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NASA NTRS1957

Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades

The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory developed and presented in this paper. Special attention is given to coupling terms not found in previous theories, and methods of solution of the equations of motion are indicated by selected examples.

VIBRATION AND FLUTTER - ROTATING-WING AIRCRAFT↗

NASA NTRS1958

Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades

The differential equations of motion for the lateral and torsional deformations of twisted rotating beams are developed for application to helicopter rotor and propeller blades. No assumption is made regarding the coincidence of the neutral, elastic, and mass axes, and the generality is such that previous theories involving various simplifications are contained as subcases to the theory presented in this paper. Special attention is given the terms which are not included in previous theories. These terms are largely coupling-type terms associated with the centrifugal forces. Methods of solution of the equations of motion are indicated by selected examples.

Houbolt, John C↗

NASA NTRSDate not supplied

Analysis of Triangular Rollable and Collapsible Composite Booms Under the Effects of Gravity and Twist

Finite element analysis is used to investigate Triangular Rollable and Collapsible (TRAC) composite booms. The TRAC booms are subjected to a suite of loading conditions, including in-plane bending, out-of-plane bending, and axial compression. Simulations containing as-designed boom geometry are performed, as are simulations with geometric deviations associated with the as-built conditions of a sample TRAC boom. Namely, a cross-sectional twist along the length of the boom is incorporated into the analysis to study the effect of the twist on the deformation characteristics of the boom. Twisting in the sample boom was observed after short-term storage in a rolled configuration and may be attributed to differential creep deformation between the inner and outer flanges of the TRAC boom. Simulations are conducted with and without the effects of gravity to understand the significance of gravity on testing conditions. Booms of three lengths are evaluated: 3 meters, 7.5 meters and 30 meters. The mechanical responses of the TRAC booms are discussed with reference to the effects of gravity, boom length and cross-sectional twisting. Gravity is found to have a more significant effect on boom mechanical response as boom length is increased. Cross-sectional twisting is found to have a more significant effect on boom mechanical response in the shorter booms.

High-strain composites↗

NASA NTRSDate not supplied

Analysis of Triangular Rollable and Collapsible (TRAC) Composite Booms under the Effects of Gravity and Twist

High-strain composites↗

NASA NTRS1987

Stresses and deformations in angle-ply composite tubes

The stress and deformations in angle-ply composite tubes subjected to axisymmetric thermal loading were investigated both experimentally and analytically. For the theoretical portion a generalized plane strain elasticity analysis was developed. The analysis included mechanical and thermal loading, and temperature-dependent material properties. The elasticity analysis was also used to study the effect of including a thin metallic coating on a graphite-epoxy tube. The stresses in the coatings were found to be quite high, exceeding the yield stress of aluminum. An important finding in the analytical studies was the fact that even tubes with a balanced-symmetric lamination sequence exhibit shear deformation, or twist. For the experimental portion an apparatus was developed to measure torsional and axial response in the temperature range of 140 to 360 K. Eighteen specimens were tested, combining three material systems, eight lamination sequences, and three off-axis ply orientation angles. For the twist response, agreement between analysis and experiment was found to be good. The axial response of the tubes tested was found to be greater than predicted by a factor of three. As a result, it is recommended that the thermally induced axial deformations be investigated, both experimentally and analytically.

Rousseau, Carl Q.↗

NASA NTRS2002

Effects of Structural Deformation and Tube Chirality on Electronic Conductance of Carbon Nanotubes

A combination of large scale classical force-field (UFF), density functional theory (DFT), and tight-binding Green's function transport calculations is used to study the electronic properties of carbon nanotubes under the twist, bending, and atomic force microscope (AFM)-tip deformation. We found that in agreement with experiment a significant change in electronic conductance can be induced by AFM-tip deformation of metallic zigzag tubes and by twist deformation of armchair tubes. The effect is explained in terms of bandstructure change under deformation.

Svizhenko, Alexei↗

NASA NTRS1984

An analysis of rotor blade twist variables associated with different Euler sequences and pretwist treatments

A nonlinear analysis which is necessary to adequately model elastic helicopter rotor blades experiencing moderately large deformations was examined. The analysis must be based on an appropriate description of the blade's deformation geometry including elastic bending and twist. Built-in pretwist angles complicate the deformation process ant its definition. Relationships between the twist variables associated with different rotation sequences and corresponding forms of the transformation matrix are lasted. Relationships between the twist variables associated with first, the pretwist combined with the deformation twist are included. Many of the corresponding forms of the transformation matrix for the two cases are listed. It is shown that twist variables connected with the combined twist treatment are related to those where the pretwist is applied initially. A method to determine the relationships and some results are outlined. A procedure to evaluate the transformation matrix that eliminates the Eulerlike sequence altogether is demonstrated. The resulting form of the transformation matrix is unaffected by rotation sequence or pretwist treatment.

