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Computer program for calculating effects of swash-plate stiffness on helicopter rotor system dynamics and stability
A theoretical model was established to predict the fatigue behavior of composite materials, with emphasis placed on predictions of the degradation of residual strength and residual stiffness during fatigue cycling. The model parameters were evaluated from three test series including static strength fatigue life and residual strength tests. The tests were applied to two graphite/epoxy laminates. Load sequence effects were emphasized for both laminates and the predicted results agreed quite well with subsequent verification tests. Dynamic as well as static stiffness reduction data were collected by use of a PDP11-03 computer, which performed quite satisfactorily and permitted the recording of a substantial amount of dynamic stiffness reduction data.
This paper presents the pertinent details of a newly developed solid rectangular hexahedron finite dynamic element, involving the derivation of the higher order stiffness and inertia dynamic correction matrices. Numerical results of a test case are also presented which indicate that adoption of the dynamic elements significantly improves the solution convergence, when compared with the related performance of the corresponding finite elements.
Program has been developed that analytically determines effects of nonuniform swash-plate support stiffness, swash-plate flexibility, and out-of-blade track on vibratory mechanical stability characteristics of helicopter rotor systems. Analysis is based on combined Laplace transform and associated matrix approach.
Abstract The following paper presents breakthrough experimental results for a new hermetic squeeze film damper (HSFD) concept that is integrally designed within an externally pressurized tilting-pad radial gas bearing support. The flexibly damped gas bearing module was designed for a 7.2″ (183 mm) diameter shaft and fabricated using direct metal laser melting (DMLM); also known as additive manufacturing. The bearing and HSFD were sized based on ongoing studies for oil-free supercritical carbon dioxide (sCO2) power turbines in the 8.5 MW–10 MW power range. The development of the new damper concept was motivated by past dynamic testing on HSFD, which generated frequency-dependent stiffness and damping force coefficients. In efforts to eliminate the frequency dependency, a new HSFD architecture was conceived that adds accumulator volumes and a pass-through channel to previously conceived HSFD flow network designs. The other motivation for the work is the need to develop a cost-effective and reliable oil-free bearing technology that is scalable to large power turbomachinery applications. There were several objectives for the following work. The first objective was to successfully design and fabricate a single piece bearing-damper using additive manufacturing, while dimensionally controlling critical design features. The paper discusses the manufacturing steps and shows cut-ups that reveal adequate clearance control capability with internal damper clearances. The second objective was to perform experimental testing with the new HSFD design in efforts to extract stiffness and damping coefficients for excitation frequencies within 20–160 Hz and peak vibration amplitudes between 0.25 mils (6.35 microns) to 1 mil (25.4 microns). The test results for a single HSFD bearing module indicated that the design modifications to the HSFD architecture were successful in eliminating nearly all the frequency dependencies for the stiffness force coefficient. The dynamic tests yielded a stiffness coefficient that varied between 112 klb/in. (19.6 MN/m) and 96 klb/in. (16.8 MN/m). The damping force coefficient however, exhibited relatively more variation with frequency with values residing between 175 lb-s/in. (31 kN-s/m) to 214 lb-s/in. (37 kN-s/m). Finally, the paper advances a three-dimensional fluid-structure interaction (FSI) model using transient finite element analysis (FEA) coupled to a computational fluid dynamics (CFD) model. The FSI analysis performed between 20 Hz and 80 Hz was used to predict the stiffness and damping of the HSFD using a quarter-section model of the damper. The FSI analysis was able to support test results by showing only a 6–7.4% change in the magnitude of force coefficients. Stiffness predictions agree reasonably well with experiments whereas damping is underpredicted.
In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).
Mathematical models for calculating flexible swash-plate effects on vibratory and mechanical stability characteristics of helicopter rotor systems
Effects of mount stiffness and damping on dynamic behavior of air lubricated pivoted-pad journal bearing-rotor system - Vol. 1
A FORTRAN IV computer program used to perform modal synthesis of structures by stiffness coupling, using the dynamic transformation method is described. The program was named SCAMP (Stiffness Coupling Approach Modal-Synthesis Program). The program begins with the entry of a substructure's physical mode shapes and eigenvalues or a substructure's mass and stiffness matrix. If the mass and stiffness matrices are entered, the eigen problem for the individual substructure is solved. Provisions are included for a maximum of 20 substructures which are coupled by stiffness matrix springs. Each substructure has a number degrees of freedom (DOF), except that for DOF greater than 100; vector sets having maximum row and column size of 100 were generated prior to entering SCAMP. The substructures are then coupled together via coupling springs, and the dynamic transformation is used to reduce the size of the eigen problem.
