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The mesh stiffness and dynamic load characteristics for several cases of the Normal Contract Ratio and High Contact ratio gearing. The considered contact ratios were grouped in the general range of 1.7,2.0, and 2.3. The HCR gearing is defined by contact ratios equal to or greater than 2.0. The HCR gearing is represented by a group of small pressure angle, fine pitch, and long addendum gearing.
Computer program for stiffness of structure with lumped masses, weightless members, and many degrees of freedom - structural dynamics
The primary aim of this investigation was verification of basic methods which are to be used in cataloging elastomer dynamic properties (stiffness and damping) in terms of viscoelastic model constants. These constants may then be used to predict dynamic properties for general elastomer shapes and operating conditions, thereby permitting optimum application of elastomers as energy absorption and/or energy storage devices in the control of vibrations in a broad variety of applications. The efforts reported involved: (1) literature search; (2) the design, fabrication and use of a test rig for obtaining elastomer dynamic test data over a wide range of frequencies, amplitudes, and preloads; and (3) the reduction of the test data, by means of a selected three-element elastomer model and specialized curve fitting techniques, to material properties. Material constants thus obtained have been used to calculate stiffness and damping for comparison with measured test data. These comparisons are excellent for a number of test conditions and only fair to poor for others. The results confirm the validity of the basic approach of the overall program and the mechanics of the cataloging procedure, and at the same time suggest areas in which refinements should be made.
Solutions to the governing equations of a spur gear transmission model, developed in NASA TM-100180 (AVSCOM TM-87-C-2), are presented. Factors affecting the dynamic load are identified. It is found that the dynamic load increases with operating speed up to a system natural frequency. At operating speeds beyond the natural frequency the dynamic load decreases dramatically. Also. it is found that the applied load and shaft inertia have little effect on the dynamic load. Damping and friction decrease the dynamic load. Finally, tooth stiffness has a significant effect on dynamic loading; the higher the stiffness, the lower the dynamic loading. Also, the higher the stiffness the higher the rotating speed required for dynamic response.
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to introduce new effective ways of simulating such equations, however existing approaches are not able to reliably return stable and accurate predictions across long temporal horizons. We aim to address this challenge by introducing an effective framework for learning evolution operators that map random initial conditions to associated ODE/PDE solutions within a short time interval. Such operators can be parametrized by deep neural networks that are trained in an entirely self-supervised manner without requiring one to generate any paired input-output observations. Global long-time predictions across a range of initial conditions can be then obtained by iteratively evaluating the trained model using each prediction as the initial condition for the next evaluation step. Here, this introduces a new approach to temporal domain decomposition that is shown to be effective in performing accurate long-time simulations for a wide range of parametric ODE and PDE systems, from wave propagation, to reaction-diffusion dynamics and stiff chemical kinetics, introducing a new way of rapidly emulating non-equilibrium processes in science and engineering.
High side loads reduce the life of the Space Shuttle Main Engine (SSME) High Pressure Oxygen Turbopump (HPOTP) bearings. High stiffness damper seals were recommended to reduce the loads on the pump and turbine end bearings in the HPOTP. The seals designed for use on the pump end are expected to adequately reduce the bearing loads; the predicted performance of the planned turbine end seal is marginal. An alternative to the suggested turbine end seal design is a damper bearing with radial holes from the pressurized center of the turbopump rotor, feeding a smooth land region between two rough-stator/smooth-rotor annular seals. An analysis was prepared to predict the leakage and rotor dynamic coefficients (stiffness, damping, and added mass) of the damper bearing. Governing equations of the seal analysis modified to model the damper bearing; differences between the upstream conditions of the damper bearing and a typical annular seal; prediction of the damper bearing analysis; and assumptions of the analysis which require further investigation are described.