Alkire, K.↗

NASA NTRS2014

Blade Displacement Predictions for the Full-Scale UH-60A Airloads Rotor

An unsteady Reynolds-Averaged Navier-Stokes solver for unstructured grids is loosely coupled to a rotorcraft comprehensive code and used to simulate two different test conditions from a wind-tunnel test of a full-scale UH-60A rotor. Performance data and sectional airloads from the simulation are compared with corresponding tunnel data to assess the level of fidelity of the aerodynamic aspects of the simulation. The focus then turns to a comparison of the blade displacements, both rigid (blade root) and elastic. Comparisons of computed root motions are made with data from three independent measurement systems. Finally, comparisons are made between computed elastic bending and elastic twist, and the corresponding measurements obtained from a photogrammetry system. Overall the correlation between computed and measured displacements was good, especially for the root pitch and lag motions and the elastic bending deformation. The correlation of root lead-lag motion and elastic twist deformation was less favorable.

Bledron, Robert T.↗

NASA NTRS1998

Measurement of Rotorcraft Blade Deformation using Projection Moire Interferometry

Projection Moire Interferometry (PMI) has been used to obtain near instantaneous, quantitative blade deformation measurements of a generic rotorcraft model at several test conditions. These laser-based measurements provide quantitative, whole field, dynamic blade deformation profiles conditionally sampled as a function of rotor azimuth. The instantaneous nature of the measurements permits computation of the mean and unsteady blade deformation, blade bending, and twist. The PMI method is presented, and the image processing steps required to obtain quantitative deformation profiles from PMI interferograms are described. Experimental results are provided which show blade bending, twist, and unsteady motion. This initial proof-of-concept test has demonstrated the capability of PMI to acquire accurate, full field rotorcraft blade deformation data.

Fleming, Gary A.↗

NASA NTRS1978

Inflight optical measurement of antenna surfaces

A technology base was developed for a wide variety of applications oriented sensors to meet requirements for the fabrication, assembly, test, surface figure monitoring, and ultimately surface figure active control of large space antennas. An optical sensor technique is described which establishes an ideal centerline at each beam during fabrication or later during assembly. Deviations from the centerline, either in lateral deformation or in twist, are measured to produce limit warnings or to evoke active control at the building machine.

Neiswander, R. S.↗

NASA NTRS1987

Plates and shells containing a surface crack under general loading conditions

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Joseph, Paul F.↗

NASA NTRS1990

Bearingless rotor aeromechanical stability measurements and correlations using nonlinear aerodynamics

The aeromechanical stability of a 1/8th Froude scaled bearingless rotor model was investigated experimentally in a wind tunnel. Both shaft-fixed and shaft-free conditions were examined to study the aeroelastic stability of a bearingless rotor without the incorporation of auxiliary dampers. This wind tunnel investigation generated a set of stability data for four different advance ratios, and a wide range of collective pitch settings. Theoretical analysis was performed using the newly developed University of Maryland Advanced Rotorcraft Code (UMARC). For analysis, the blade is modeled as an elastic beam undergoing flap bending, lag bending, elastic twist, and axial deformation. Blade response is calculated using a finite element method in time. Nonlinear aerodynamic effects are included by using a semiempirical stall modeling. The linearized periodic rotor perturbation equations in the nonrotating frame are solved for stability roots using Floquet transition matrix theory, as well as constant coefficient approximation. The predicted results are compared with the experimental data.

