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NASA NTRS1989

Enhanced element-specific modal formulations for flexible multibody dynamics

The accuracy of current flexible multibody formalisms based on assumed modes is examined in the context of standard spacecraft motions involving structural components undergoing both slow and fast overall translational and rotational motions as well as small deformations. Limitations of current techniques in treating: (1) element-specific coupling behavior of large motion and small deformation, and (2) motion-induced structural stiffness variations, are noted. The roles of nonlinear and linear elastic structural theories in accurately predicting transient large-displacement dynamic behavior of flexible multibody systems are examined in detail. Coupling effects between deformation and overall motion are carefully scrutinized in the context of assumed-mode discretization techniques. Consistently linearized beam, plate, and shell formulations involving in-plane stretch variables are proposed and shown to yield very accurate simulation results and extremely fast modal convergence for most motions involving small strains. In some particular cases, however, in which membrane stiffness dominates bending stiffness, a nonlinear strain formulation is required in order to capture proper coupling between deformation and overall motion.

Ryan, Robert R.↗

NASA NTRS1989

Vibration transmission through rolling element bearings in geared rotor system, part 1

A mathematical model is proposed to examine the vibration transmission through rolling element bearings in geared rotor systems. Current bearing models, based on either ideal boundary conditions for the shaft or purely translational stiffness element description, cannot explain how the vibratory motion may be transmitted from the rotating shaft to the casing. This study clarifies this issue qualitatively and quantitatively by developing a comprehensive bearing stiffness matrix of dimension 6 model for the precision rolling element bearings from basic principles. The proposed bearing formulation is extended to analyze the overall geared rotor system dynamics including casing and mounts. The bearing stiffness matrix is included in discrete system models using lumped parameter and/or dynamic finite element techniques. Eigensolution and forced harmonic response due to rotating mass unbalance or kinematic transmission error excitation for a number of examples are computed.

Singh, Rajendra↗

NASA NTRS1989

Nonlinear and distributed parameter models of the mini-mast truss

Large spacecraft such as Space Station Freedom employ large trusses in their construction. The structural dynamics of such trusses often exhibit nonlinear behavior and little damping which can impact significantly the performance of control systems. The Mini-MAST truss was constructed to research such structural dynamics and control systems. The Mini-MAST truss is an object of study for the guest investigator program as part of NASA's controls-structures interaction program. The Mini-MAST truss is deployable and about 65 ft long. Although the bending characteristics of the Mini-MAST truss are essentially linear, the angular deflection under torsional loading has exhibited significant hysteresis and nonlinear stiffness. It is the purpose to develop nonlinear and distributed parameter models of the truss and to compare the model dynamics with actual measurements. Distributed parameter models have the advantage of requiring fewer model parameters. A tangent function is used to describe the nonlinear stiffness in torsion, partly because of the convenience of its easily expressed inverse. Hysteretic slip elements are introduced and extended to a continuum to account for the observed hysteresis in torsion. The contribution of slipping to the structural damping is analyzed and found to be strongly dependent on the applied loads. Because of the many factors which affect the damping and stiffness in a truss, it is risky to assume linearity.

Taylor, Lawrence W., Jr.↗

NASA NTRS1990

Fractography of composite delamination

The microdamage that occurs for Mode 1 and Mode 2 delamination was examined by potting delaminated specimens in a clear epoxy, sectioning through the damage, polishing the cut sections and examining using light microscopy. For Mode 1 delamination of unidirectional carbon fiber reinforced plastic (CFRP) composites, the major observation was fiber bridging including large ligaments of fiber bundles. The Mode 2 delamination of unidirectional laminates revealed a very narrow crack opening with only occasional fiber bridging. Impact testing by repetitive impacts with increasing energy was studied and it was found that this technique does not discern changes in the type of damage with increasing cumulative impact energy. Instead, the changes in the impact response, notably stiffness, are the result of changes in the extent of damage. For laminates with a brittle thermoplastic matrix, 3501-6, there were distinct changes in stiffness that corresponded to the development of through the thickness damage and then to the extension of the damage to the specimen edges. For PEEK and polycarbonate, the changes in stiffness were not as abrupt as for the thermoset. None the less, the damage progressed in the same manner.