The Inflatable Re-entry Vehicle Experiment (IRVE) is a 3.0 meter, 60 degree half-angle sphere cone, inflatable aeroshell experiment designed to demonstrate various aspects of inflatable technology during Earth re-entry. IRVE will be launched on a Terrier-Improved Orion sounding rocket from NASA s Wallops Flight Facility in the fall of 2006 to an altitude of approximately 164 kilometers and re-enter the Earth s atmosphere. The experiment will demonstrate exo-atmospheric inflation, inflatable structure leak performance throughout the flight regime, structural integrity under aerodynamic pressure and associated deceleration loads, thermal protection system performance, and aerodynamic stability. Structural integrity and dynamic response of the inflatable will be monitored with photogrammetric measurements of the leeward side of the aeroshell during flight. Aerodynamic stability and drag performance will be verified with on-board inertial measurements and radar tracking from multiple ground radar stations. In addition to demonstrating inflatable technology, IRVE will help validate structural, aerothermal, and trajectory modeling and analysis techniques for the inflatable aeroshell system. This paper discusses the structural analysis and testing of the IRVE inflatable structure. Equations are presented for calculating fabric loads in sphere cone aeroshells, and finite element results are presented which validate the equations. Fabric material properties and testing are discussed along with aeroshell fabrication techniques. Stiffness and dynamics tests conducted on a small-scale development unit and a full-scale prototype unit are presented along with correlated finite element models to predict the in-flight fundamental mod
Relatively new developments in manufacturing methods have made it possible to produce machined parts with a wall thickness of less than 0.010". While the parts are being machined. Fillets of relatively large radius to thickness ratios are created by the milling tool. This paper discusses an accurate new technique for finite-element modeling of fillets for dynamic and stiffness analysis using efficient plate elements rather than more computationally intensive, high density solid meshes, A simple filleted cantilever beam of 0.040" thickness, 1.6" length, 1" depth, and 0.250" radius in the corner was modeled using both solid elements and several different plate element geometries. The finite element results were then compared with static and modal testing of a machined sample. The highest-scoring plate element technique uses a bridge of elements that is constructed through the tangent point of the Fillet radius such that the thickness of the element matches tile volume of the fillet. This model produces errors of less than 4.6 percent for static loading and less than 7.4 percent for modal analysis. This simple plate element technique will prove critical for efficient, timely, and accurate dynamic analysis of complex thin-walled structures.
For turbulent reacting flow systems, identification of low-dimensional representations of the thermo-chemical state space is vitally important, primarily to significantly reduce the computational cost of device-scale simulations. Principal component analysis (PCA), and its variants, are a widely employed class of methods. Recently, an alternative technique that focuses on higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been shown to effectively provide a low-dimensional representation by capturing the stiff chemical dynamics associated with spatiotemporally localized reaction zones. While its effectiveness has only been demonstrated based on a priori analyses with linear reconstruction, in this work, we employ nonlinear techniques to reconstruct the full thermo-chemical state and evaluate the efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA-/PCA-based dimensionality reduction (encoding) with an artificial neural network (ANN) based reconstruction (decoding) and examine, a priori, the reconstruction errors of the thermo-chemical state. In addition, we evaluate the errors in species production rates and heat release rates, which are nonlinear functions of the reconstructed state, as a measure of the overall accuracy of the dimensionality reduction technique. We employ four datasets to assess CoK-PCA/PCA coupled with ANN-based reconstruction: zero-dimensional (homogeneous) reactor for autoignition of an ethylene/air mixture that has conventional single-stage ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage (low and high temperature) ignition kinetics, a one-dimensional freely propagating premixed ethylene/air laminar flame, and a two-dimensional dataset representing turbulent autoignition of ethanol in a homogeneous charge compression ignition (HCCI) engine. Finally, results from the analyses demonstrate the robustness of the CoK-PCA based low-dimensional manifold with ANN reconstruction in accurately capturing the data, specifically from the reaction zones.
