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At least 163 records · Page 9

Instability analysis procedure for 3-level multi-bearing rotor-foundation systems

A procedure for the instability analysis of a three-level multispan rotor systems is described. This procedure is based on a distributed mass elastic representation of the rotor system in several eight-coefficient bearings. Each bearing is supported from an elastic foundation on damped, elastic pedestals. The foundation is represented as a general distributed mass elastic structure on discrete supports, which may have different stiffness and damping properties in the horizontal and vertical directions. This system model is suited to studies of instability threshold conditions for multirotor turbomachines on either massive or flexible foundations. The instability conditions is found by obtaining the eigenvalues of the system determinant, which is obtained by the transfer matrix method from the three-level system model. The stability determinant is solved for the lowest rotational speed at which the system damping becomes zero in the complex eigenvalue, and for the whirl frequency corresponding to the natural frequency of the unstable mode. An efficient algorithm for achieving this is described. Application of this procedure to a rigid rotor in two damped-elastic bearings and flexible supports is described. A second example discusses a flexible rotor with four damped-elastic bearings. The third case compares the stability of a six-bearing 300 Mw turbine generator unit, using two different bearing types. These applications validate the computer program and various aspects of the analysis.

Zhou, S.↗

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Pavarino, Luca F.↗

Multibody model reduction by component mode synthesis and component cost analysis

The classical assumed-modes method is widely used in modeling the dynamics of flexible multibody systems. According to the method, the elastic deformation of each component in the system is expanded in a series of spatial and temporal functions known as modes and modal coordinates, respectively. This paper focuses on the selection of component modes used in the assumed-modes expansion. A two-stage component modal reduction method is proposed combining Component Mode Synthesis (CMS) with Component Cost Analysis (CCA). First, each component model is truncated such that the contribution of the high frequency subsystem to the static response is preserved. Second, a new CMS procedure is employed to assemble the system model and CCA is used to further truncate component modes in accordance with their contribution to a quadratic cost function of the system output. The proposed method is demonstrated with a simple example of a flexible two-body system.

Spanos, J. T.↗

Component mode synthesis of large rotor systems

A scheme is presented for calculating the vibrations of large multi-component flexible rotor systems based on the component mode synthesis method. It is shown that, by a modal expansion of the elastic interconnecting elements, the system modal equation can be conveniently constructed from the undamped eigen representations of the component subsystems. The capability of the component mode method is demonstrated in two examples: a transient simulation of a two-spool gas turbine engine equipped with a squeeze-film damper; and an unbalance response analysis of the Space Shuttle Main Engine oxygen turbopump in which the dynamics of the rotor and the housing are both considered.

Li, D. F.↗

An integrated approach to the synthesis of geometrically non-linear structures

An integrated approach to the minimum weight design of geometrically nonlinear three-dimensional truss structures with geometric imperfections, subject to inequality constraints on static displacements, stresses, local buckling and cross sectional areas, is investigated. The integrated structural synthesis problem involves design and response quantities as independent variables and equilibrium equations, describing the finite element model, as equality constraints. The nonlinear structural analysis and the optimization are thus merged together into a single process. A computer program developed to compute the constraint values and analytical gradients is coupled with a generalized reduced gradient algorithm to solve the integrated problem. Numerical results for a geometrically nonlinear shallow dome example problem are presented for various types of imperfections. Furthermore, it is found that the algorithm is capable of detecting and guarding against system as well as element elastic instability using equilibrium information only, that is, without imposing system and local buckling inequality constraints.

Smaoui, H.↗

A three body dynamic simulation of a seated tractor rocket escape system for the Space Shuttle

In the tractor-rocket seated-extraction candidate system for Space Shuttle Orbiter crew escape, the crewmember is pulled from his seat and away from the Orbiter via an elastic pendant, using a system of rails to guide the extraction trajectory through an opening on the window frame for flight deck crew and through the side hatch for the middeck crew. A three-body simulation has been developed to model the flight-mechanics aspects of the concept, where the three bodies are the astronaut (six DOF), the tractor rocket (six DOF), and the Shuttle Orbiter (three DOF); attention is given to crewmembers' clearance of the Orbiter structure and engine plumes.