The present work addresses the development of an experimental and computational procedure for validating finite element models. A torus structure, part of an inflatable/rigidizable Hexapod, is used to demonstrate the approach. Because of fabrication, materials, and geometric uncertainties, a statistical approach combined with optimization is used to modify key model parameters. Static test results are used to update stiffness parameters and dynamic test results are used to update the mass distribution. Updated parameters are computed using gradient and non-gradient based optimization algorithms. Results show significant improvements in model predictions after parameters are updated. Lessons learned in the areas of test procedures, modeling approaches, and uncertainties quantification are presented.
A method is presented for determining the dynamic coefficients of bearing oil film. By varying the support stiffness and damping, eight dynamic coefficients of the bearing were determined. Simple and easy to apply, the method can be used in solving practical machine problems.
The gust response of a coupled hingeless rotor-fuselage system is studied in both hover and forward flight. Each rotor blade undergoes flap bending, lag bending, and torsional deflections. The blades are discretized into beam elements, each with fifteen nodal degrees of freedom. The fuselage is permitted three translational (vertical, longitudinal, and lateral) and two rotational (pitch and roll) degrees of freedom. The formulation considers a three-dimensional gust field wherein each gust velocity component can have an arbitrary variation in space and time. Aerodynamic loads are obtained using quasisteady strip theory. Wake-induced effects are introduced through dynamic inflow modeling. Dynamic stall and reverse flow effects are also included. Equations governing the rotor-fuselage gust response are linearized about the vehicle propulsive trim state and the blade steady-state defected positions, and solved by time integration. The effects of several parameters on the helicopter gust response are illustrated, including dynamic inflow, lag stiffness, forward speed, gust profile, gust penetration rate, and gust velocity direction.
The NASA In-Space Propulsion (ISP) program has been sponsoring system design development and hardware demonstration activities of solar sail technology over the past 16 months. Efforts to validate by test a moderate-scale (10-m) 1/4 symmetry ground demonstration sail system are nearly complete. Results of testing and analytical model validation of component and assembly functional, strength, stiffness, shape, and dynamic behavior are discussed.
The NASA In-Space Propulsion (ISP) program sponsored intensive solar sail technology and systems design, development, and hardware demonstration activities over the past 3 years. Efforts to validate a scalable solar sail system by functional demonstration in relevant environments, together with test-analysis correlation activities on a scalable solar sail system have recently been successfully completed. A review of the program, with descriptions of the design, results of testing, and analytical model validations of component and assembly functional, strength, stiffness, shape, and dynamic behavior are discussed. The scaled performance of the validated system is projected to demonstrate the applicability to flight demonstration and important NASA road-map missions.
The mass and stiffness distributions for helicopter rotor blades are tailored in such a way to give a predetermined placement of blade natural frequencies. The optimal design is pursued with respect of minimum weight, sufficient inertia, and reasonable dynamic characteristics. Finite element techniques are used as a tool. Rotor types include hingeless, articulated, and teetering.
The paper develops an efficient free-vibration analysis procedure of two-dimensional structures. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and inertia matrices. A plane rectangular dynamic element is developed in detail. Numerical solution results of free-vibration analysis presented herein clearly indicate that these dynamic elements combined with a suitable quadratic matrix eigenproblem solution technique effect a most economical and efficient solution for such an analysis when compared with the usual finite element method.
Dynamic mechanical measurement results are presented for the case of carbon fiber-reinforced, epoxy matrix composite laminates subjected to loading perpendicular to the lamination plane, as well as for neat epoxy resin under the same conditions, where temperatures ranged between 20 and 200 C and deformation levels lie within the linear viscoelastic region. In-phase and out-of-phase stiffnesses are found to become superposed, forming master curves that cover a 12-decade frequency range. The application of a master curve scaling procedure shows that the in-phase stiffness has the same shape, and out-of-phase stiffness has the same dispersion, for all laminates irrespective of stacking sequence and are, in turn, nearly identical to those for the neat epoxy resin. An empirical function is found for the relaxation modulus which, when converted to a dynamic modulus, yields good overall agreement for both of the dynamic stiffness components as a function of frequency.
This purpose of this report is to provides details of the measurement of the control system stiffness of the UH-60A rotor hub mounted on the Large Rotor Test Apparatus (UH-60A/LRTA). The UH-60A/LRTA was used in the 40- by 80-Foot Wind Tunnel to complete the full-scale wind tunnel test portion of the NASA / ARMY UH-60A Airloads Program. This report describes the LRTA control system and highlights the differences between the LRTA and UH-60A aircraft. The test hardware, test setup, and test procedures are also described. Sample results are shown, including the azimuthal variation of the measured control system stiffness for three different loadings and two different dynamic actuator settings. Finally, the azimuthal stiffness is converted to fixed system values using multi-blade transformations for input to comprehensive rotorcraft prediction codes.