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Natural organisms make a wide variety of exquisitely complex, nano-, micro-, and macroscale structured materials in an energy-efficient and highly reproducible manner. During these processes, the information-carrying biomolecules (e.g., proteins, peptides, and carbohydrates) enable (1) hierarchical organization to assemble scaffold materials and execute high-level functions and (2) exquisite control over inorganic materials synthesis, generating biominerals whose properties are optimized for their functions. Inspired by nature, significant efforts have been devoted to developing functional materials that can rival those natural molecules by mimicking in vivo functions using engineered proteins, peptides, DNAs, sequence-defined synthetic molecules (e.g., peptoids), and other biomimetic polymers. Among them, peptoids, a new type of synthetic mimetics of peptides and proteins, have received particular attention because they combine the merits of both synthetic polymers (e.g., high chemical stability and efficient synthesis) and biomolecules (e.g., sequence programmability and biocompatibility). The lack of both chirality and hydrogen bonds in their backbone results in a highly designable peptoid-based system with reduced structural complexity and side chain-chemistry-dominated properties. Here in this Account, we present our recent efforts in this field by programming amphiphilic peptoid sequences for (1) the controlled self-assembly into different hierarchically structured nanomaterials with favorable properties and (2) manipulating inorganic (nano)crystal nucleation, growth, and assembly into superstructures. First, we designed a series of amphiphilic peptoids with controlled side chain chemistries that self-assembled into 1D highly stiff and dynamic nanotubes, 2D membrane-mimetic nanosheets, hexagonally patterned nanoribbons, and 3D nanoflowers. These crystalline nanostructures exhibited sequence-dependent properties and showed promise for different applications. The corresponding peptoid self-assembly pathways and mechanisms were also investigated by leveraging in situ atomic force microscopy studies and molecular dynamics simulations, which showed precise sequence dependency. Second, inspired by peptide- and protein-controlled formation of hierarchical inorganic nanostructures in nature, we developed peptoid-based biomimetic approaches for controlled synthesis of inorganic materials (e.g., noble metals and calcite), in which we took advantage of the substantial side chain chemistry of peptoids and investigated the relationship between the peptoid sequences and the morphology and growth kinetics of inorganic materials. For example, to overcome the challenges (e.g., complexity of protein- and peptide-folding, poor thermal and chemical stabilities) facing the area of protein- and peptide-controlled synthesis of inorganic materials, we recently reported the design of sequence-defined peptoids for controlled synthesis of highly branched plasmonic gold particles. Moreover, we developed a rule of thumb for designing peptoids that predictively enabled the morphological evolution from spherical to coral-shaped gold nanoparticles (NPs). With this Account, we hope to stimulate the research interest of chemists and materials scientists and promote the predictive synthesis of functional and robust materials through the design of sequence-defined synthetic molecules.
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A wind tunnel suspension system for testing flutter models under various loads and at various angles of attack is described. The invention comprises a mounting bracket assembly affixing the suspension system to the wind tunnel, a drag-link assembly and a compound spring arrangement comprises a plunge spring working in opposition to a compressive spring so as to provide a high stiffness to trim out steady state loads and simultaneously a low stiffness to dynamic loads. By this arrangement an airfoil may be tested for oscillatory response in both plunge and pitch modes while being held under high lifting loads in a wind tunnel.
The analysis and the accompanying FORTRAN code, SEALPAL1, to simulate liquid annular seals with axial taper, Moody friction factors, and pre-swirl, are discussed. The output of the code includes all dynamic coefficients (stiffness, dampings, and inertias), leakage rate, torque, and horsepower loss. The computer code results were compared with five cases from the literature. The agreement was very good in almost all instances, except several predicted cross coupled stiffnesses were significantly lower than those appearing in the literature. This disagreement could reflect a theoretical or a programming error by the researcher or in the literature, or it could be a result of the difference in friction factor models or other assumptions employed.
Calculation of elastic constants requires initializing a lattice of atoms, an h matrix defining the computational cell boundaries, and the parameters defining the interatomic potentials, then numerically integrating the equations of motion for the atoms and the computational cell boundaries, calculating strains and stresses at each timestep, and updating at each timestep the average quantities required for calculation of fluctuations. Enforcements of the DYNAMO FORTRAN code included addition of documentation, improved memory management and data flow, and enabling use of several interatomic potentials. Documentation included headers for each subroutine, which document the parameters input to the routine, algorithms employed, and output.
An effort is currently being carried out by the Jet Propulsion Laboratory (JPL) to study mission feasibility and to define functional requirements for various subsystems of the Space Infrared Telescope Facility (SIRTF). As a major part of this effort, structural design requirements have been derived based on the stated mission objectives. Design concerns addressed by these requirements include the limits on mass and location of the center of gravity, launch stiffness and dynamic characteristics, design loads and analysis criteria, survivability of the TITAN IV/Centaur launch environment, thermal control for maintaining a near absolute-zero operating temperature, and helium cryogen volume and storage for a five-year mission. To illustrate how the structural design requirements can be met, a point design of the SIRTF flight hardware system was developed, modeled, and analyzed. A description of the key features of this point design, along with pertinent modeling and analysis results, are discussed in this Paper.
