted to a better understanding and more precise definition of other lubrication regimes between these extremes. One such regime, elastohydrodynamic lubrication, occurs in nonconformal contacts, where the pressures are high and the bearing surfaces deform elastically. In this situation the viscosity of the lubricant may raise considerably, and this further assists the formation of an effective fluid film. The science of these three lubrication regimes (hydrodynamic, elastohydrodynamic, and boundary) are described and the manner in which this science is used in the design of machine elements is examined.
Radioisotope thermoelectric generator (RTG) packages designed for space missions generally do not require active cooling. However, the heat they generate cannot remain inside of the launch vehicle bay and requires active removal. Therefore, before the Shuttle bay door is closed, the RTG coolant tubes attached to the heat rejection fins must be filled with water, which will circulate and remove most of the heat from the cargo bay. There is concern that charging a system at initial temperature around 200 C with water at 24 C can cause unacceptable thermal stresses in the RTG shell and fins. A computer model is developed to estimate the transient temperature distribution resulting from such charging. The thermal stresses resulting from the temperature gradients do not exceed the elastic deformation limit for the material. Since the simplified mathematical model for thermal stresses tends to overestimate stresses, it is concluded that the RTG can be cooled by introducing water at 24 C to the initially hot fin coolant tubes while the RTG is in the Shuttle cargo bay.
Static testing of a segmented, gas-lubricated, piston-ring was accomplished. The ring utilizes high-pressure gas generated during the diesel cycle to energize a hydrostatic gas film between the piston and cylinder liner. The configuration was deficient in overall performance, because all segments of a ring set failed to form a fluid-film simultaneously, when exposed to internal preload. The difficulty was traced to the moment balance required to prevent the segments from overturning and contacting the cylinder walls. Some individual sectors formed a film and performed well in every respect including load capability to 6,000 N. These results produce optimism as to the ultimate feasibility of hydrostatic, gas-lubricated piston rings. In addition to test results, the principles of operation, and theoretical developments are presented. Breathable liner concepts are suggested for future consideration. In these configurations, solid hydrostatic pistons are coupled with flexible liners that elastically deform to form a gas-film under hydrostatic pressurization. Breathable liners afford the mechanical simplicity required for mass produced engines, and initial examination indicates satisfactory operation.