Bascom, W. D.↗

NASA NTRS1990

Linear iterative solvers for implicit ODE methods

The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.

Saylor, Paul E.↗

NASA NTRS1989

Traction-drive force transmission for telerobotic joints

The U.S. Space Station Program is providing many technological developments to meet the increasing demands of designing such a facility. One of the key areas of research is that of telerobotics for space station assembly and maintenance. Initial implementation will be teleoperated, but long-term plans call for autonomous robotics. One of the essential components for making this transition successful is the manipulator joints mechanism. Historically, teleoperated manipulators and industrial robotics have had very different mechanisms for force transmission. This is because the design objectives are almost mutually exclusive. A teleoperator must have very low friction and inertia to minimize operator fatigue; backlash and stiffness are of secondary concern. A robot, however, must have minimum backlash, and high stiffness for accurate and rapid positioning. A joint mechanism has yet to be developed that can optimize these divergent performance objectives. A joint mechanism that approaches this optimal performance was developed for NASA Langley, Automation Technology Branch. It is a traction-drive differential that uses variable preload mechanisms. The differential provides compact, dexterous motion range with a torque density similar to geared systems. The traction drive offers high stiffness and zero backlash, for good robotic performance, and the variable loading mechanism (VLM) minimizes the drive-train friction, for improved teleoperation.

Kuban, D. P.↗

NASA NTRS1989

Response of notched AS4/PEEK laminates to tension/compression loading

Fatigue life, damage-initiation and propagation, and residual strength data are presently examined to ascertain the response of notched AS4/PEEK specimens to fully reversed tension/compression loading. Stiffness measurements made during the low-level fatigue history show that compression stiffness and tension stiffness degrade throughout the fatigue life. Damage to specimens fatigued at higher cyclic stresses developed primarily in the direction perpendicular to the loading. As in the case of specimens fatigued at lower stress levels, residual compressive stress decreased with damage development.

Simonds, Robert A.↗

NASA NTRS1991

Model Of Bearing With Hydrostatic Damper

Improved mathematical model of rotational and vibrational dynamics of bearing package in turbopump incorporates effects of hydrostatic damper. Part of larger finite-element model representing rotational and vibrational dynamics of rotor and housing of pump. Includes representations of deadband and nonlinear stiffness and damping of ball bearings, nonlinear stiffness and damping of hydrostatic film, and stiffness of bearing support. Enables incorporation of effects of hydrostatic damper into overall rotor-dynamic mathematical model without addition of mathematical submodel of major substructure.

Goggin, David G.↗

NASA NTRS1990

The effect of weak interface on transverse properties of a ceramic matrix composite

Experimental studies conducted at NASA Lewis on SiC reaction-bonded Si3N4 composite system showed that transverse stiffness and strength were much lower than those predicted from existing analytical models based on good interfacial bonding. It was believed that weakened interfaces were responsible for the decrease in tranverse properties. To support this claim, a two-dimensional FEM analysis was performed for a transverse representative volume element. Specifically, the effect of fiber/matrix displacement compatibility at the interface was studied under both tensile and compressive transverse loadings. Interface debonding was represented using active gap elements connecting the fiber and matrix. The analyses show that the transverse tensile strength and stiffness are best predicted when a debonded interface is assumed for the composite. In fact, the measured properties can be predicted by simply replacing the fibers by voids. Thus, it is found that little or no interfacial bonding exists in the composite, and that an elastic analysis can predict the transverse stiffness and strength.

Shimansky, R. A.↗

NASA NTRS1991

Non-linear dynamics of a geared rotor-bearing system with multiple clearances

The nonlinear frequency response characteristics of a geared rotor-bearing system are examined. A three-DOF dynamic model is developed which includes nonlinearities associated with radial clearances in the radial rolling element bearings and backlash between a spur gear pair; linear time-invariant gear meshing stiffness is assumed. The corresponding linear system problem is also solved, and predicted natural frequencies and modes match with finite element method results. The applicability of both analytical and numerical solution techniques to the multi-DOF nonlinear problem is investigated. Satisfactory agreement is found between the theory presented here and the available experimental data. Nonlinear modal interactions and differences between internal static transmission error excitation and external torque excitation are discussed. In addition, parametric studies are performed to understand the effect of system parameters such as bearing stiffness to gear mesh stiffness ratio, alternating to mean force ratio and radial bearing preload to mean force ratio on the nonlinear dynamic behavior.