Ondler, R. M.↗

10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations↗

Elastically Deformable Side-Edge Link for Trailing-Edge Flap Aeroacoustic Noise Reduction

A system is provided for reducing aeroacoustic noise generated by an aircraft having wings equipped with trailing-edge flaps. The system includes a plurality of elastically deformable structures. Each structure is coupled to and along one of the side edges of one of the trailing-edge flaps, and is coupled to a portion of one of the wings that is adjacent to the one of the side edges. The structures elastically deform when the trailing-edge flaps are deployed away from the wings.

Khorrami, Mehdi R.↗

Connection forces in deformable multibody dynamics

In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.

Shabana, A. A.↗

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys

An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

36 MATERIALS SCIENCE↗

Effect of suspension-line viscous damping on parachute opening load amplification.

A digital computer program was used to investigate the effects of suspension-line viscous damping on the opening loads of a high-altitude parachute system having a specified configuration. It was found (1) that the nonlinear elastic characteristics of the suspension system produce an amplification of the opening load when the viscous damping is negligible, (2) that the load amplification is markedly reduced when the suspension-line viscous damping coefficient is increased, and (3) that the suspension-line viscous damping is an important parameter of opening load amplification for high-velocity parachute inflations.

Poole, L. R.↗

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small.

Sinha, Alok↗

Dynamic analysis of flexible gear trains/transmissions - An automated approach

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane's method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.

Amirouche, F. M. L.↗

On dynamic stability boundaries for binary systems

Dynamic stability boundaries are developed for linear two-degree-of-freedom systems with damping and elastic couplings. Special emphasis is placed on the influence of natural frequency proximity and those instabilities which stem from skew-symmetric stiffness properties. These arise in aeroelasticity and flight dynamics systems. Insight is provided into the destabilizing effects of the 'dreaded modal resonance' which results when the two natural frequencies in the modal natural frequency ratio match or nearly match.

Young, M. I.↗

The Role of Guidance, Navigation, and Control in Hypersonic Vehicle Multidisciplinary Design and Optimization

Airbreathing hypersonic systems offer distinct performance advantages over rocket-based systems for space access vehicles. However, these performance advantages are dependent upon advances in current state-of-the-art technologies in many areas such as ram/scramjet propulsion integration, high temperature materials, aero-elastic structures, thermal protection systems, transition to hypersonics and hypersonic control elements within the framework of complex physics and new design methods. The complex interactions between elements of an airbreathing hypersonic vehicle represent a new paradigm in vehicle design to achieve the optimal performance necessary to meet space access mission objectives. In the past, guidance, navigation, and control (GNC) analysis often follows completion of the vehicle conceptual design process. Individual component groups design subsystems which are then integrated into a vehicle configuration. GNC is presented the task of developing control approaches to meet vehicle performance objectives given that configuration. This approach may be sufficient for vehicles where significant performance margins exist. However, for higher performance vehicles engaging the GNC discipline too late in the design cycle has been costly. For example, the X-29 experimental flight vehicle was built as a technology demonstrator. One of the many technologies to be demonstrated was the use of light-weight material composites for structural components. The use of light-weight materials increased the flexibility of the X- 29 beyond that of conventional metal alloy constructed aircraft. This effect was not considered when the vehicle control system was designed and built. The impact of this is that the control system did not have enough control authority to compensate for the effects of the first fundamental structural mode of the vehicle. As a result, the resulting pitch rate response of the vehicle was below specification and no post-design changes could recover the desired capability.

Ouzts, Peter J.↗

Towards an Aero-Propulso-Servo-Elasticity Analysis of a Commercial Supersonic Transport

This paper covers the development of an aero-propulso-servo-elastic (APSE) model using computational fluid dynamics (CFD) and linear structural deformations. The APSE model provides the integration of the following two previously developed nonlinear dynamic simulations: a variable cycle turbofan engine and an elastic supersonic commercial transport vehicle. The primary focus of this study is to provide a means to include relevant dynamics of a turbomachinery propulsion system into the aeroelastic studies conducted during a vehicle design, which have historically neglected propulsion effects. A high fidelity CFD tool is used here for the integration platform. The elastic vehicle neglecting the propulsion system serves as a comparison of traditional approaches to the APSE results. An overview of the methodology is presented for integrating the propulsion system and elastic vehicle. Static aeroelastic analysis comparisons between the traditional and developed APSE models for a wing tip detection indicate that the propulsion system impact on the vehicle elastic response could increase the detection by approximately ten percent.

aeroservoelasticity↗