Three case studies are presented that illustrate the importance of dynamic considerations in the design of machinery supported by rolling element bearings. The first case concerns a milling spindle that experienced internal rubs and high bearing loads, and required retrofit of an additional . damped bearing. The second case deals with a small high-speed generator that suffered high vibration due to flexible mounting. The third case is a propulsion fan simulator rig whose bearings failed catastrophically due to improper bearing installation (which resulted in inadequate dynamic bearing stiffness) and lack of health monitoring instrumentation.
There has been considerable interest over the past several years in applying feedback control methods to problems of structural acoustics. One problem of particular interest is the control of sound radiation from aircraft panels excited on one side by a turbulent boundary layer (TBL). TBL excitation appears as many uncorrelated sources acting on the panel, which makes it difficult to find a single reference signal that is coherent with the excitation. Feedback methods have no need for a reference signal, and are thus suited to this problem. Some important considerations for the structural acoustics problem include the fact that the required controller bandwidth can easily extend to several hundred Hertz, so a digital controller would have to operate at a few kilohertz. In addition, aircraft panel structures have a reasonably high modal density over this frequency range. A model based controller must therefore handle the modally dense system, or have some way to reduce the bandwidth of the problem. Further complicating the problem is the fact that the stiffness and dynamic properties of an aircraft panel can vary considerably during flight due to altitude changes resulting in significant resonant frequency shifts. These considerations make the tradeoff between robustness to changes in the system being controlled and controller performance especially important. Recent papers concerning the design and implementation of robust controllers for structural acoustic problems highlight the need to consider both performance and robustness when designing the controller. While robust control methods such as H1 can be used to balance performance and robustness, their implementation is not easy and requires assumptions about the types of uncertainties in the plant being controlled. Achieving a useful controller design may require many tradeoff studies of different types of parametric uncertainties in the system. Another approach to achieving robustness to plant changes is to make the controller adaptive. For example, a mathematical model of the plant could be periodically updated as the plant changes, and the feedback gains recomputed from the updated model. To be practical, this approach requires a simple plant model that can be updated quickly with reasonable computational requirements. A recent paper by the authors discussed one way to simplify a feedback controller, by reducing the number of actuators and sensors needed for good performance. The work was done on a tensioned aircraft-style panel excited on one side by TBL flow in a low speed wind tunnel. Actuation was provided by a piezoelectric (PZT) actuator mounted on the center of the panel. For sensing, the responses of four accelerometers, positioned to approximate the response of the first radiation mode of the panel, were summed and fed back through the controller. This single input-single output topology was found to have nearly the same noise reduction performance as a controller with fifteen accelerometers and three PZT patches. This paper extends the previous results by looking at how constrained layer damping (CLD) on a panel can be used to enhance the performance of the feedback controller thus providing a more robust and efficient hybrid active/passive system. The eventual goal is to use the CLD to reduce sound radiation at high frequencies, then implement a very simple, reduced order, low sample rate adaptive controller to attenuate sound radiation at low frequencies. Additionally this added damping smoothes phase transitions over the bandwidth which promotes robustness to natural frequency shifts. Experiments were conducted in a transmission loss facility on a clamped-clamped aluminum panel driven on one side by a loudspeaker. A generalized predictive control (GPC) algorithm, which is suited to online adaptation of its parameters, was used in single input-single output and multiple input-single output configurations. Because this was a preliminary look at the potential constrained layer damping for adaptive control, static feedback control with no online adaptation was used. Two configurations of CLD in addition to a bare panel configuration were studied. For each CLD configuration, two sensor arrangements for the feedback controller were compared. The first arrangement used fifteen accelerometers on the panel to estimate the responses of the first six radiation modes of the panel. The second sensor arrangement was simpler, using the summed responses of only four accelerometers to approximate the response of the first radiation mode of the panel. In all cases a PZT patch was mounted at the center of the panel for control input. The performance of the controller was quantified using the responses of the fifteen accelerometers on the panel to estimate radiated sound power. The paper begins with a brief discussion of the GPC algorithm and the experimental setup. The experimental results are discussed next, comparing the CLD and sensor configurations, followed by discussion and conclusions.