This paper describes a theoretical model for analyzing the dynamic characteristics of wedge-shaped underplatform dampers for turbine blades, with the objective that this model can be used to minimize the need for conducting expensive experiments for optimizing such dampers. The theoretical model presented in the paper has several distinct features to achieve this objective including: (i) it makes use of experimentally measured contact characteristics (hysteresis loops) for description of the basic contact behavior of a given material combination with representative surface finish, (ii) the damper motion between the blade platform locations is determined according to the motion of the platforms, (iii) three-dimensional damper motion is included in the model, and (iv) normal load variation across the contact surfaces during vibration is included, thereby accommodating contact opening and closing during vibration. A dedicated nonlinear vibration analysis program has been developed for this study and predictions have been verified against experimental data obtained from two test rigs. Two cantilever beams were used to simulate turbine blades with real underplatform dampers in the first experiment. The second experiment comprised real turbine blades with real underplatform damper. Correlation of the predictions and the experimental results revealed that the analysis can predict (i) the optimum damping condition, (ii) the amount of response reduction, and (iii) the natural frequency shift caused by friction dampers, all with acceptable accuracy. It has also been shown that the most commonly used underplatform dampers in practice are prone to rolling motion, an effect which reduces the damping in certain modes of vibration usually described as the lower nodal diameter bladed-disk modes.

Underplatform Dampers for Turbine Blades: Theoretical Modeling, Analysis, and Comparison With Experimental Data

The problem of understanding and modeling the complicated physics underlying the action and response of the interfaces in typical structures under dynamic loading conditions has occupied researchers for many decades. This handbook presents an integrated approach to the goal of dynamic modeling of typical jointed structures, beginning with a mathematical assessment of experimental or simulation data, development of constitutive models to account for load histories to deformation, establishment of kinematic models coupling to the continuum models, and application of finite element analysis leading to dynamic structural simulation. In addition, formulations are discussed to mitigate the very short simulation time steps that appear to be required in numerical simulation for problems such as this. This handbook satisfies the commitment to DOE that Sandia will develop the technical content and write a Joints Handbook. The content will include: (1) Methods for characterizing the nonlinear stiffness and energy dissipation for typical joints used in mechanical systems and components. (2) The methodology will include practical guidance on experiments, and reduced order models that can be used to characterize joint behavior. (3) Examples for typical bolted and screw joints will be provided.

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Handbook on dynamics of jointed structures.

Nonlinear normal modes modal interactions and isolated resonance curves

Nonlinear vibration analysis of bladed disks with dry friction dampers

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.

/pdf/a-microslip-friction-model-with-normal-load-variation-2l7glo4oea.pdf

A microslip friction model with normal load variation induced by normal motion

A semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix, and the latter by the generalized quasilinear matrix which is updated at each iteration. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented

Forced harmonic response analysis of nonlinear structures using describing functions

Magnus effects on stability of wraparound-finned missiles

Almost all of the research on  ight dynamicsof unguidedmissiles with wraparound  ns is based on linear system models.This is in sharp contrast with the research on  ight dynamicsof planar  nned unguidedmissiles, which has focusedmostlyonnonlinearproblems since the 1950s.A general  fth-ordernonlinearautonomousdynamicsystem model is developed for unguidedmissiles with fourwraparound  ns. Aerodynamiccharacteristics of a basic planar  nner and a basic wraparound  nner are obtained by using a panel code, Missile DATCOM empirical database, and published experimental data. Effects of nonlinear aerodynamic terms on location and stability of equilibrium points of a basic planar  nner and a basic wraparound  nner are investigated. It is shown that wraparound and planar  nned unguided missiles have different aerodynamic and  ight dynamic characteristics.

Nonlinear Yaw-Pitch-Roll Coupling of Unguided Missiles with Wraparound Fins

¨A simple optimal external cone guration design method is proposed that can be used in conceptual and preliminary design stages of an unguided missile development project. Cost and constraint functions are derived from the results of linear time-invariant aeroballistic theory (constant roll rate and forward speed, decoupled axial and transverse dynamics ); therefore different phases of e ight are examined separately. Curvee tting is used to reduce the number of trial cases and hence the work required to obtain aerodynamic and inertial data. Optimal cone gurations are determined by using a modie ed steepest-descent algorithm. A case study is presented in which the external cone guration of an unguided light assault missile is optimized for free e ight at low subsonic speed. Three cost functions related to stability, range, and warhead performance, respectively, and two inequality constraint functions related directly to stability and indirectly to dispersion are considered in the case study.

Optimal External Configuration Design of Unguided Missiles

using base cavity as a possible means of enhancing Wrap-around tail fins (WAF) are widely used dynamic stability of WAF configurations is as aerodynamic stabilizers for unguided missiles. presented. Stability calculations based on WAF configurations have much more complicated aeroballistic range test results of WAF models with flight dynamics when compared to the ones with base cavity are used to underline the fact that wrapplanar fins. General linear free flight dynamic around fins are neat but nasty, stability criteria of unguided missiles with WAF are well known. However, until now simplified criteria that consider a static side moment due to WAF as the only significant out-of-plane effect were utilized in design. The aim of this paper is to show that reliable stability analysis requires consideration of side moments due to classical Magnus effect and WAF both at the same time. An account of the literature on cn C,.

Omer Tanrikulu

Papers

Forced harmonic response analysis of nonlinear structures using describing functions

Magnus effects on stability of wraparound-finned missiles

Nonlinear Yaw-Pitch-Roll Coupling of Unguided Missiles with Wraparound Fins

Optimal External Configuration Design of Unguided Missiles

Wrap-around finned missiles: neat but nasty