Kahraman, A.↗

NASA NTRS1990

Defect sensitivity of filament-wound structures in compression

Compression testing of 12-ply graphite/bismaleimide laminated plates with induced and natural defects is discussed, and emphasis is placed on resultant changes in strength and stiffness. Ply drops, ply cuts, and fiber crossovers are studied by comparison with a quasi-isotropic control group. It is observed that, as expected, failure initiates at the defects and progresses via delamination, sublaminate buckling, angle-ply cracking, and longitudinal ply failure. The ultimate stress is reduced by approximately 40 percent for all types of defects except the unsymmetrical cut-ply specimens which averages a 54-percent reduction. The average stiffness reduction of 10 percent is observed for specimens with induced defects. Fiber crossovers are found to reduce the laminate strength and stiffness significantly.

Jensen, David W.↗

NASA NTRS1992

Variable-Compliance Couplings For Heavy Lifting

New coupling devices contain manual or electronically controlled, motorized drives that vary stiffnesses. Short, clamped lengths of cable provide compliance. Using threaded rods, cables stretched, relaxed, or folded to make coupling more or less stiff. In more-advanced device, brackets holding cables moved by stepping motor via gearbox and ball screw. Motor operates under computer control with position feedback. Control computer commands greater stiffness during operations requiring precise positioning, and greater compliance to accommodate manufacturing tolerances. Intended for use in wrist joints of robotic manipulators and other industrial equipment that must lift heavy objects.

Kerley, James↗

NASA NTRS1991

End-effector for robotic assembly of welded truss structures in space

In June 1987, work was initiated at LaRC on end-effectors and preloaded joints for robotic truss assembly. This is part of an on-going research effort centered on a test facility that assembles 1 inch x 2 m identical struts into an 8 m diameter x 1.5 m deep platform truss. A detailed description of the test facility was published. The end-effector being used for the LaRC assembly demonstration is quite suitable for the Precision Segmented Reflector or other precision applications. These require high stiffness provided by mechanical joint preloads. Stiffness obtained in this manner is only required and provided over a load range far less than the ultimate strength of the strut tubes. Beyond this useful range, truss behavior is somewhat unpredictable. Mechanically preloaded joints of this type are less suitable for applications such as the Aero Brake where predictable strength and stiffness are required over a greater fraction of the load bearing capacity of component parts. Preliminary studies of the Aerobrake support truss indicate that struts of at least 3 different diameters and various lengths would improve performance. The double-ended end-effector currently in service is designed for only one diameter and length. Anticipated single-ended versions can accommodate varying lengths but not multiple diameters. Tradeoff considerations for welded joints relative to their mechanically preloaded counterparts are presented. Conclusions from this research are as follows: (1) repair by cut and re-weld on the original weld site should be research; (2) welded joints, though repairable, should not be used where high repair frequencies are anticipated; and (3) welded joints should be considered for an Aero Brake truss.

Brewer, William V.↗

NASA NTRS1991

Nondestructive Structural Damage Detection in Flexible Space Structures Using Vibration Characterization

Spacecraft are susceptible to structural damage over their operating life from impact, environmental loads, and fatigue. Structural damage that is not detected and not corrected may potentially cause more damage and eventually catastrophic structural failure. NASA's current fleet of reusable spacecraft, namely the Space Shuttle, has been flown on several missions. In addition, configurations of future NASA space structures, e.g. Space Station Freedom, are larger and more complex than current structures, making them more susceptible to damage as well as being more difficult to inspect. Consequently, a reliable structural damage detection capability is essential to maintain the flight safety of these structures. Visual inspections alone can not locate impending material failure (fatigue cracks, yielding); it can only observe post-failure situations. An alternative approach is to develop an inspection and monitoring system based on vibration characterization that assesses the integrity of structural and mechanical components. A methodology for detecting structural damage is presented. This methodology is based on utilizing modal test data in conjunction with a correlated analytical model of the structure to: (1) identify the structural dynamic characteristics (resonant frequencies and mode shapes) from measurements of ambient motions and/or force excitation; (2) calculate modal residual force vectors to identify the location of structural damage; and (3) conduct a weighted sensitivity analysis in order to assess the extent of mass and stiffness variations, where structural damage is characterized by stiffness reductions. The approach is unique from other existing approaches in that varying system mass and stiffness, mass center locations, the perturbation of both the natural frequencies and mode shapes, and statistical confidence factors for structural parameters and experimental instrumentation are all accounted for directly.