Wang, James M.↗

NASA NTRS2005

Two SMA-Actuated Miniature Mechanisms

The figures depict two miniature mechanisms actuated by strips made of shape-memory alloy (SMA). A typical SMA is a nickel-titanium alloy known by the trade name "Flexinol" or "Nitinol." In preparation for a typical application, a suitably sized and shaped piece of an SMA is deformed by a predetermined amount at the lower of two operating temperatures, then mounted in a mechanism. When stroking of the mechanism in one direction is desired, the piece of SMA is heated above a transition temperature to make it return to the "remembered" undeformed state. When stroking of the mechanism in the opposite direction is desired, the SMA is cooled below the transition temperature to make it return to the deformed state. Also, the SMA alloy chosen for a specific application is one that has a transition temperature somewhat above the ambient temperature, so that stroking in one direction or the opposite direction can be achieved by heating the SMA, or refraining from heating the SMA, respectively, above the transition temperature. In the present mechanisms as in typical other SMA mechanisms, the heating is effected by electric currents applied via electrical contacts at the ends of the SMA strips. The purpose served by the mechanism of Figure 1 is to lock or release a flexible latch attachment. In preparation for use in this mechanism, two initially straight SMA strips are deformed into curved springs that, when mounted in the mechanism at ambient temperature, clamp the knob at the lower end of the flexible latch attachment. When heated above their transition temperature by an electric current, the SMA strips return to their original straight configuration, thereby releasing the knob. This mechanism is redundant in the sense that as long as at least one of the two SMA strips straightens when commanded to do so, the knob is released. The mechanism of Figure 2 is suited to any of a variety of applications in which there are requirements for a small mechanism that affords lowtorque rotary actuation through a finite angular range. As shown here, the mechanism is used to rotate a coverlatch pin to a release position. In this case, a straight and flat SMA strip is torsionally deformed to a twist angle of about 90deg by use of a torsion bias spring. When the SMA strip is heated, it rotates to its original straight and flat condition.

Willey, Cliff E.↗

NASA NTRS1976

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗

NASA NTRS1974

Arbitrarily Curved and Twisted Space Beams

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that (1) extensional effects are included; (2) the strain-displacement relations are derived; and (3) the expressions for the stress resultants are developed from the strain displacement relations. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. The governing equations are given in the form of first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented.

Hunter, W. F.↗

NASA NTRS1988

Variable response load limiting device

An energy absorbing device used as a load limiting member in a structure to control its response to applied loads is described. It functions by utilizing a spool assembly having flanged ends and an interior cavity of sufficiently large diameter to cause it to deform plastically at a prescribed load. In application, the spool is utilized as a pivot point for the legs of an airplane seat. When properly designed and integrated into the seat arrangement the spool will twist about its axis, deforming plastically when the impact load exceeds the spool yield value. Through this deformation, the spool absorbs the kinetic energy of the movement of the seat at a substantially constant rate, thereby controlling the level of loads transmitted to the seat occupant. By proper sizing and collection of materials, it is possible to control load response in a predictable manner.

Mcsmith, Dwight D.↗

NASA NTRS2005

Error Due to Wing Bending in Single-Camera Photogrammetric Technique

The error due to wing bending introduced into single-camera photogrammetric computations used for the determination of wing twist or control surface angular deformation is described. It is shown that the error due to wing bending when determining main wing element-induced twist is typically less than 0.05deg at the wing tip and may not warrant additional correction. It is also shown that the angular error in control surface deformation due to bending can be as large as 1deg or more if the control surface is at a large deflection angle compared to the main wing element. A correction procedure suitable for control surface measurements is presented. Simulations of the error based on typical wind tunnel measurement geometry, and results from a controlled experimental test in the test section of the National Transonic Facility (NTF) are presented to confirm the validity of the method used for correction of control surface photogrammetric deformation data. An example of a leading edge (LE) slat measurement is presented to illustrate the error due to wing bending and its correction.

Burner, Alpheus W., Jr.↗

NASA NTRS2010

Experimental Investigation of the NASA Common Research Model

An experimental aerodynamic investigation of the NASA Common Research Model has been conducted in the NASA NTF (National Transonic Facility). Data have been obtained at chord Reynolds numbers of 5, 19.8 and 30 million for the WB and WBT0 configurations. Data have also been obtained at a chord Reynolds number of 5 million for the WBNP, WBT+2 and WBT-2 configurations. Force and moment, surface pressure and surface flow visualization data were obtained but only the force and moment data are presented herein. Model deformation measurements, aeroelastic, nacelle/pylon Reynolds number and tail effects have been assessed. The model deformation measurements showed more twist as you go out the wing span, with a break in the high q(sub infinity) data close to CL = 0.6 which is consistent with separation near the tip. Increases in dynamic pressure give an increase in pitching moment and drag and a decrease in lift for the WB and WBT0 configuration at Mach = 0.7, 0.85 and 0.87. The addition of a nacelle/pylon gave an increase in drag, decrease in lift and a less nose down pitching moment around the design lift condition of 0.5. Increases in chord Reynolds number have been found to follow the normal Reynolds number trends except at the 19.8 million low q(sub infinity) cases. The abnormality of the 19.8 million low q(sub infinity) cases is being investigated. The tail effects also follow the expected trends. All of the data shown fall within the 2-sigma limits for repeatability.

Rivers, Melissa B.↗