Ricles, James M.↗

NASA NTRS1991

Structural behavior of scientific balloons - Finite element simulation and verification

An off-the-shelf nonlinear finite element code was used to analyze fully inflated scientific balloons. The thin balloon film was modeled by shell bending elements. Numerical difficulties caused by insignificant bending stiffness terms were overcome by introducing some artificial bending stiffness. This approximation is justified by the fact that in thin shells with nonzero Gaussian curvature the membrane solution component is essentially independent of the bending solution component. Perturbation of the coveraged solution by increasing the bending stiffness by a full decade verified this assertion. This analytical approach was experimentally verified. As a result of this verification process it was discovered that the generally accepted linearly visco-elastic model for polyethylene film is inappropriate for a significant planar (as opposed to uniaxial) stress state. A linear elastic model presents a good approximation for planar stress states.

Schur, Willi W.↗

NASA NTRS1992

Generation and comparison of globally isotropic space-filling truss structures

The purposes of this paper are to present a rationale for obtaining space-filling truss structures that behave like a globally isotropic continuum and to use continuum modeling to investigate their relative structural efficiencies (e.g., modulus-to-density, strength-to-density, and part-count-to-volume ratios). The trusses considered herein are generated by replication of a characteristic truss cell uniformly through space. The characteristic cells are categorized by one of a set of possible geometric symmetry groups derived using the techniques of crystallography. The implied elastic symmetry associated with each geometric symmetry group is identified to simplify the task of determining stiffness tailoring rules for guaranteeing global isotropy. Four truss geometries are analyzed to determine stiffness tailoring necessary for isotropy. All geometries exhibit equivalent isotropic Poisson's ratios of 1/4 and equivalent modulus-to-density ratios of 1/6 times the modulus-to-density ratio of the material used in their members. The truss configuration that has the lowest percent difference in member lengths is shown to have the lowest component part-count-to-volume ratios of all geometries considered when compared on a basis of equal stiffness, equal strength, and equal mass.

Lake, Mark S.↗

NASA NTRS1991

Effect of damage on elastically tailored composite laminates

A variationally consistent theory is derived in order to predict the response of anisotropic thin-walled closed sections subjected to axial load, torsion and bending. The theory is valid for arbitrary cross-sections made of laminated composite materials with variable thickness and stiffness. Closed form expressions for the stiffness coefficients are provided as integrals in terms of lay-ups parameters and cross-sectional geometry. A comparison of stiffness coefficients and response with finite element predictions and a closed form solution is performed. The theory is applied to the investigation of the effect of damage on the extension-twist coupling in a thin-walled closed section beam. The damage is simulated as a progressive ply-by-ply failure. Results show that damage can have a significant effect on the extension-twist coupling.

Armanios, Erian↗

NASA NTRS1992

Damage detection in elastic structures using vibratory residual forces and weighted sensitivity

A methodology is presented for detecting structural damage in elastic structures by nondestructive means. Measured modal test data along with a correlated analytical structural model are used to locate potentially damaged regions using residual modal force vectors and to conduct a weighted sensitivity analysis to assess the extent of mass and/or stiffness variations, where damage is characterized as a stiffness reduction. The current approach is unique among other approaches in that it accounts for (1) variations in system mass, system stiffness, and mass center (locations), (2) perturbations of both the natural frequencies and modal vectors, and (3) statistical confidence factors for the structural parameters and potential experimental instrumentation error. Moreover, this procedure can be used with either full or reduced models. A wide variety of numerical examples are presented that show that the current method provides a precise indication of both the location and the extent of structural damage.

Ricles, J. M.↗